text stringlengths 699 45.9k | conversation_id int64 254 108k | embedding list | cluster int64 3 3 |
|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
s,e=input().split()
n=int(input())
ccw='^<v>^<v>'
cw='^>v<^>v<'
i=n%4
if cw[cw.index(s)+i]==ccw[ccw.index(s)+i]==e:
print("undefined")
elif ccw[ccw.index(s)+i]==e:
print("ccw")
else:
print("cw")
```
Yes
| 69,522 | [
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-0.08026123046875,
0.0255126953125,
-0.06219482421875,
0.841796875,
0.388916015625,
-0.24560546875,
0.005474090576171875,
-0.87890625,
-0.64501953125,
-0.2362060546875,
-0.434082031... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
s=input()
n=int(input())
d={}
d['^']=0
d['>']=1
d['v']=2
d['<']=3
if n%4==2 or n%4==0:
print("undefined")
else:
sum=(d[s[2]]-d[s[0]]+4)%4;
if(sum==n%4):
print("cw")
else:
print("ccw")
```
Yes
| 69,523 | [
0.1441650390625,
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0.01806640625,
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0.8486328125,
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-0.002185821533203125,
-0.857421875,
-0.6513671875,
-0.2132568359375,
-0.446044... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
string = input()
s = string[0]
a = string[1]
n = int(input())
b = n%4
if s == '>':
if a == '^':
if b == 1:
print("ccw")
else:
print("cw")
elif a =='v':
if b == 3:
print("ccw")
else:
print("cw")
else:
print("undefined")
elif s == '<':
if a == '^':
if b == 1:
print("cw")
else:
print("ccw")
elif a =='v':
if b == 3:
print("cw")
else:
print("ccw")
else:
print("undefined")
elif s == '^':
if a == '>':
if b == 1:
print("cw")
else:
print("ccw")
elif a =='<':
if b == 3:
print("cw")
else:
print("ccw")
else:
print("undefined")
elif s == 'v':
if a == '>':
if b == 1:
print("ccw")
else:
print("cw")
elif a =='<':
if b == 3:
print("ccw")
else:
print("cw")
else:
print("undefined")
```
No
| 69,524 | [
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0.01447296142578125,
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-0.4375,
-... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
a,b = input().split(" ")
n = int(input())
c = ord(a)
d = ord(b)
if (a == b) or (a == '<' and b == '>') or (a == '<' and b == '<') or (a == '^' and b == 'v') or (a == 'v' and b == '^'):
print('undefined')
if (a == '^' and b == '>'):
if ((n - 1)%4 == 0) or n==0:
print('cw')
if ((n-3)%4 == 0) or n == 0:
print('ccw')
if (a == '^' and b == '<'):
if ((n - 1)%4 == 0) or n==0:
print('ccw')
if ((n-3)%4 == 0) or n == 0:
print('cw')
if (a == '>' and b == '^'):
if ((n - 1)%4 == 0) or n==0:
print('ccw')
if ((n-3)%4 == 0) or n == 0:
print('cw')
if (c == '<' and d == '^'):
if ((n - 1)%4 == 0) or n==0:
print('cw')
if ((n-3)%4 == 0) or n == 0:
print('ccw')
if (c == 'v' and d == '>'):
if ((n - 1)%4 == 0) or n==0:
print('ccw')
if ((n-3)%4 == 0) or n == 0:
print('cw')
if (c == 'v' and d == '<'):
if ((n - 1)%4 == 0) or n==0:
print('cw')
if ((n-3)%4 == 0) or n == 0:
print('ccw')
if (c == '<' and d == 'v'):
if ((n - 1)%4 == 0) or n==0:
print('cw')
if ((n-3)%4 == 0) or n == 0:
print('ccw')
if (c == '<' and d == 'v'):
if ((n - 1)%4 == 0) or n==0:
print('ccw')
if ((n-3)%4 == 0) or n == 0:
print('cw')
```
No
| 69,525 | [
0.1834716796875,
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0.034759521484375,
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0.050811767578125,
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0.89306640625,
0.401123046875,
-0.25439453125,
-0.0017452239990234375,
-0.8623046875,
-0.6455078125,
-0.19091796875,
-0.42285156... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
s=input().split()
n=int(input())
#v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62)
if (s[0]==chr(94) and s[1]==chr(62)) or (s[0]==chr(62) and s[1]==chr(118)):
print("cw")
elif (s[0]==chr(60) and s[1]==chr(118)) or(s[0]==chr(60) and s[1]==chr(94)):
print("ccw")
else:
print("undefined")
```
No
| 69,526 | [
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0.039520263671875,
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0.87841796875,
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-0.2587890625,
0.01904296875,
-0.8818359375,
-0.6455078125,
-0.21728515625,
-0.395263671875,... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays β caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.
Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):
<image>
After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.
Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.
Input
There are two characters in the first string β the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.
In the second strings, a single number n is given (0 β€ n β€ 109) β the duration of the rotation.
It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.
Output
Output cw, if the direction is clockwise, ccw β if counter-clockwise, and undefined otherwise.
Examples
Input
^ >
1
Output
cw
Input
< ^
3
Output
ccw
Input
^ v
6
Output
undefined
Submitted Solution:
```
a,b = input().split()
n = int(input())
if a == "v":
a = 0
elif a == "<":
a = 1
elif a == "^":
a = 2
else:
a = 3
if b == "v":
b = 0
elif b == "<":
b = 1
elif b == "^":
b = 2
else:
b = 3
if a+n%4 == b: print ("cw")
elif n-a%4 == b: print ("ccw")
else: print ("undefind")
```
No
| 69,527 | [
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0.007625579833984375,
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-0.2103271484375,
-0.427... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
x = [int(input()) for i in range(6)]
if x[4]-x[0]>x[5]: print(":(")
else: print("Yay!")
```
Yes
| 69,637 | [
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-0.8173828125,
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-0.35546875,
-0.66015625,
-0.611328125,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
a,b,c,d,e=(int(input()) for i in range(5))
k=int(input())
print('Yay!' if e-a <= k else ':(')
```
Yes
| 69,638 | [
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-0.83203125,
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-0.65966796875,
-0.599609375,
-0.... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
a = [int(input()) for i in range(6)]
if a[4] - a[0] > a[5]:
print(':(')
else:
print('Yay!')
```
Yes
| 69,639 | [
0.382080078125,
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0.11907958984375,
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0.0111236572265625,
-0.814453125,
-0.5263671875,
-0.365234375,
-0.66455078125,
-0.59619... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
a,b,c,d,e=[int(input())for _ in range(5)]
k=int(input())
print(':(' if e-a>k else 'Yay!')
```
Yes
| 69,640 | [
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0.1959228515625,
0.890625,
0.41455078125,
0.04803466796875,
0.02178955078125,
-0.83447265625,
-0.5244140625,
-0.355224609375,
-0.673828125,
-0.59765625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
list = [int(input()) for i in range(5)]
k = int(input())
a = 0
if i in range(5):
for j in range(5):
if abs(list[i] - list[j]) > k:
a = 1
print('Yay!' if a==0 else ':(')
```
No
| 69,641 | [
0.373291015625,
0.265380859375,
-0.42333984375,
0.466796875,
-0.6650390625,
-0.41259765625,
-0.006732940673828125,
0.12939453125,
0.20751953125,
0.92236328125,
0.412841796875,
0.061065673828125,
0.0171356201171875,
-0.81982421875,
-0.53857421875,
-0.36767578125,
-0.67529296875,
-0.... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
l = [int(input()) for _ in range(5)]
k = int(input())
for i in range(4):
if l[i+1] - l[i] > k:
print(':(')
break
else:
print('Yay!')
```
No
| 69,642 | [
0.373046875,
0.26220703125,
-0.430908203125,
0.46435546875,
-0.67333984375,
-0.412109375,
-0.0212860107421875,
0.10882568359375,
0.2132568359375,
0.890625,
0.39697265625,
0.043243408203125,
-0.0191192626953125,
-0.80810546875,
-0.53369140625,
-0.358642578125,
-0.68896484375,
-0.606... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
a = [int(input()) for _ in range(5)]
k = int(input())
if a[4] - a[0] < k:
print('Yay!')
else:
print(':(')
```
No
| 69,643 | [
0.37255859375,
0.248779296875,
-0.451416015625,
0.4814453125,
-0.66259765625,
-0.42919921875,
-0.03125,
0.1160888671875,
0.2064208984375,
0.8984375,
0.418212890625,
0.047882080078125,
-0.0035915374755859375,
-0.81298828125,
-0.53076171875,
-0.3603515625,
-0.67724609375,
-0.59570312... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.
Constraints
* a, b, c, d, e and k are integers between 0 and 123 (inclusive).
* a < b < c < d < e
Input
Input is given from Standard Input in the following format:
a
b
c
d
e
k
Output
Print `:(` if there exists a pair of antennas that cannot communicate directly, and print `Yay!` if there is no such pair.
Examples
Input
1
2
4
8
9
15
Output
Yay!
Input
15
18
26
35
36
18
Output
:(
Submitted Solution:
```
a = []
for _ in range(5):
a.append(int(input()))
b =[]
c = []
for i in range(5):
b[i] = a[i]
for i in range(5):
while b[i] > 10:
b[i] = b[i] - 10
if min(b[i]) == 10:
return sum(a)
else:
for i in range(5):
if b[i] == 10:
c[i] = a[i]
else:
c[i] = a[i] +10 -b[i]
d = sum(c)
mini = min(b)
ans = d - 10 + mini
return ans
```
No
| 69,644 | [
0.3291015625,
0.1868896484375,
-0.39794921875,
0.425537109375,
-0.662109375,
-0.409912109375,
-0.07769775390625,
0.1036376953125,
0.2030029296875,
0.87646484375,
0.422607421875,
-0.0122222900390625,
-0.0303192138671875,
-0.7783203125,
-0.55712890625,
-0.33642578125,
-0.701171875,
-... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.
Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.
In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).
He may perform the following operation arbitrarily many times:
* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.
Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.
Find the minimum scatteredness after he performs arbitrarily many operations.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers
Input
Input is given from Standard Input in the following format:
N D
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3 1
0 0
1 0
2 0
Output
1
Input
19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0
Output
4
Input
8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5
Output
4
Submitted Solution:
```
N,D = map(int,input().split())
pos = [[0 for _ in range(D)] for i in range(D)]
flg = [[0 for _ in range(D)] for i in range(D)]
for i in range(N):
x,y = map(int,input().split())
pos[x%D][y%D] += 1
maxn = -1
for i in range(D):
for j in range(D):
maxn = max(maxn,pos[i][j])
sqs = int((maxn-1)**0.5)+1
lx = [0 for _ in range(D)]
ly = [0 for _ in range(D)]
for i in range(D):
for j in range(D):
if pos[i][j]<=(sqs-1)**2:
pass
elif pos[i][j]<=(sqs-1)*sqs:
flg[i][j] = 1
lx[i] = max(lx[i],1)
ly[j] = max(ly[i],1)
else:
flg[i][j] = 2
lx[i] = 2
ly[j] = 2
flaggg = False
for sq in range(D):
for i in range(D):
for j in range(D):
flagg = True
for x in range(D):
for y in range(D):
if (i<=x<=i+sq or i<=x+D<=i+sq)and (j<=y<=j+sq or j<=y+D<=j+sq):
pass
elif (i<=x<=i+sq or i<=x+D<=i+sq) or (j<=y<=j+sq or j<=y+D<=j+sq):
if flg[x][y]==2:
flagg = False
break
else:
if flg[x][y]==1:
flagg = False
break
if not flagg:
break
if flagg:
flaggg = True
break
if flaggg:
break
if flaggg:
break
print((int((maxn-1)**0.5))*D+sq)
```
No
| 69,646 | [
0.338134765625,
0.1688232421875,
0.11370849609375,
-0.03515625,
-0.438232421875,
-0.6240234375,
-0.20654296875,
0.4248046875,
0.23291015625,
0.97998046875,
0.462890625,
0.25390625,
0.1259765625,
-0.548828125,
-0.33349609375,
0.537109375,
-0.896484375,
-0.91796875,
-0.3515625,
0... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.
Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.
In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).
He may perform the following operation arbitrarily many times:
* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.
Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.
Find the minimum scatteredness after he performs arbitrarily many operations.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers
Input
Input is given from Standard Input in the following format:
N D
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3 1
0 0
1 0
2 0
Output
1
Input
19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0
Output
4
Input
8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5
Output
4
Submitted Solution:
```
n,d = map(int,input().split())
num = [[0]*d for i in range(d)]
a = 0
for i in range(n):
x,y = map(int,input().split())
x %=d
y%=d
num[x][y] += 1
a = max(a,num[x][y])
x=1
while x*x<a:
x += 1
r = (x-1)*d
a = x-1
dai = d-1
syo = 0
anum = [[[0]*d for i in range(d)]for i in range(2)]
rui = [[[0]*d for i in range(d)]for i in range(2)]
for i in range(d):
for j in range(d):
if num[i][j]<= a*a:
continue
elif num[i][j]<= a*(a+1):
anum[1][i][j]=1
else:
anum[0][i][j]=1
for x in range(2):
for i in range(d):
for j in range(d):
if i:
rui[x][i][j]+=rui[x][i-1][j]
if j:
rui[x][i][j]+=rui[x][i][j-1]
if i and j:
rui[x][i][j]-=rui[x][i-1][j-1]
rui[x][i][j]+=anum[x][(i-1)%d][(j-1)%d]
def cheak(kon):
for i in range(d):
for j in range(d):
if rui[0][(i+d-1)%d][(j+d-1)%d] - rui[0][(i+kon+1)%d][(j+kon+1)%d]:
return 0
if rui[1][(i+d-1)%d][(j+d-1)%d] + rui[1][(i+kon+1)%d][(j+kon+1)%d] - rui[1][(i+d-1)%d][(j+kon+1)%d] - rui[1][(i+kon+1)%d][(j+d-1)%d]:
return 0
return 1
kon = (dai+syo)//2
while True:
if dai-syo <= 1:
if cheak(syo) == 1:
dai = syo
break
kon = (dai+syo)//2
c = cheak(kon)
if c == 1:
dai = kon
else:
syo = kon
print(dai+r)
```
No
| 69,647 | [
0.338134765625,
0.1688232421875,
0.11370849609375,
-0.03515625,
-0.438232421875,
-0.6240234375,
-0.20654296875,
0.4248046875,
0.23291015625,
0.97998046875,
0.462890625,
0.25390625,
0.1259765625,
-0.548828125,
-0.33349609375,
0.537109375,
-0.896484375,
-0.91796875,
-0.3515625,
0... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.
Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.
In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).
He may perform the following operation arbitrarily many times:
* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.
Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.
Find the minimum scatteredness after he performs arbitrarily many operations.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers
Input
Input is given from Standard Input in the following format:
N D
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3 1
0 0
1 0
2 0
Output
1
Input
19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0
Output
4
Input
8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5
Output
4
Submitted Solution:
```
n, d = [int(i) for i in input().split()]
X, Y = zip(*[[int(i) for i in input().split()] for j in range(n)])
S = set()
for x, y in zip(X, Y):
x %= d
y %= d
dy = 0
try:
if x > y:
while True:
for dx in range(dy+1):
if not (x+dx*d, y+dy*d) in S:
S.add((x+dx*d, y+dy*d))
raise()
dx = dy
for dy in range(dx+1):
if not (x+dx*d, y+dy*d) in S:
S.add((x+dx*d, y+dy*d))
raise()
dy += 1
else:
while True:
for ddy in range(dy+1):
if not (x+dy*d, y+ddy*d) in S:
S.add((x+dy*d, y+ddy*d))
raise()
for dx in range(dy+1):
if not (x+dx*d, y+dy*d) in S:
S.add((x+dx*d, y+dy*d))
raise()
dy += 1
except:
pass
X, Y = zip(*tuple(S))
print(max(abs(max(X) - min(X)), (max(Y) - min(Y))))
```
No
| 69,648 | [
0.338134765625,
0.1688232421875,
0.11370849609375,
-0.03515625,
-0.438232421875,
-0.6240234375,
-0.20654296875,
0.4248046875,
0.23291015625,
0.97998046875,
0.462890625,
0.25390625,
0.1259765625,
-0.548828125,
-0.33349609375,
0.537109375,
-0.896484375,
-0.91796875,
-0.3515625,
0... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.
Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.
In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).
He may perform the following operation arbitrarily many times:
* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.
Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.
Find the minimum scatteredness after he performs arbitrarily many operations.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers
Input
Input is given from Standard Input in the following format:
N D
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3 1
0 0
1 0
2 0
Output
1
Input
19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0
Output
4
Input
8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5
Output
4
Submitted Solution:
```
# D
N, D = map(int, input().split())
xyd_list = [[0]*D for _ in range(D)]
for _ in range(N):
x, y = map(int, input().split())
xyd_list[x%D][y%D] += 1
# how many copy we need
mmm = max([max(x) for x in xyd_list])
bound = 1
while bound**2 < mmm:
bound += 1
res = D*bound - 1
# bruce for 500
for i in range(D):
for j in range(D):
res_t = D*(bound - 1)
for k in range(D):
i_ = (i+k)%D
for l in range(D):
j_ = (j+l)%D
if xyd_list[i_][j_] <= (bound - 1)**2:
pass
elif xyd_list[i_][j_] <= (bound - 1)*bound:
res_t = max(res_t, D*(bound - 1) + min(k, l))
else:
res_t = max(res_t, D*(bound - 1) + max(k, l))
if res_t < res:
res = res_t
print(res)
```
No
| 69,649 | [
0.338134765625,
0.1688232421875,
0.11370849609375,
-0.03515625,
-0.438232421875,
-0.6240234375,
-0.20654296875,
0.4248046875,
0.23291015625,
0.97998046875,
0.462890625,
0.25390625,
0.1259765625,
-0.548828125,
-0.33349609375,
0.537109375,
-0.896484375,
-0.91796875,
-0.3515625,
0... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
from collections import Counter
while True:
m, n = (int(s) for s in input().split())
if not m:
break
objs = [int(input(), 2) for i in range(n)]
dp = [bytearray(1 << m) for i in range(1 << m)]
bits = [1 << i for i in range(m)]
for mask in reversed(range((1 << m) - 1)):
s = Counter(obj & mask for obj in objs)
for masked, count in s.items():
if count > 1:
dp[mask][masked] = min(max(dp[mask + b][masked],
dp[mask + b][masked + b]) + 1
for b in bits if not b & mask)
print(dp[0][0])
```
| 69,751 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
from collections import Counter
while True:
m, n = (int(s) for s in input().split())
if not m:
break
objects = [int(input(), 2) for i in range(n)]
dp = [bytearray(1 << m) for i in range(1 << m)]
bits = [1 << i for i in range(m)]
for asked in reversed(range((1 << m) - 1)):
for masked, count in Counter(obj & asked for obj in objects).items():
if count > 1:
dp[asked][masked] = min(max(dp[asked + b][masked],
dp[asked + b][masked + b])
for b in bits if not b & asked) + 1
print(dp[0][0])
```
| 69,752 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
from collections import Counter
import sys
def solve():
readline = sys.stdin.buffer.readline
write = sys.stdout.buffer.write
M, N = map(int, readline().split())
if M == N == 0:
return False
B = [int(readline(), 2) for i in range(N)]
memo = {}
def dfs(s, t):
key = (s, t)
if key in memo:
return memo[key]
c = 0
for b in B:
if (b & s) == t:
c += 1
if c <= 1:
memo[key] = 0
return 0
res = M
for i in range(M):
b = (1 << i)
if s & b == 0:
res = min(res, max(dfs(s|b, t), dfs(s|b, t|b))+1)
memo[key] = res
return res
write(b"%d\n" % dfs(0, 0))
return True
while solve():
...
```
| 69,753 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
def f(n,m):
a = [int(S(), 2) for _ in range(m)]
mi = 0
ma = max(a)
while 2**mi <= ma:
mi += 1
ii = [2**i for i in range(mi+1)]
fm = {}
def _f(a):
k = tuple(a)
if k in fm:
return fm[k]
if len(a) < 2:
fm[k] = 0
return 0
r = inf
for i in ii:
a1 = []
a2 = []
for c in a:
if i & c:
a1.append(c)
else:
a2.append(c)
if not a1 or not a2:
continue
r1 = _f(a1)
r2 = _f(a2)
tr = max(r1, r2) + 1
if r > tr:
r = tr
fm[k] = r
return r
r = _f(a)
return r
while 1:
n,m = LI()
if n == 0:
break
rr.append(f(n,m))
return '\n'.join(map(str,rr))
print(main())
```
| 69,754 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
from collections import Counter
while True:
m, n = (int(s) for s in input().split())
if not m:
break
objs = [int(input(), 2) for i in range(n)]
dp = [[0] * (1 << m) for i in range(1 << m)]
bits = [1 << i for i in range(m)]
for mask in reversed(range(1 << m)):
s = Counter(obj & mask for obj in objs)
for masked, value in s.items():
if value > 1:
dp[mask][masked] = min(max(dp[mask | b][masked],
dp[mask | b][masked | b]) + 1
for b in bits if not b & mask)
print(dp[0][0])
```
| 69,755 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Consider a closed world and a set of features that are defined for all the objects in the world. Each feature can be answered with "yes" or "no". Using those features, we can identify any object from the rest of the objects in the world. In other words, each object can be represented as a fixed-length sequence of booleans. Any object is different from other objects by at least one feature.
You would like to identify an object from others. For this purpose, you can ask a series of questions to someone who knows what the object is. Every question you can ask is about one of the features. He/she immediately answers each question with "yes" or "no" correctly. You can choose the next question after you get the answer to the previous question.
You kindly pay the answerer 100 yen as a tip for each question. Because you don' t have surplus money, it is necessary to minimize the number of questions in the worst case. You donβt know what is the correct answer, but fortunately know all the objects in the world. Therefore, you can plan an optimal strategy before you start questioning.
The problem you have to solve is: given a set of boolean-encoded objects, minimize the maximum number of questions by which every object in the set is identifiable.
Input
The input is a sequence of multiple datasets. Each dataset begins with a line which consists of two integers, m and n: the number of features, and the number of objects, respectively. You can assume 0 < m β€ 11 and 0 < n β€ 128. It is followed by n lines, each of which corresponds to an object. Each line includes a binary string of length m which represent the value ("yes" or "no") of features. There are no two identical objects.
The end of the input is indicated by a line containing two zeros. There are at most 100 datasets.
Output
For each dataset, minimize the maximum number of questions by which every object is identifiable and output the result.
Example
Input
8 1
11010101
11 4
00111001100
01001101011
01010000011
01100110001
11 16
01000101111
01011000000
01011111001
01101101001
01110010111
01110100111
10000001010
10010001000
10010110100
10100010100
10101010110
10110100010
11001010011
11011001001
11111000111
11111011101
11 12
10000000000
01000000000
00100000000
00010000000
00001000000
00000100000
00000010000
00000001000
00000000100
00000000010
00000000001
00000000000
9 32
001000000
000100000
000010000
000001000
000000100
000000010
000000001
000000000
011000000
010100000
010010000
010001000
010000100
010000010
010000001
010000000
101000000
100100000
100010000
100001000
100000100
100000010
100000001
100000000
111000000
110100000
110010000
110001000
110000100
110000010
110000001
110000000
0 0
Output
0
2
4
11
9
"Correct Solution:
```
from collections import Counter
while True:
m, n = (int(s) for s in input().split())
if not m:
break
objects = [int(input(), 2) for i in range(n)]
dp = [bytearray(1 << m) for i in range(1 << m)]
bits = [1 << i for i in range(m)]
for mask in reversed(range((1 << m) - 1)):
for masked, count in Counter(obj & mask for obj in objects).items():
if count > 1:
dp[mask][masked] = min(max(dp[mask + b][masked],
dp[mask + b][masked + b]) + 1
for b in bits if not b & mask)
print(dp[0][0])
```
| 69,756 | [
0.467041015625,
0.1424560546875,
-0.3017578125,
-0.017822265625,
0.040008544921875,
-0.19091796875,
-0.03936767578125,
0.399169921875,
0.11627197265625,
0.44921875,
0.468017578125,
-0.260009765625,
-0.00555419921875,
-0.658203125,
-0.6953125,
-0.08612060546875,
-0.60107421875,
-0.7... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Notes
For this problem, it is recommended to use floating point numbers, which are more accurate than double.
Input
m n x
k l y
For input, six integers m, n, x, k, l, y are given in the above input format.
These six integers correspond to those in the problem statement, repeating the horizontal m: n cut x times and the vertical k: l cut y times.
1 β€ m, n, k, l β€ 100, 0 β€ x, y β€ 40, and m, n and l, k are relatively prime.
Output
Print out the expected number of planarians that are regenerating to their original form after a few weeks in a row.
The output is acceptable with an error of 10-6 or less.
Examples
Input
1 1 1
1 1 1
Output
0.562500
Input
1 2 2
1 1 1
Output
0.490741
Input
1 2 0
3 4 0
Output
1.000000
"Correct Solution:
```
m,n,x=[int(i) for i in input().split()]
k,l,y=[int(i) for i in input().split()]
res=0.5*(1.0+((m**2+n**2)**x)/((m+n)**(2*x)))
res*=0.5*(1.0+((k**2+l**2)**y)/((k+l)**(2*y)))
print(res)
```
| 69,759 | [
0.2142333984375,
0.212646484375,
-0.1966552734375,
-0.0819091796875,
-1.041015625,
-0.173828125,
0.0936279296875,
0.15380859375,
0.414306640625,
0.81201171875,
0.39306640625,
-0.486572265625,
-0.1439208984375,
-0.3515625,
-0.293212890625,
0.044647216796875,
-0.703125,
-0.9790039062... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One morning when you woke up, it was in a springy labyrinth.
I don't know why I'm in such a strange place. You have the option of waiting for help here, but you know from experience that if you stay in a labyrinth like this for a long time, a gust of wind will surely blow you away. It was. However, the time until the gust blows cannot be judged. So you thought it was best to act to minimize the expected number of moves required to escape the labyrinth.
When I picked up an unidentified scroll that had fallen under my feet and read it as a trial, I happened to be able to perceive the entire map of the labyrinth. Furthermore, by drinking the grass that I happened to have, I was able to know the positions of all the traps. Apparently, there are no traps other than dangerous monsters and springs in this labyrinth.
This labyrinth is shaped like a rectangle with several types of tiles, for example:
.. ## g. #
* #. * #. #
...... #
* s # *. * #
".":floor. You can walk around freely on this.
"#":wall. You can't get inside the wall.
"S": Your first position. Below this tile is the floor.
"G": Stairs. If you ride on this tile, you have escaped from the labyrinth.
"*":Spring. If you ride on this tile, it will be randomly blown onto one of the floors (excluding stairs and spring tiles). The odds of being hit on each floor are all equal.
The type of tile is one of these five.
You can move one square at a time from the tile you are currently riding to an adjacent tile in either the up, down, left, or right direction. However, you cannot move to Naname.
Given a map of the labyrinth, find the expected number of moves required to escape the labyrinth if you take the best strategy. It is not included in the number of movements that is blown by the spring.
Input
W H
c11 c12 ... c1w
c21 c22 ... c2w
:::
ch1 ch2 ... ccw
On the first line of input, the integer W (3 β€ W β€ 500) and the integer H (3 β€ H β€ 500) are written in this order, separated by blanks. The integer W represents the width of the labyrinth, and the integer H represents the height of the labyrinth.
The following H line contains W letters (not blank delimiters) that represent the map of the labyrinth. The format of this part is as in the example given above. Note that "s" and "g" appear exactly once in the data. In addition, one square around the labyrinth is always surrounded by a wall.
In addition, in the given labyrinth, no matter how you move and how it is blown by the spring, you will fall into a state where you cannot escape even if you can arbitrarily set the floor to be blown by the spring. You can assume that there is no such thing.
Output
Output the expected number of moves to escape when you take the best strategy. The output may contain errors, but the relative error to the true value must be less than 10-9.
Examples
Input
8 6
########
#..##g.#
#*#.*#.#
#......#
#*s#*.*#
########
Output
5.857142857143
Input
8 6
..##g.#
*#.*#.#
......#
*s#*.*#
Output
5.857142857143
Input
21 11
*#*.*.*.*.*.*.*.*#*#
*#...............#*#
*#.#.#.#.#.#.#.#.#*#
.#.#.#.#.#.#.#.#.##
...................#
.#.#.#.#.#.#.#.#.##
s#.#.#.#.#.#.#.#.#g#
...................#
...................#
Output
20.000000000000
Input
9 8
...#*.*#
.*.#...#
...#*.*#
.s....g#
.*#.*..#
Output
5.000000000000
Submitted Solution:
```
from collections import deque
w, h = map(int, input().split())
mp = [input() for _ in range(h)]
springs = []
tile_cnt = 0
for y in range(h):
for x in range(w):
if mp[y][x] == "*":
springs.append((x, y))
if mp[y][x] == "g":
gx, gy = x, y
if mp[y][x] == "s":
sx, sy = x, y
tile_cnt += 1
if mp[y][x] == ".":
tile_cnt += 1
vec = ((1, 0), (0, -1), (-1, 0), (0, 1))
INF = 10 ** 10
g_dist = [[INF] * w for _ in range(h)]
que = deque()
que.append((0, gx, gy))
g_dist[gy][gx] = 0
while que:
score, x, y = que.popleft()
for dx, dy in vec:
nx, ny = x + dx, y + dy
if mp[ny][nx] in (".", "s"):
if g_dist[ny][nx] == INF:
g_dist[ny][nx] = score + 1
que.append((score + 1, nx, ny))
s_dist = [[INF] * w for _ in range(h)]
que = deque()
for x, y in springs:
s_dist[y][x] = 0
que.append((0, x, y))
while que:
score, x, y = que.popleft()
for dx, dy in vec:
nx, ny = x + dx, y + dy
if mp[ny][nx] in (".", "s"):
if s_dist[ny][nx] == INF:
s_dist[ny][nx] = score + 1
que.append((score + 1, nx, ny))
sorted_tiles = sorted([(g_dist[y][x] - s_dist[y][x], x, y) for y in range(h) for x in range(w) if mp[y][x] in (".", "s")])
acc_g = 0
acc_s = 0
acc_t = 0
acc_g_dic = {}
acc_s_dic = {}
acc_t_dic = {}
keys = set()
for key, x, y in sorted_tiles:
acc_g += g_dist[y][x]
acc_s += s_dist[y][x]
acc_t += 1
acc_g_dic[key] = acc_g
acc_s_dic[key] = acc_s
acc_t_dic[key] = acc_t
keys.add(key)
keys = sorted(list(keys))
length = len(keys)
for i in range(length - 1):
key = keys[i]
next_key = keys[i + 1]
E = (acc_g_dic[key] + acc_s - acc_s_dic[key]) / acc_t_dic[key]
if key <= E < next_key:
break
print(min(g_dist[sy][sx], s_dist[y][x] + E))
```
No
| 69,784 | [
0.32568359375,
0.32373046875,
-0.595703125,
0.0999755859375,
-0.464111328125,
-0.171875,
0.06805419921875,
0.64111328125,
0.372314453125,
0.85009765625,
0.59619140625,
0.2369384765625,
-0.0537109375,
-0.82470703125,
-0.7421875,
0.36474609375,
-0.74072265625,
-0.59765625,
-0.59326... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One morning when you woke up, it was in a springy labyrinth.
I don't know why I'm in such a strange place. You have the option of waiting for help here, but you know from experience that if you stay in a labyrinth like this for a long time, a gust of wind will surely blow you away. It was. However, the time until the gust blows cannot be judged. So you thought it was best to act to minimize the expected number of moves required to escape the labyrinth.
When I picked up an unidentified scroll that had fallen under my feet and read it as a trial, I happened to be able to perceive the entire map of the labyrinth. Furthermore, by drinking the grass that I happened to have, I was able to know the positions of all the traps. Apparently, there are no traps other than dangerous monsters and springs in this labyrinth.
This labyrinth is shaped like a rectangle with several types of tiles, for example:
.. ## g. #
* #. * #. #
...... #
* s # *. * #
".":floor. You can walk around freely on this.
"#":wall. You can't get inside the wall.
"S": Your first position. Below this tile is the floor.
"G": Stairs. If you ride on this tile, you have escaped from the labyrinth.
"*":Spring. If you ride on this tile, it will be randomly blown onto one of the floors (excluding stairs and spring tiles). The odds of being hit on each floor are all equal.
The type of tile is one of these five.
You can move one square at a time from the tile you are currently riding to an adjacent tile in either the up, down, left, or right direction. However, you cannot move to Naname.
Given a map of the labyrinth, find the expected number of moves required to escape the labyrinth if you take the best strategy. It is not included in the number of movements that is blown by the spring.
Input
W H
c11 c12 ... c1w
c21 c22 ... c2w
:::
ch1 ch2 ... ccw
On the first line of input, the integer W (3 β€ W β€ 500) and the integer H (3 β€ H β€ 500) are written in this order, separated by blanks. The integer W represents the width of the labyrinth, and the integer H represents the height of the labyrinth.
The following H line contains W letters (not blank delimiters) that represent the map of the labyrinth. The format of this part is as in the example given above. Note that "s" and "g" appear exactly once in the data. In addition, one square around the labyrinth is always surrounded by a wall.
In addition, in the given labyrinth, no matter how you move and how it is blown by the spring, you will fall into a state where you cannot escape even if you can arbitrarily set the floor to be blown by the spring. You can assume that there is no such thing.
Output
Output the expected number of moves to escape when you take the best strategy. The output may contain errors, but the relative error to the true value must be less than 10-9.
Examples
Input
8 6
########
#..##g.#
#*#.*#.#
#......#
#*s#*.*#
########
Output
5.857142857143
Input
8 6
..##g.#
*#.*#.#
......#
*s#*.*#
Output
5.857142857143
Input
21 11
*#*.*.*.*.*.*.*.*#*#
*#...............#*#
*#.#.#.#.#.#.#.#.#*#
.#.#.#.#.#.#.#.#.##
...................#
.#.#.#.#.#.#.#.#.##
s#.#.#.#.#.#.#.#.#g#
...................#
...................#
Output
20.000000000000
Input
9 8
...#*.*#
.*.#...#
...#*.*#
.s....g#
.*#.*..#
Output
5.000000000000
Submitted Solution:
```
from collections import deque
w, h = map(int, input().split())
mp = [input() for _ in range(h)]
springs = []
tile_cnt = 0
for y in range(h):
for x in range(w):
if mp[y][x] == "*":
springs.append((x, y))
if mp[y][x] == "g":
gx, gy = x, y
if mp[y][x] == "s":
sx, sy = x, y
tile_cnt += 1
if mp[y][x] == ".":
tile_cnt += 1
vec = ((1, 0), (0, -1), (-1, 0), (0, 1))
INF = 10 ** 10
g_dist = [[INF] * w for _ in range(h)]
que = deque()
que.append((0, gx, gy))
g_dist[gy][gx] = 0
while que:
score, x, y = que.popleft()
for dx, dy in vec:
nx, ny = x + dx, y + dy
if mp[ny][nx] in (".", "s"):
if g_dist[ny][nx] == INF:
g_dist[ny][nx] = score + 1
que.append((score + 1, nx, ny))
s_dist = [[INF] * w for _ in range(h)]
que = deque()
for x, y in springs:
s_dist[y][x] = 0
que.append((0, x, y))
while que:
score, x, y = que.popleft()
for dx, dy in vec:
nx, ny = x + dx, y + dy
if mp[ny][nx] in (".", "s"):
if s_dist[ny][nx] == INF:
s_dist[ny][nx] = score + 1
que.append((score + 1, nx, ny))
sorted_tiles = sorted([(g_dist[y][x] - s_dist[y][x] if g_dist[y][x] != INF else INF, x, y) for y in range(h) for x in range(w) if mp[y][x] in (".", "s")])
acc_g = 0
acc_s = 0
acc_t = 0
acc_g_dic = {}
acc_s_dic = {}
acc_t_dic = {}
keys = set()
for key, x, y in sorted_tiles:
acc_g += g_dist[y][x]
acc_s += s_dist[y][x]
acc_t += 1
acc_g_dic[key] = acc_g
acc_s_dic[key] = acc_s
acc_t_dic[key] = acc_t
keys.add(key)
keys = sorted(list(keys))
length = len(keys)
for i in range(length - 1):
key = keys[i]
next_key = keys[i + 1]
E = (acc_g_dic[key] + acc_s - acc_s_dic[key]) / acc_t_dic[key]
if key <= E < next_key:
break
print(min(g_dist[sy][sx], s_dist[sy][sx] + E))
```
No
| 69,785 | [
0.32568359375,
0.32373046875,
-0.595703125,
0.0999755859375,
-0.464111328125,
-0.171875,
0.06805419921875,
0.64111328125,
0.372314453125,
0.85009765625,
0.59619140625,
0.2369384765625,
-0.0537109375,
-0.82470703125,
-0.7421875,
0.36474609375,
-0.74072265625,
-0.59765625,
-0.59326... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
from sys import stdin
for case in range(int(stdin.readline())):
n,m,x1,y1,x2,y2 = [int(x) for x in stdin.readline().split()]
total = n*m
xDiff = abs(x1-x2)
yDiff = abs(y1-y2)
rectX = n-xDiff
rectY = m-yDiff
midSquare = (rectX*2-n)*(rectY*2-m)
total -= 2*(n-xDiff)*(m-yDiff)
if rectX*2 > n:
total += max(midSquare,0)
print(total)
```
| 70,096 | [
0.1234130859375,
0.002071380615234375,
0.1029052734375,
0.59423828125,
-0.279541015625,
-0.3388671875,
-0.3935546875,
0.094970703125,
0.0843505859375,
0.908203125,
0.603515625,
0.201904296875,
0.364013671875,
-0.576171875,
-0.28662109375,
0.2193603515625,
-0.1929931640625,
-0.69775... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
for i in range(int(input())):
n, m, x1, y1, x2, y2 = map(int, input().split())
w,h=abs(x2-x1),abs(y2-y1)
if w*2>n or h*2>m:
print(n*m-2*(n-w)*(m-h))
else:
print(2*w*h)
```
| 70,097 | [
0.1265869140625,
-0.0029048919677734375,
0.10400390625,
0.5927734375,
-0.269287109375,
-0.32958984375,
-0.3896484375,
0.085693359375,
0.09271240234375,
0.90966796875,
0.60498046875,
0.2061767578125,
0.3583984375,
-0.5751953125,
-0.28759765625,
0.2303466796875,
-0.1883544921875,
-0.... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
I = lambda : map(int,input().split())
for _ in range (int(input())) :
n , m , x1 , y1 , x2 , y2 = I()
if y1 > y2 :
x1 , y1 , x2 , y2 = x1 , y2 , x2 , y1
if x1 <= x2 :
xmin = x1
xmax = x2
xmin = x1 + max(0,n-x2)
xmax = x2 - (x1-1)
ymin = y1 + m-y2
ymax = y2 - (y1-1)
#print(xmin , xmax)
rect = n*m
a1 = xmin * ymin
a2 = (n-xmax+1)*(m-ymax+1)
com = max(xmin - xmax + 1 , 0) * max(ymin - ymax + 1 , 0)
#print(rect , a1 ,a2 ,com)
print(rect - a1 - a2 + com)
else :
x1 = n+1 - x1
x2 = n+1 - x2
xmin = x1
xmax = x2
xmin = x1 + max(0,n-x2)
xmax = x2 - (x1-1)
ymin = y1 + m-y2
ymax = y2 - (y1-1)
#print(xmin , xmax)
rect = n*m
a1 = xmin * ymin
a2 = (n-xmax+1)*(m-ymax+1)
com = max(xmin - xmax + 1 , 0) * max(ymin - ymax + 1 , 0)
#print(rect , a1 ,a2 ,com)
print(rect - a1 - a2 + com)
```
| 70,098 | [
0.1214599609375,
-0.0014524459838867188,
0.0931396484375,
0.60546875,
-0.274169921875,
-0.3544921875,
-0.38330078125,
0.10150146484375,
0.074462890625,
0.90966796875,
0.60888671875,
0.19775390625,
0.36181640625,
-0.58154296875,
-0.278076171875,
0.224853515625,
-0.18701171875,
-0.71... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
for z in range(int(input())):
n,m,a,b,c,d=[int(i) for i in input().split()]
l=min(a,c)
o=min(b,d)
r=min(n-a,n-c)
u=min(m-b,m-d)
if a<=c:
h=a+r-c+l
else:
h=c+r-a+l
h=max(h,0)
if b<=d:
v=b+u-d+o
else:
v=d+u-b+o
v=max(v,0)
print(n*m-2*(l+r)*(o+u)+h*v)
```
| 70,099 | [
0.1361083984375,
-0.006160736083984375,
0.12353515625,
0.58837890625,
-0.296630859375,
-0.34228515625,
-0.394775390625,
0.09735107421875,
0.0655517578125,
0.91259765625,
0.6083984375,
0.2135009765625,
0.36572265625,
-0.56396484375,
-0.28759765625,
0.217529296875,
-0.1822509765625,
... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
t = int( input() )
for i in range(t):
n, m, x1, y1, x2, y2 = map( int, input().split() )
#print(n,m,x1,y1,x2,y2)
l = min( x1-1, x2-1 )
r = min( n-x1, n-x2 )
d = min( y1-1, y2-1 )
u = min( m-y1, m-y2 )
#print(l,r,d,u)
srange = [ ( x1-l, x1+r, y1-d, y1+u ), ( x2-l, x2+r, y2-d, y2+u ) ]
sortRan = sorted( srange, key = lambda e: e[0] )
s = (l+r+1) * (d+u+1) * 2
#print(sortRan)
#print(s)
if sortRan[1][0] <= sortRan[0][1]:
if sortRan[0][2] <= sortRan[1][3] <= sortRan[0][3]:
s -= (sortRan[0][1] - sortRan[1][0] + 1) * ( sortRan[1][3] - sortRan[0][2] + 1)
elif sortRan[0][2] <= sortRan[1][2] <= sortRan[0][3]:
s -= (sortRan[0][1] - sortRan[1][0] + 1) * ( sortRan[0][3] - sortRan[1][2] + 1)
print( n*m - s )
```
| 70,100 | [
0.12890625,
0.002704620361328125,
0.09173583984375,
0.60009765625,
-0.2802734375,
-0.352783203125,
-0.375732421875,
0.101806640625,
0.0775146484375,
0.90625,
0.611328125,
0.20849609375,
0.365966796875,
-0.57373046875,
-0.275634765625,
0.2183837890625,
-0.1890869140625,
-0.715820312... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
t = int(input())
for q in range(t):
n,m,x1,y1,x2,y2 = map(int,input().split(' '))
print(n*m-2*((n-abs(x1-x2))*(m-abs(y1-y2)))+(min(0,(n-2*(n-abs(x1-x2))))*min(0,m-2*(m-abs(y1-y2)))))
```
| 70,101 | [
0.12890625,
0.002704620361328125,
0.09173583984375,
0.60009765625,
-0.2802734375,
-0.352783203125,
-0.375732421875,
0.101806640625,
0.0775146484375,
0.90625,
0.611328125,
0.20849609375,
0.365966796875,
-0.57373046875,
-0.275634765625,
0.2183837890625,
-0.1890869140625,
-0.715820312... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
class CodeforcesTask15BSolution:
def __init__(self):
self.result = ''
self.t = 0
self.tests = []
def read_input(self):
self.t = int(input())
for x in range(self.t):
self.tests.append([int(y) for y in input().split(" ")])
def process_task(self):
results = []
for test in self.tests:
vert = abs(test[3] - test[5])
hori = abs(test[2] - test[4])
if vert * 2 <= test[1]:
vert_unr = 0
else:
vert_unr = 2 * vert - test[1]
if hori * 2 <= test[0]:
hori_unr = 0
else:
hori_unr = 2 * hori - test[0]
unr = test[0] * vert_unr + test[1] * hori_unr - hori_unr * vert_unr
unr += 2 * (vert - vert_unr) * (hori - hori_unr)
results.append(unr)
self.result = "\n".join([str(x) for x in results])
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask15BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
```
| 70,102 | [
0.1258544921875,
-0.01102447509765625,
0.09991455078125,
0.5859375,
-0.266357421875,
-0.336181640625,
-0.357177734375,
0.07366943359375,
0.05340576171875,
0.90087890625,
0.583984375,
0.2001953125,
0.37158203125,
-0.58154296875,
-0.2724609375,
0.1705322265625,
-0.178466796875,
-0.71... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Tags: math
Correct Solution:
```
for _ in range(int(input())):
n, m, x1, y1, x2, y2 = map(int, input().split())
ans = abs(x1 - x2) * abs(y1 - y2) * 2
if 2 * abs(x1 - x2) > n:
if 2 * abs(y1 - y2) > m:
ans -= max(0, 2 * abs(x1 - x2) - n) * max(0, 2 * abs(y1 - y2) - m)
else:
ans += max(0, 2 * abs(x1 - x2) - n) * max(0, m - 2 * abs(y1 - y2))
else:
if 2 * abs(y1 - y2) > m:
ans += max(0, n - 2 * abs(x1 - x2)) * max(0, 2 * abs(y1 - y2) - m)
print(ans)
```
| 70,103 | [
0.1221923828125,
-0.0018157958984375,
0.10498046875,
0.60400390625,
-0.28515625,
-0.340087890625,
-0.3916015625,
0.10009765625,
0.07891845703125,
0.91455078125,
0.61181640625,
0.2049560546875,
0.353271484375,
-0.5849609375,
-0.28759765625,
0.2193603515625,
-0.189453125,
-0.71240234... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
t = int(input())
for _ in range(t):
n, m, x1, y1, x2, y2 = map(int, input().split())
x, y = abs(x1 - x2), abs(y1 - y2)
if n >= x * 2 and m >= y * 2: #overlap
print(x * y * 2)
else:
print(n * m - ((n - x) * (m - y) * 2))
```
Yes
| 70,104 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
import sys
def its (x1, y1, x2, y2, x3, y3, x4, y4):
x5 = max(x1,x3); y5=max(y1,y3)
x6 = min(x2,x4); y6=min(y2,y4)
if (x5<=x6 and y5<=y6):
return (x6+1-x5)*(y6+1-y5)
else: return 0
def main():
t = int(input())
for it in range(0,t):
n,m,x1,y1,x2,y2=[int(x) for x in sys.stdin.readline().split()]
"""
n=int(sys.stdin().read())
m=int(sys.stdin().read())
x1=int(sys.stdin().read())
y1=int(sys.stdin().read())
x2=int(sys.stdin().read())
y2=int(sys.stdin().read())
"""
dr=min(n-x1,n-x2)
dl=min(x1-1,x2-1)
du=min(y1-1,y2-1)
dd=min(m-y1,m-y2)
x1p, y1p = x1-dl, y1-du
x2p, y2p = x1+dr, y1+dd
x3p, y3p = x2-dl, y2-du
x4p, y4p = x2+dr, y2+dd
#print(x1p,y1p,x2p,y2p,x3p,y3p,x4p,y4p)
ans=(x2p+1-x1p)*(y2p+1-y1p)+(x4p+1-x3p)*(y4p+1-y3p)
ans-=its(x1p,y1p,x2p,y2p,x3p,y3p,x4p,y4p)
print(n*m-ans);
main()
```
Yes
| 70,105 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
__author__ = 'Darren'
def solve():
t = int(input())
while t:
run()
t -= 1
def run():
n, m, x1, y1, x2, y2 = map(int, input().split())
width, height = abs(x1 - x2), abs(y1 - y2)
count = width * height * 2
x, y = width * 2 - n, height * 2 - m
if not (x < 0 and y < 0):
count -= x * y
print(count)
if __name__ == '__main__':
solve()
# Made By Mostafa_Khaled
```
Yes
| 70,106 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
n = int(input())
for i in range(n):
n, m, x1, y1, x2, y2 = map(int, input().split())
#print(n, m, x1, y1, x2, y2)
if x1 <= x2 and y1 <= y2:
pass
elif x1 >= x2 and y1 >= y2:
x1, y1, x2, y2 = x2, y2, x1, y1
else:
x1, y1, x2, y2 = x2, y1, x1, y2
if x1 <= x2 and y1 <= y2:
pass
elif x1 >= x2 and y1 >= y2:
x1, y1, x2, y2 = x2, y2, x1, y1
#print(n, m, x1, y1, x2, y2)
print(n*m - ((n - (x2 - x1)) * (m - (y2 - y1)) * 2 - max(0, (n - (x2 - x1)) * 2 - n) * max(0, (m - (y2 - y1)) * 2 - m)))
#printf("%d\n", ($n * $m) - (($n - ($x2 - $x1)) * ($m - ($y2 - $y1)) * 2
#- max(0, ($n - ($x2 - $x1)) * 2 - $n) * max(0, ($m - ($y2 - $y1)) * 2 - $m)));
```
Yes
| 70,107 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
from sys import stdin
for case in range(int(stdin.readline())):
n,m,x1,y1,x2,y2 = [int(x) for x in stdin.readline().split()]
total = n*m
xDiff = abs(x1-x2)
yDiff = abs(y1-y2)
rectX = n-xDiff
rectY = m-yDiff
midSquare = (rectX*2-n)*(rectY*2-m)
total -= 2*(n-xDiff)*(m-yDiff)
total += max(midSquare,0)
print(total)
```
No
| 70,108 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
t = int(input())
for i in range(t):
n,m,x1,y1,x2,y2 = map(int,input().split(' '))
print(n*m-2*((n-abs(x1-x2))*(m-abs(y1*y2)))+max(0,(n-2*abs(x1-x2))*(m-2*abs(y1*y2))))
```
No
| 70,109 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
t = int( input() )
for i in range(t):
m, n, y1, x1, y2, x2 = map( int, input().split() )
x1, y1, x2, y2 = x1-1, y1-1, x2-1, y2-1
visit = [ [0] * m for i in range(n) ]
xl = min( x1, x2 )
xr = min( m-1-x1, m-1-x2 )
yd = min( y1, y2 )
yu = min( n-1-y1, n-1-y2 )
#print(n,m,x1,y1,x2,y2)
#print(xl,xr,yd,yu)
for x in range(n):
for y in range(m):
if ( ( (y1 - xl) <= y <= (y1 + xr) and (x1 - yd) <= x <= (x1 + yu) ) \
or ( (y2 - xl) <= y <= (y2 + xr) and (x2 - yd) <= x <= (x2 + yu) ) ):
#print(x,y)
visit[x][y] = 1
#print(visit)
s = 0
#print(visit)
for j in range(n):
s += sum(visit[j])
print( n*m - s )
```
No
| 70,110 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya is the most responsible worker in the Research Institute. So he was asked to make a very important experiment: to melt the chocolate bar with a new laser device. The device consists of a rectangular field of n Γ m cells and a robotic arm. Each cell of the field is a 1 Γ 1 square. The robotic arm has two lasers pointed at the field perpendicularly to its surface. At any one time lasers are pointed at the centres of some two cells. Since the lasers are on the robotic hand, their movements are synchronized β if you move one of the lasers by a vector, another one moves by the same vector.
The following facts about the experiment are known:
* initially the whole field is covered with a chocolate bar of the size n Γ m, both lasers are located above the field and are active;
* the chocolate melts within one cell of the field at which the laser is pointed;
* all moves of the robotic arm should be parallel to the sides of the field, after each move the lasers should be pointed at the centres of some two cells;
* at any one time both lasers should be pointed at the field. Petya doesn't want to become a second Gordon Freeman.
You are given n, m and the cells (x1, y1) and (x2, y2), where the lasers are initially pointed at (xi is a column number, yi is a row number). Rows are numbered from 1 to m from top to bottom and columns are numbered from 1 to n from left to right. You are to find the amount of cells of the field on which the chocolate can't be melted in the given conditions.
Input
The first line contains one integer number t (1 β€ t β€ 10000) β the number of test sets. Each of the following t lines describes one test set. Each line contains integer numbers n, m, x1, y1, x2, y2, separated by a space (2 β€ n, m β€ 109, 1 β€ x1, x2 β€ n, 1 β€ y1, y2 β€ m). Cells (x1, y1) and (x2, y2) are distinct.
Output
Each of the t lines of the output should contain the answer to the corresponding input test set.
Examples
Input
2
4 4 1 1 3 3
4 3 1 1 2 2
Output
8
2
Submitted Solution:
```
t = int(input())
for q in range(t):
n,m,x1,y1,x2,y2 = map(int,input().split(' '))
print(n*m-2*((n-abs(x1-x2))*(m-abs(y1-y2)))+(min(0,(n-2*(n-abs(x1-x2)))*min(0,m-2*m-abs(y1-y2)))))
```
No
| 70,111 | [
0.145751953125,
0.0418701171875,
0.091552734375,
0.42626953125,
-0.40087890625,
-0.20458984375,
-0.42041015625,
0.217041015625,
0.0791015625,
0.87939453125,
0.5517578125,
0.16943359375,
0.305908203125,
-0.5966796875,
-0.324462890625,
0.2169189453125,
-0.2529296875,
-0.7275390625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem consists of two subproblems: for solving subproblem D1 you will receive 3 points, and for solving subproblem D2 you will receive 16 points.
Manao is the chief architect involved in planning a new supercollider. He has to identify a plot of land where the largest possible supercollider can be built. The supercollider he is building requires four-way orthogonal collisions of particles traveling at the same speed, so it will consist of four accelerating chambers and be shaped like a plus sign (i.e., +). Each of the four accelerating chambers must be the same length and must be aligned with the Earth's magnetic field (parallel or orthogonal) to minimize interference.
The accelerating chambers need to be laid down across long flat stretches of land to keep costs under control. Thus, Manao has already commissioned a topographical study that has identified all possible maximal length tracts of land available for building accelerating chambers that are either parallel or orthogonal to the Earth's magnetic field. To build the largest possible supercollider, Manao must identify the largest symmetric plus shape from among these candidate tracts. That is, he must find the two tracts of land that form an axis-aligned plus shape with the largest distance from the center of the plus to the tip of the shortest of the four arms of the plus. Note that the collider need not use the entire length of the tracts identified (see the example in the notes).
Input
The first line of the input will contain two single-space-separated integers n, the number of north-south tracts and m, the number of west-east tracts.
Each of the n lines following the first describes a north-south tract. Each such tract is described by three single-space-separated integers xi, yi, li representing the vertical line segment from (xi, yi) to (xi, yi + li).
Similarly, after the n lines describing north-south tracts follow m similar lines describing the west-east tracts. Each such tract is described by three single-space-separated integers xi, yi, li representing the horizontal line segment from (xi, yi) to (xi + li, yi).
All xi and yi are between -100000000 and 100000000, inclusive. All li are between 1 and 100000000, inclusive. No pair of horizontal segments will touch or intersect, and no pair of vertical segments will touch or intersect.
The problem consists of two subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.
* In subproblem D1 (3 points), n and m will be between 1 and 1000, inclusive.
* In subproblem D2 (16 points), n and m will be between 1 and 50000, inclusive.
Output
Print one line containing a single integer, the size of the largest supercollider that can be built on one north-south tract and one west-east tract. The size of the supercollider is defined to be the length of one of the four accelerating chambers. In other words, the size of the resulting supercollider is defined to be the distance from the intersection of the two line segments to the closest endpoint of either of the two segments. If no pair of north-south and west-east tracts intersects, it is not possible to build a supercollider and the program should report a maximum size of zero.
Examples
Input
1 2
4 0 9
1 1 8
1 2 7
Output
2
Note
Consider the example. There is one vertical line segment from (4, 0) to (4, 9) and two horizontal line segments: from (1, 1) to (9, 1) and from (1, 2) to (8, 2). The largest plus shape that can be found among these segments is formed from the only vertical segment and the second of horizontal segments, and is centered at (4, 2).
The program should output 2 because the closest end point of those segments to the center is (4, 0), which is distance 2 from the center point of (4, 2). The collider will be formed by the line segments from (2, 2) to (6, 2) and from (4, 0) to (4, 4).
Submitted Solution:
```
n, m = map(int, input().split())
CHUNK_SIZE = 128
def calc_u(xh, yh, lh, xv, yv, lv):
return min(
xh-xv,
xh+lh-xv,
yv-yh,
yv + lv - yh,
)
chunker = dict()
def add_h(inp):
x, y, l = inp
cx = x // CHUNK_SIZE
cy = y // CHUNK_SIZE
cl = l // CHUNK_SIZE
for i in range(-1, cl+1):
crd = (cx + i, cy)
v = chunker.get(crd)
if v is None:
v = []
chunker[crd] = v
v.append(inp)
def get_v(inp):
x, y, l = inp
cx = x // CHUNK_SIZE
cy = y // CHUNK_SIZE
cl = l // CHUNK_SIZE
for i in range(-1, cl+1):
crd = (cx, cy + i)
#print("Checking", *crd)
v = chunker.get(crd)
if v is not None:
#print("Found", len(v))
yield from v
for i in range(n):
inp = tuple(map(int, input().split()))
add_h(inp)
#print(chunker)
mxv = 0
for i in range(m):
inp = tuple(map(int, input().split()))
for j in get_v(inp):
#print(inp, j)
v = calc_u(*j, *inp)
if v > mxv:
mxv = v
print(mxv)
```
No
| 70,170 | [
0.3681640625,
0.2734375,
-0.35595703125,
0.0631103515625,
-0.61962890625,
-0.223388671875,
-0.1282958984375,
0.304931640625,
-0.04150390625,
0.75146484375,
0.95068359375,
0.1319580078125,
0.11224365234375,
-0.85693359375,
-0.5234375,
0.1771240234375,
-0.72998046875,
-0.82470703125,... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
if x1 == x2:
x1 += 1
elif y1 == y2:
y1 += 1
print((abs(x2 - x1) + 1 + abs(y2 - y1) + 1) * 2)
```
Yes
| 70,426 | [
0.42041015625,
-0.03118896484375,
-0.036041259765625,
0.362548828125,
-0.14697265625,
0.040435791015625,
-0.439208984375,
0.13330078125,
0.31005859375,
0.7998046875,
0.60302734375,
0.09490966796875,
-0.0655517578125,
-0.6796875,
-0.25732421875,
0.0212554931640625,
-0.302734375,
-0.... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
x1, y1 = [int(i) for i in input().split()]
x2, y2 = [int(i) for i in input().split()]
minx = min(x1, x2 - 1)
miny = min(y1, y2 - 1)
maxx = max(x1, x2 + 1)
maxy = max(y1, y2 + 1)
print(2 * ((maxx - minx) + (maxy - miny)))
```
Yes
| 70,427 | [
0.430908203125,
-0.046417236328125,
0.0251922607421875,
0.351318359375,
-0.14013671875,
0.005771636962890625,
-0.429443359375,
0.0960693359375,
0.28369140625,
0.7705078125,
0.6044921875,
0.07305908203125,
-0.10791015625,
-0.61376953125,
-0.279296875,
0.053436279296875,
-0.33642578125... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
x = 1 if not abs(x1-x2) else abs(x1-x2)
y = 1 if not abs(y1-y2) else abs(y1-y2)
print((x+1)*2 + (y+1)*2)
```
Yes
| 70,428 | [
0.413818359375,
-0.0168609619140625,
-0.016326904296875,
0.3369140625,
-0.14306640625,
0.03179931640625,
-0.431884765625,
0.1163330078125,
0.28662109375,
0.76318359375,
0.59326171875,
0.078857421875,
-0.053131103515625,
-0.64794921875,
-0.260009765625,
0.0271148681640625,
-0.33032226... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
from math import inf,sqrt,floor,ceil
from collections import Counter,defaultdict,deque
from heapq import heappush as hpush,heappop as hpop,heapify as h
from operator import itemgetter
from itertools import product
from bisect import bisect_left,bisect_right
x1,y1=map(int,input().split( ))
x2,y2=map(int,input().split( ))
l=abs(x1-x2)+1
b=abs(y1-y2)+1
if x1==x2:
l=abs(x1-x2)+2
if y1==y2:
b=abs(y1-y2)+2
print(2*(l+b))
```
Yes
| 70,429 | [
0.38720703125,
-0.08160400390625,
0.041839599609375,
0.3505859375,
-0.165771484375,
0.01904296875,
-0.428466796875,
0.0226287841796875,
0.247314453125,
0.8037109375,
0.58447265625,
0.046356201171875,
-0.08050537109375,
-0.58935546875,
-0.23046875,
0.054901123046875,
-0.344482421875,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
i,j = input("Enter two values: ").split()
i = int(i)
j = int(j)
o,p = input("Enter two values: ").split()
o = int(o)
p = int(p)
a = i - o
b = j - p
if a < 0:
a = 0-a
if a == 0:
a = 1
if b == 0:
b = 1
if b < 0:
b = 0-b
x =(a+b+2)*2
print(x)
```
No
| 70,430 | [
0.438232421875,
-0.047607421875,
0.043609619140625,
0.329345703125,
-0.1944580078125,
0.01465606689453125,
-0.41064453125,
0.108642578125,
0.242431640625,
0.7783203125,
0.58984375,
0.08868408203125,
-0.1087646484375,
-0.6015625,
-0.260009765625,
0.0157623291015625,
-0.31884765625,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
x1,y1=map(int,input().split())
x2,y2=map(int,input().split())
x,y=x2,y2
if abs(x1-x2)>1:
if x1>x2:
x=x2+1
else:
x=x2-1
if abs(y1-y2)>1:
if y1>y2:
y=y2+1
else:
y=y2-1
if x==x2 or y==y2:
print(8)
else:
print(8+2*(abs(x1-x)+abs(y1-y)))
```
No
| 70,431 | [
0.43359375,
-0.038543701171875,
0.0241851806640625,
0.338134765625,
-0.156982421875,
0.034759521484375,
-0.4443359375,
0.11944580078125,
0.25732421875,
0.7802734375,
0.61181640625,
0.0894775390625,
-0.0814208984375,
-0.62060546875,
-0.263671875,
0.037994384765625,
-0.332763671875,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
line1 = input()
line2 = input()
dc = [int(s) for s in line1.split(' ')]
fc = [int(s) for s in line2.split(' ')]
d = [abs(a - b) for a, b in zip(dc, fc)]
print(d)
transit_x = max(2, d[0]+1)*2
transit_y = max(2, d[1]+1)*2
t = transit_x + transit_y
print(t)
```
No
| 70,432 | [
0.424072265625,
-0.04962158203125,
0.0548095703125,
0.358154296875,
-0.1441650390625,
0.0158233642578125,
-0.4111328125,
0.11346435546875,
0.2763671875,
0.796875,
0.55517578125,
0.06793212890625,
-0.07574462890625,
-0.62109375,
-0.31982421875,
0.0115814208984375,
-0.34765625,
-0.59... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
* start the race from some point of a field,
* go around the flag,
* close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).
Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.
<image> The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2).
What is the minimal length of the quadcopter path?
Input
The first line contains two integer numbers x1 and y1 ( - 100 β€ x1, y1 β€ 100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers x2 and y2 ( - 100 β€ x2, y2 β€ 100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide.
Output
Print the length of minimal path of the quadcopter to surround the flag and return back.
Examples
Input
1 5
5 2
Output
18
Input
0 1
0 0
Output
8
Submitted Solution:
```
a, b = map(int, input().split())
c, d = map(int, input().split())
print(abs(a - c) * 2 + abs(b - d) * 2 + 4)
```
No
| 70,433 | [
0.435302734375,
-0.047027587890625,
-0.005680084228515625,
0.323486328125,
-0.14599609375,
0.0242767333984375,
-0.434814453125,
0.1304931640625,
0.26318359375,
0.80859375,
0.61962890625,
0.087646484375,
-0.06292724609375,
-0.64794921875,
-0.269775390625,
0.0165557861328125,
-0.313964... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Tags: hashing, strings
Correct Solution:
```
n,m=list(map(int,input().split()))
s=[]
h=[]
mod=10**9
mod+=7
for i in range(n):
s=(input())
s=s.lower()
hw=0
for i in range(m):
hw+=ord(s[i])*(10**(m-i))
h.append(hw%mod)
h1=[[] for i in range(n-m+1)]
for i in range(m):
hw=0
s=input()
s=s.lower()
aux=[]
for i in range(m):
hw+=ord(s[i])*(10**(m-i))
hw%=mod
h1[0].append(hw)
yy=1
for i in range(m,n):
hw-=(ord(s[i-m])*(10**(m)))
hw*=10
hw+=(ord(s[i])*(10))
hw%=mod
h1[yy].append(hw)
yy+=1
t=False
y=0
for i in range(len(h1)):
x=0
while x<n-m+1:
if h1[i][0]==h[x]:
y=0
ans=[x+1,i+1]
while y<m and h1[i][y]==h[x]:
x+=1
y+=1
else:
x+=1
if y==m:
break
if y==m:
break
print(ans[0],ans[1])
```
| 70,466 | [
-0.07012939453125,
0.1865234375,
0.075927734375,
0.1329345703125,
-0.53857421875,
-0.76953125,
-0.3818359375,
0.368408203125,
-0.13720703125,
0.796875,
0.42333984375,
0.312744140625,
0.1669921875,
-0.54296875,
-0.328369140625,
0.278076171875,
-0.37158203125,
-0.66357421875,
-0.63... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Tags: hashing, strings
Correct Solution:
```
n, m = list(map(int, input().strip().split(' ')))
mat1, mat2 = [], []
for i in range(0, n): mat1.append(tuple(input().strip()))
for i in range(0, m): mat2.append(tuple(input().strip()))
ix, jx, flg = -1, -1, 0
matr, matc = [], []
for i in range(0, n-m+1):
si, se = i, i+m
matr.append(hash(tuple(mat1[si:se])))
matcur2 = []
for c2i in range(0, m): matcur2.append(tuple(mat2[c2i][si:se]))
matc.append(hash(tuple(matcur2)))
nx = len(matr)
ix, jx = -1, -1
for ix in range(0, nx):
flg=0
for jx in range(0, nx):
if matr[ix]==matc[jx]:
flg=1
break
if flg==1: break
print(str(ix+1)+" "+str(jx+1))
```
| 70,467 | [
-0.0806884765625,
0.1932373046875,
0.0989990234375,
0.1453857421875,
-0.537109375,
-0.78076171875,
-0.37939453125,
0.348388671875,
-0.12158203125,
0.79833984375,
0.4423828125,
0.341552734375,
0.1527099609375,
-0.56494140625,
-0.3388671875,
0.275634765625,
-0.38623046875,
-0.6616210... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Tags: hashing, strings
Correct Solution:
```
n, m = list(map(int, input().strip().split(' ')))
L, M = [], []
for i in range(n):
L.append(tuple(input().strip()))
for i in range(0, m):
M.append(tuple(input().strip()))
k=0
row, col = [], []
for i in range(n-m+1):
init, end = i, i+m
row.append(hash(tuple(L[init:end])))
D = []
for j in range(0, m):
D.append(tuple(M[j][init:end]))
col.append(hash(tuple(D)))
for ix in range(len(row)):
k=0
for jx in range(len(row)):
if row[ix]==col[jx]:
k=1
break
if k==1:
break
print(ix+1,end=' ')
print(jx+1)
```
| 70,468 | [
-0.091552734375,
0.177001953125,
0.08795166015625,
0.134521484375,
-0.54443359375,
-0.76513671875,
-0.389892578125,
0.3466796875,
-0.12310791015625,
0.771484375,
0.4375,
0.32666015625,
0.1552734375,
-0.54296875,
-0.35205078125,
0.283935546875,
-0.379638671875,
-0.65576171875,
-0.... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Tags: hashing, strings
Correct Solution:
```
n, m = [int(x) for x in input().split()]
list1 = []
list2 = []
for i in range(n):
list1.append(input())
for j in range(m):
list2.append(input())
list3 = []
for i in range(n - m + 1):
y = ""
for j in range(m):
y += list1[j + i]
list3.append(y)
list4 = []
for i in range(n - m + 1):
y = ""
for j in range(m):
y += list2[j][i:i + m]
list4.append(y)
for i in list3:
if i in list4:
exit(print(list3.index(i) + 1, list4.index(i) + 1))
```
| 70,469 | [
-0.08740234375,
0.182861328125,
0.088623046875,
0.1483154296875,
-0.54296875,
-0.76123046875,
-0.383056640625,
0.35400390625,
-0.1298828125,
0.791015625,
0.4384765625,
0.32861328125,
0.141357421875,
-0.5419921875,
-0.3349609375,
0.270751953125,
-0.3798828125,
-0.66455078125,
-0.6... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Tags: hashing, strings
Correct Solution:
```
n, m = [int(x) for x in input().split()]
list1 = []
list2 = []
for i in range(n):
list1.append(input())
for j in range(m):
list2.append(input())
list3 = []
for i in range(n - m + 1):
y = ""
for j in range(m):
y += list1[j + i]
list3.append(y)
list4 = []
for i in range(n - m + 1):
y = ""
for j in range(m):
y += list2[j][i:i + m]
list4.append(y)
for i in list3:
if i in list4:
print(list3.index(i) + 1, list4.index(i) + 1)
quit()
```
| 70,470 | [
-0.08740234375,
0.182861328125,
0.088623046875,
0.1483154296875,
-0.54296875,
-0.76123046875,
-0.383056640625,
0.35400390625,
-0.1298828125,
0.791015625,
0.4384765625,
0.32861328125,
0.141357421875,
-0.5419921875,
-0.3349609375,
0.270751953125,
-0.3798828125,
-0.66455078125,
-0.6... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Submitted Solution:
```
n,m=map(int,input().split())
nm=[];mn=[]
for i in range(n):
nm.append(input())
for j in range(m):
mn.append(input())
a={}
for j in range(n-m+1):
for k in range(m):
a[mn[k][j:j+m]]=a.get(mn[k][j:j+m],[])
a[mn[k][j:j+m]].append(j+1)
for i in range(n-m):
try:r=a[nm[i]];cnt=1
except:continue
for j in range(1,m):
try:
r=list(set(a[nm[i+j]]).intersection(r));cnt+=1
except:break
if len(r)>=1 and cnt==m:
exit(print(i+1,r[0]))
if n==m==200:
print(1,1)
```
No
| 70,471 | [
0.01445770263671875,
0.1943359375,
0.02923583984375,
0.12841796875,
-0.6630859375,
-0.70654296875,
-0.454345703125,
0.501953125,
-0.1539306640625,
0.7509765625,
0.356689453125,
0.243896484375,
0.0921630859375,
-0.43408203125,
-0.364013671875,
0.2271728515625,
-0.278076171875,
-0.57... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Submitted Solution:
```
n,m=map(int,input().strip().split(' '))
Dicti={}
M=[]
DP=[]
for i in range(m):
DP.append([[0]]*n)
for i in range(n):
s=input()
if s in Dicti:
Dicti[s].append(i+1)
else:
Dicti[s]=[i+1]
for i in range(m):
M.append(input())
for i in range(m):
j=0
while j+m<=n :
a=M[i][j:j+m]
if a in Dicti:
DP[i][j]=Dicti[a]
else :
DP[i][j]=[-5]
j=j+1
for i in range(n):
j=1
d=DP[0][i][0]
e=True
while j<m and e==True:
e=False
for k in range(len(DP[j][i])):
if DP[j][i][k]==d+1:
d=DP[j][i][k]
e=True
break
j=j+1
if j==m:
print(d-m+1,end=' ')
print(i+1)
```
No
| 70,472 | [
0.03179931640625,
0.1964111328125,
0.026611328125,
0.1463623046875,
-0.67578125,
-0.71826171875,
-0.44189453125,
0.51171875,
-0.1414794921875,
0.75048828125,
0.3583984375,
0.2244873046875,
0.09722900390625,
-0.438720703125,
-0.3818359375,
0.220947265625,
-0.27490234375,
-0.57373046... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Submitted Solution:
```
n,m=map(int,input().strip().split(' '))
Dicti={}
M=[]
DP=[]
for i in range(m):
DP.append([0]*n)
for i in range(n):
Dicti[input()]=i+1
for i in range(m):
M.append(input())
for i in range(m):
j=0
k=0
while j!=n:
a=M[i][j:j+m]
if a in Dicti:
DP[i][j]=Dicti[a]
else :
DP[i][j]=-5
j=j+1
for i in range(n):
j=1
d=DP[0][i]
while j<m and DP[j][i]==d+1:
d=DP[j][i]
j=j+1
if j==m:
print(DP[0][i],end=' ')
print(i+1)
```
No
| 70,473 | [
0.03179931640625,
0.1964111328125,
0.026611328125,
0.1463623046875,
-0.67578125,
-0.71826171875,
-0.44189453125,
0.51171875,
-0.1414794921875,
0.75048828125,
0.3583984375,
0.2244873046875,
0.09722900390625,
-0.438720703125,
-0.3818359375,
0.220947265625,
-0.27490234375,
-0.57373046... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The stardate is 1983, and Princess Heidi is getting better at detecting the Death Stars. This time, two Rebel spies have yet again given Heidi two maps with the possible locations of the Death Star. Since she got rid of all double agents last time, she knows that both maps are correct, and indeed show the map of the solar system that contains the Death Star. However, this time the Empire has hidden the Death Star very well, and Heidi needs to find a place that appears on both maps in order to detect the Death Star.
The first map is an N Γ M grid, each cell of which shows some type of cosmic object that is present in the corresponding quadrant of space. The second map is an M Γ N grid. Heidi needs to align those two maps in such a way that they overlap over some M Γ M section in which all cosmic objects are identical. Help Heidi by identifying where such an M Γ M section lies within both maps.
Input
The first line of the input contains two space-separated integers N and M (1 β€ N β€ 2000, 1 β€ M β€ 200, M β€ N). The next N lines each contain M lower-case Latin characters (a-z), denoting the first map. Different characters correspond to different cosmic object types. The next M lines each contain N characters, describing the second map in the same format.
Output
The only line of the output should contain two space-separated integers i and j, denoting that the section of size M Γ M in the first map that starts at the i-th row is equal to the section of the second map that starts at the j-th column. Rows and columns are numbered starting from 1.
If there are several possible ways to align the maps, Heidi will be satisfied with any of those. It is guaranteed that a solution exists.
Example
Input
10 5
somer
andom
noise
mayth
eforc
ebewi
thyou
hctwo
again
noise
somermayth
andomeforc
noiseebewi
againthyou
noisehctwo
Output
4 6
Note
The 5-by-5 grid for the first test case looks like this:
mayth
eforc
ebewi
thyou
hctwo
Submitted Solution:
```
N, M = input().split(' ')
N = int(N)
M = int(M)
matrix_1 = []
matrix_2 = []
for i in range(N):
matrix_1.append(input())
for i in range(M):
matrix_2.append(input())
def find(word):
if word in matrix_2[0]:
return matrix_2[0].index(word)
return False
def go():
for i in range(N-M+1):
x = find(matrix_1[i])
if x is not False:
found = True
for j in range(1, M):
if matrix_2[j][x:x+M] != matrix_1[i + j]:
found = False
break
if found:
return '{} {}'.format(i + 1, x + 1)
print(go())
```
No
| 70,474 | [
0.03521728515625,
0.195068359375,
0.0230865478515625,
0.16455078125,
-0.65576171875,
-0.71875,
-0.44970703125,
0.51123046875,
-0.162353515625,
0.73876953125,
0.3671875,
0.2330322265625,
0.0762939453125,
-0.4423828125,
-0.3740234375,
0.2186279296875,
-0.2498779296875,
-0.576171875,
... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Anchored Balloon
A balloon placed on the ground is connected to one or more anchors on the ground with ropes. Each rope is long enough to connect the balloon and the anchor. No two ropes cross each other. Figure E-1 shows such a situation.
<image>
Figure E-1: A balloon and ropes on the ground
Now the balloon takes off, and your task is to find how high the balloon can go up with keeping the rope connections. The positions of the anchors are fixed. The lengths of the ropes and the positions of the anchors are given. You may assume that these ropes have no weight and thus can be straightened up when pulled to whichever directions. Figure E-2 shows the highest position of the balloon for the situation shown in Figure E-1.
<image>
Figure E-2: The highest position of the balloon
Input
The input consists of multiple datasets, each in the following format.
> n
> x1 y1 l1
> ...
> xn yn ln
>
The first line of a dataset contains an integer n (1 β€ n β€ 10) representing the number of the ropes. Each of the following n lines contains three integers, xi, yi, and li, separated by a single space. Pi = (xi, yi) represents the position of the anchor connecting the i-th rope, and li represents the length of the rope. You can assume that β100 β€ xi β€ 100, β100 β€ yi β€ 100, and 1 β€ li β€ 300. The balloon is initially placed at (0, 0) on the ground. You can ignore the size of the balloon and the anchors.
You can assume that Pi and Pj represent different positions if i β j. You can also assume that the distance between Pi and (0, 0) is less than or equal to liβ1. This means that the balloon can go up at least 1 unit high.
Figures E-1 and E-2 correspond to the first dataset of Sample Input below.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output a single line containing the maximum height that the balloon can go up. The error of the value should be no greater than 0.00001. No extra characters should appear in the output.
Sample Input
3
10 10 20
10 -10 20
-10 10 120
1
10 10 16
2
10 10 20
10 -10 20
2
100 0 101
-90 0 91
2
0 0 53
30 40 102
3
10 10 20
10 -10 20
-10 -10 20
3
1 5 13
5 -3 13
-3 -3 13
3
98 97 168
-82 -80 193
-99 -96 211
4
90 -100 160
-80 -80 150
90 80 150
80 80 245
4
85 -90 290
-80 -80 220
-85 90 145
85 90 170
5
0 0 4
3 0 5
-3 0 5
0 3 5
0 -3 5
10
95 -93 260
-86 96 211
91 90 177
-81 -80 124
-91 91 144
97 94 165
-90 -86 194
89 85 167
-93 -80 222
92 -84 218
0
Output for the Sample Input
17.3205081
16.0000000
17.3205081
13.8011200
53.0000000
14.1421356
12.0000000
128.3928757
94.1879092
131.1240816
4.0000000
72.2251798
Example
Input
3
10 10 20
10 -10 20
-10 10 120
1
10 10 16
2
10 10 20
10 -10 20
2
100 0 101
-90 0 91
2
0 0 53
30 40 102
3
10 10 20
10 -10 20
-10 -10 20
3
1 5 13
5 -3 13
-3 -3 13
3
98 97 168
-82 -80 193
-99 -96 211
4
90 -100 160
-80 -80 150
90 80 150
80 80 245
4
85 -90 290
-80 -80 220
-85 90 145
85 90 170
5
0 0 4
3 0 5
-3 0 5
0 3 5
0 -3 5
10
95 -93 260
-86 96 211
91 90 177
-81 -80 124
-91 91 144
97 94 165
-90 -86 194
89 85 167
-93 -80 222
92 -84 218
0
Output
17.3205081
16.0000000
17.3205081
13.8011200
53.0000000
14.1421356
12.0000000
128.3928757
94.1879092
131.1240816
4.0000000
72.2251798
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
eps = 1e-7
def bs(f, mi, ma):
mm = -1
while ma > mi + eps:
m1 = (mi*2+ma) / 3.0
m2 = (mi+ma*2) / 3.0
r1 = f(m1)
r2 = f(m2)
if r1 < r2:
mi = m1
else:
ma = m2
return f((ma+mi)/2.0)
def main():
rr = []
def f(n):
a = [LI() for _ in range(n)]
def _f(x,y):
r = inf
for px,py,l in a:
r = min(r, l**2 - (x-px)**2 - (y-py)**2)
return r
def _fy(y):
def _ff(x):
return _f(x,y)
return bs(_ff, -100, 100)
r = bs(_fy,-100,100)
return "{:0.7f}".format(r**0.5)
while 1:
n = I()
if n == 0:
break
rr.append(f(n))
return '\n'.join(map(str,rr))
print(main())
```
| 70,691 | [
0.25244140625,
0.241455078125,
0.09173583984375,
0.09844970703125,
-0.2403564453125,
-0.08294677734375,
-0.1348876953125,
0.50341796875,
0.82080078125,
0.529296875,
0.6650390625,
0.0947265625,
-0.042877197265625,
-0.72119140625,
-0.50146484375,
0.456298828125,
-0.73291015625,
-0.83... | 3 |
Provide a correct Python 3 solution for this coding contest problem.
Anchored Balloon
A balloon placed on the ground is connected to one or more anchors on the ground with ropes. Each rope is long enough to connect the balloon and the anchor. No two ropes cross each other. Figure E-1 shows such a situation.
<image>
Figure E-1: A balloon and ropes on the ground
Now the balloon takes off, and your task is to find how high the balloon can go up with keeping the rope connections. The positions of the anchors are fixed. The lengths of the ropes and the positions of the anchors are given. You may assume that these ropes have no weight and thus can be straightened up when pulled to whichever directions. Figure E-2 shows the highest position of the balloon for the situation shown in Figure E-1.
<image>
Figure E-2: The highest position of the balloon
Input
The input consists of multiple datasets, each in the following format.
> n
> x1 y1 l1
> ...
> xn yn ln
>
The first line of a dataset contains an integer n (1 β€ n β€ 10) representing the number of the ropes. Each of the following n lines contains three integers, xi, yi, and li, separated by a single space. Pi = (xi, yi) represents the position of the anchor connecting the i-th rope, and li represents the length of the rope. You can assume that β100 β€ xi β€ 100, β100 β€ yi β€ 100, and 1 β€ li β€ 300. The balloon is initially placed at (0, 0) on the ground. You can ignore the size of the balloon and the anchors.
You can assume that Pi and Pj represent different positions if i β j. You can also assume that the distance between Pi and (0, 0) is less than or equal to liβ1. This means that the balloon can go up at least 1 unit high.
Figures E-1 and E-2 correspond to the first dataset of Sample Input below.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output a single line containing the maximum height that the balloon can go up. The error of the value should be no greater than 0.00001. No extra characters should appear in the output.
Sample Input
3
10 10 20
10 -10 20
-10 10 120
1
10 10 16
2
10 10 20
10 -10 20
2
100 0 101
-90 0 91
2
0 0 53
30 40 102
3
10 10 20
10 -10 20
-10 -10 20
3
1 5 13
5 -3 13
-3 -3 13
3
98 97 168
-82 -80 193
-99 -96 211
4
90 -100 160
-80 -80 150
90 80 150
80 80 245
4
85 -90 290
-80 -80 220
-85 90 145
85 90 170
5
0 0 4
3 0 5
-3 0 5
0 3 5
0 -3 5
10
95 -93 260
-86 96 211
91 90 177
-81 -80 124
-91 91 144
97 94 165
-90 -86 194
89 85 167
-93 -80 222
92 -84 218
0
Output for the Sample Input
17.3205081
16.0000000
17.3205081
13.8011200
53.0000000
14.1421356
12.0000000
128.3928757
94.1879092
131.1240816
4.0000000
72.2251798
Example
Input
3
10 10 20
10 -10 20
-10 10 120
1
10 10 16
2
10 10 20
10 -10 20
2
100 0 101
-90 0 91
2
0 0 53
30 40 102
3
10 10 20
10 -10 20
-10 -10 20
3
1 5 13
5 -3 13
-3 -3 13
3
98 97 168
-82 -80 193
-99 -96 211
4
90 -100 160
-80 -80 150
90 80 150
80 80 245
4
85 -90 290
-80 -80 220
-85 90 145
85 90 170
5
0 0 4
3 0 5
-3 0 5
0 3 5
0 -3 5
10
95 -93 260
-86 96 211
91 90 177
-81 -80 124
-91 91 144
97 94 165
-90 -86 194
89 85 167
-93 -80 222
92 -84 218
0
Output
17.3205081
16.0000000
17.3205081
13.8011200
53.0000000
14.1421356
12.0000000
128.3928757
94.1879092
131.1240816
4.0000000
72.2251798
"Correct Solution:
```
"""http://mayokoex.hatenablog.com/entry/2015/06/11/124120γεη
§γγΎγγ"""
"""δΈεζ’η΄’γθ³’γ"""
import sys
MI = 1e-6
def calc(x,y,b):
res = 90000
for bx,by,l in b:
d = l**2-(x-bx)**2-(y-by)**2
if d < res:
res = d
return res
def search_y(x,b):
p = [-100,-33,33,100]
for t in range(100):
if abs(p[0]-p[3]) < MI:
return (calc(x,p[0],b)+calc(x,p[3],b))/2
l = calc(x,p[1],b)
r = calc(x,p[2],b)
if l < r:
p[0] = p[1]
else:
p[3] = p[2]
p[1] = (2*p[0]+p[3])/3
p[2] = (p[0]+2*p[3])/3
return (calc(x,p[0],b)+calc(x,p[3],b))/2
def search(b):
p = [-100,-33,33,100]
for t in range(100):
if abs(p[0]-p[3]) < MI:
return (search_y(p[0],b)+search_y(p[3],b))/2
l = search_y(p[1],b)
r = search_y(p[2],b)
if l < r:
p[0] = p[1]
else:
p[3] = p[2]
p[1] = (2*p[0]+p[3])/3
p[2] = (p[0]+2*p[3])/3
return (search_y(p[0],b)+search_y(p[3],b))/2
def solve(n):
b = [[int(x) for x in sys.stdin.readline().split()] for i in range(n)]
ans = 0
print(search(b)**0.5)
while 1:
n = int(sys.stdin.readline())
if n == 0:
break
solve(n)
```
| 70,692 | [
0.25244140625,
0.241455078125,
0.09173583984375,
0.09844970703125,
-0.2403564453125,
-0.08294677734375,
-0.1348876953125,
0.50341796875,
0.82080078125,
0.529296875,
0.6650390625,
0.0947265625,
-0.042877197265625,
-0.72119140625,
-0.50146484375,
0.456298828125,
-0.73291015625,
-0.83... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
from sys import stdin
input=stdin.readline
for _ in range(int(input())):
n=int(input())
c=[]
f=[]
for i in range(n):
l=list(map(int,input().split()))
c.append(l[:2])
f.append(l[2:])
l=-10**5
u=10**5
r=10**5
d=-10**5
for i in range(n):
if f[i][0]==0:
l=max(l,c[i][0])
if f[i][1]==0:
u=min(u,c[i][1])
if f[i][2]==0:
r=min(r,c[i][0])
if f[i][3]==0:
d=max(d,c[i][1])
if l<=r and u>=d:
print(1,l,u)
else:
print(0)
```
Yes
| 70,825 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
import sys
q = int(input())
for _ in range(q):
n = int(input())
minx, maxx, miny, maxy = -100000, 100000, -100000, 100000
for i in range(n):
x, y, f1, f2, f3, f4 = map(int, sys.stdin.readline().split())
if f1 == 0:
minx = max(x, minx)
if f3 == 0:
maxx = min(maxx, x)
if f2 == 0:
maxy = min(maxy, y)
if f4 == 0:
miny = max(y, miny)
if minx > maxx or miny > maxy:
print(0)
continue
else:
print(1, minx, miny)
```
Yes
| 70,826 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
from sys import stdin
M = 10 ** 5
def solve(points):
min_x, min_y, max_x, max_y = -M, -M, M, M
for p in points:
x, y, f1, f2, f3, f4 = p
if not f1:
min_x = max(x, min_x)
if not f3:
max_x = min(x, max_x)
if not f4:
min_y = max(min_y, y)
if not f2:
max_y = min(max_y, y)
if (min_x <= max_x) and (min_y <= max_y):
print(1, min_x, min_y)
else:
print(0)
q = int(stdin.readline().strip())
for _ in range(q):
n = int(stdin.readline().strip())
points = []
for _ in range(n):
points.append([int(i) for i in stdin.readline().strip().split()])
solve(points)
```
Yes
| 70,827 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
###### ### ####### ####### ## # ##### ### #####
# # # # # # # # # # # # # ###
# # # # # # # # # # # # # ###
###### ######### # # # # # # ######### #
###### ######### # # # # # # ######### #
# # # # # # # # # # #### # # #
# # # # # # # ## # # # # #
###### # # ####### ####### # # ##### # # # #
from __future__ import print_function # for PyPy2
from collections import Counter, OrderedDict
from itertools import permutations as perm
from fractions import Fraction
from collections import deque
from sys import stdin
from bisect import *
from heapq import *
# from math import *
g = lambda : stdin.readline().strip()
gl = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
mod = int(1e9)+7
inf = float("inf")
# range = xrange
t, = gil()
for _ in range(t):
xmin, xmax = -int(1e5), int(1e5)
ymin, ymax = xmin, xmax
n, = gil()
isPos = True
for _ in range(n):
rx, ry, lt, up, rt, dw = gil()
if not isPos : continue
if lt^rt: #either left or right
if lt:
isPos &= (xmin <= rx)
xmax = min(xmax, rx)
else:
isPos &= (rx <= xmax)
xmin = max(xmin, rx)
elif lt == rt == 0:
isPos &= (xmin <= rx <= xmax)
xmax = xmin = rx
if up^dw : # either up or down
if up:
isPos &= (ry <= ymax)
ymin = max(ymin, ry)
else:
isPos &= (ry >= ymin)
ymax = min(ymax, ry)
elif up == dw == 0:
isPos &= (ymin <= ry <= ymax)
ymax = ymin = ry
if isPos:
print(1, xmin, ymin)
else:
print(0)
```
Yes
| 70,828 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
t=int(input())
while t>0:
t-=1
n=int(input())
b=[]
for i in range(n):
a=[int(x) for x in input().split()]
b.append(a)
#XYLDRU
L=[]
R=[]
U=[]
D=[]
for a in b:
if a[2]==0:
L.append(a[0])
if a[3]==0:
D.append(a[1])
if a[4]==0:
R.append(a[0])
if a[5]==0:
U.append(a[1])
L.sort(reverse=True)
R.sort()
U.sort(reverse=True)
D.sort()
if len(L)==0:
L.insert(0,-10000)
if len(U) ==0:
U.insert(0,-10000)
if len(R)==0:
R.insert(0,10000)
if len(D) ==0:
D.insert(0,10000)
if L[0]>R[0] or U[0]>D[0]:
print(0)
continue
print(1,L[0],U[0])
```
No
| 70,829 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
def intersection(X,curr,x):
if curr == 'a':
if X[0] > x:
return []
X[1] = min(X[1],x)
else:
if X[1] > x:
return []
X[0] = min(X[0],x)
return X
def solve(n,ans):
found = True
X = [-10**5,10**5]
Y = [-10**5,10**5]
for i in range(n):
x,y,a,b,c,d = map(int,input().split())
if found:
if a+c == 1:
if a == 1:
if not intersection(X,'a',x):
found = False
else:
if not intersection(X,'c',x):
found = False
elif a+c == 0:
if X[0] <= x and X[1] >= x:
X = [x,x]
else:
found = False
if b+d == 1:
if d == 1:
if not intersection(Y,'a',y):
found = False
else:
if not intersection(Y,'c',y):
found = False
elif b+d == 0:
if Y[0] <= y and Y[1] >= y:
Y = [y,y]
else:
found = False
#print(X,Y)
if not found:
ans.append(0)
else:
ans.append('1 '+str(X[0])+' '+str(Y[0]))
def main():
ans = []
q = int(input())
for i in range(q):
n = int(input())
solve(n,ans)
for i in ans:
print(i)
main()
```
No
| 70,830 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
import sys
#sys.stdin = open("input.txt")
t = int(input())
for i in range (t):
n = int(input())
p = []
X = 0
Y = 0
for k in range (n):
x,y,s,a,d,b = map(int,input().split())
p.append([x,y,s,a,d,b])
if (n == 1):
if (p[0][5] == 1 and p[0][2] == 1 ):
X = -100000
Y = -100000
else:
X = p[0][0]
Y = p[0][1]
print(1,X,Y)
else:
verdetto = True
for k in range (n-1):
for z in range (k+1,n):
if ( p[k][0] > p[z][0]):
if (p[z][4] == 0 and p[k][2] == 0):
verdetto = False
if (p[k][0] < p[z][0]):
if (p[k][4] == 0 and p[z][2] == 0):
verdetto = False
if (p[k][1] > p[z][1]):
if (p[z][3] == 0 and p[k][5] == 0):
verdetto = False
if (p[k][1] < p[z][1]):
if (p[k][3] == 0 and p[z][5] == 0):
verdetto = False
if verdetto == True:
for k in range (n-1):
if (p[k][0]!= p[k+1][0]):
if (p[k][0]>p[k+1][0]):
dx = p[k][0]-p[k+1][0]
if (p[k+1][4] == 1):
X = p[k][0]
else:
X = p[k+1][0]
else:
dx = p[k+1][0]-p[k][0]
if (p[k][4] == 1):
X = p[k+1][0]
else:
X = p[k][0]
else:
X = p[k][0]
if (p[k][1]!=p[k+1][1]):
if (p[k][1]>=p[k+1][1]):
dy = p[k][1]-p[k+1][1]
if (p[k+1][3] == 1):
Y = p[k][1]
else:
Y = p[k+1][1]
else:
dy = p[k+1][1]-p[k][1]
if (p[k][3] == 1):
Y = p[k+1][1]
else:
Y = p[k][1]
else:
Y = p[k][1]
print(1,X,Y)
else:
print(0)
```
No
| 70,831 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
n robots have escaped from your laboratory! You have to find them as soon as possible, because these robots are experimental, and their behavior is not tested yet, so they may be really dangerous!
Fortunately, even though your robots have escaped, you still have some control over them. First of all, you know the location of each robot: the world you live in can be modeled as an infinite coordinate plane, and the i-th robot is currently located at the point having coordinates (x_i, y_i). Furthermore, you may send exactly one command to all of the robots. The command should contain two integer numbers X and Y, and when each robot receives this command, it starts moving towards the point having coordinates (X, Y). The robot stops its movement in two cases:
* either it reaches (X, Y);
* or it cannot get any closer to (X, Y).
Normally, all robots should be able to get from any point of the coordinate plane to any other point. Each robot usually can perform four actions to move. Let's denote the current coordinates of the robot as (x_c, y_c). Then the movement system allows it to move to any of the four adjacent points:
1. the first action allows it to move from (x_c, y_c) to (x_c - 1, y_c);
2. the second action allows it to move from (x_c, y_c) to (x_c, y_c + 1);
3. the third action allows it to move from (x_c, y_c) to (x_c + 1, y_c);
4. the fourth action allows it to move from (x_c, y_c) to (x_c, y_c - 1).
Unfortunately, it seems that some movement systems of some robots are malfunctioning. For each robot you know which actions it can perform, and which it cannot perform.
You want to send a command so all robots gather at the same point. To do so, you have to choose a pair of integer numbers X and Y so that each robot can reach the point (X, Y). Is it possible to find such a point?
Input
The first line contains one integer q (1 β€ q β€ 10^5) β the number of queries.
Then q queries follow. Each query begins with one line containing one integer n (1 β€ n β€ 10^5) β the number of robots in the query. Then n lines follow, the i-th of these lines describes the i-th robot in the current query: it contains six integer numbers x_i, y_i, f_{i, 1}, f_{i, 2}, f_{i, 3} and f_{i, 4} (-10^5 β€ x_i, y_i β€ 10^5, 0 β€ f_{i, j} β€ 1). The first two numbers describe the initial location of the i-th robot, and the following four numbers describe which actions the i-th robot can use to move (f_{i, j} = 1 if the i-th robot can use the j-th action, and f_{i, j} = 0 if it cannot use the j-th action).
It is guaranteed that the total number of robots over all queries does not exceed 10^5.
Output
You should answer each query independently, in the order these queries appear in the input.
To answer a query, you should do one of the following:
* if it is impossible to find a point that is reachable by all n robots, print one number 0 on a separate line;
* if it is possible to find a point that is reachable by all n robots, print three space-separated integers on the same line: 1 X Y, where X and Y are the coordinates of the point reachable by all n robots. Both X and Y should not exceed 10^5 by absolute value; it is guaranteed that if there exists at least one point reachable by all robots, then at least one of such points has both coordinates not exceeding 10^5 by absolute value.
Example
Input
4
2
-1 -2 0 0 0 0
-1 -2 0 0 0 0
3
1 5 1 1 1 1
2 5 0 1 0 1
3 5 1 0 0 0
2
1337 1337 0 1 1 1
1336 1337 1 1 0 1
1
3 5 1 1 1 1
Output
1 -1 -2
1 2 5
0
1 -100000 -100000
Submitted Solution:
```
#from sys import stdin,stdout
#input=stdin.readline
#import math,bisect
#from itertools import permutations
#from collections import Counter
for _ in range(int(input())):
n=int(input())
mxx=100000
mnx=-100000
mxy=100000
mny=-100000
sab=[]
for i in range(n):
x,y,left,up,right,down=map(int,input().split())
if left==right==up==down==0:
sab.append([x,y])
else:
if left==0:
if mnx<x:
mnx=max(mnx,x)
if right==0:
if mxx>x:
mxx=min(mxx,x)
if up==0:
if mxy>y:
mxy=min(mxy,y)
if down==0:
if mny<y:
mny=max(mny,y)
if mnx>mxx or mny>mxy:
print(0)
else:
if len(sab)==0:
print(1,mnx,mny)
elif len(sab)==1:
print(sab[0][0])
elif len(sab)>1:
f=0
x1=sab[0][0]
y1=sab[0][1]
for i in range(1,len(sab)):
if x1!=sab[i][0] or y1!=sab[i][1]:
f=1
if f==1:
print(0)
else:
print(1,x1,y1)
else:
print(1,mxx,mxy)
```
No
| 70,832 | [
0.39794921875,
0.399169921875,
-0.5546875,
0.2252197265625,
-0.359130859375,
-0.053192138671875,
-0.288330078125,
0.5634765625,
0.57763671875,
0.84716796875,
0.367431640625,
0.439208984375,
0.09893798828125,
-0.8193359375,
-0.5966796875,
0.1676025390625,
-0.12042236328125,
-0.78710... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
import sys
n, k = list(map(int, input().split(' ')))
activate = list(map(int, input().split(' '))) # ιζΎηθ½ι
deactivate = list(map(int, input().split(' '))) # ιζ±ηθ½ι
ls = list(zip(activate[0:-1], deactivate[0:-1]))
diff = ls[0][0] - ls[0][1]
presum = [0 for _ in range(n + 2)]
for i in range(1, n + 1):
presum[i] = presum[i - 1] + activate[i - 1]
ret = 0
if k == 0:
for i in range(1, n + 1):
# ζ
ε΅0οΌδΈιθ¦θθθΏεΈ¦
ret = max(ret, presum[n] - presum[i - 1] - deactivate[i - 1])
elif k == 1:
ret = max(ret, presum[n - 1] - min(deactivate), presum[n] - min(deactivate) - deactivate[n - 1])
deac = sorted(deactivate[0:n - 1])
ac = sorted(activate[1:n - 1])
# ζ
ε΅5οΌζΏζ΄»1οΌθ·³θΏ1δΈͺθηΉ
ret = max(ret, presum[n] - deactivate[0] - ac[0])
# ζ
ε΅4
ret = max(ret, presum[n] - deac[0] - deac[1])
# ζ
ε΅7 1θΏnοΌζΏζ΄»i
for i in range(2, n + 1):
ret = max(ret, presum[n] - presum[i - 1] - deactivate[i - 1])
else:
# ζ
ε΅1
for i in range(1, n):
ret = max(ret, presum[n] - deactivate[i - 1])
# ζ
ε΅2
ret = max(ret, activate[n - 1] - deactivate[n - 1])
print(ret)
```
Yes
| 70,921 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
N, K = map(int, input().split())
A = list(map(int, input().split()))
D = list(map(int, input().split()))
suf_min = [None]*N
suf_min[-1] = A[-1]
suf_sum = [None]*N
suf_sum[-1] = A[-1]
suf_ans = [None]*N
suf_ans[-1] = max(A[-1] - D[-1], 0)
for i in range(N-2, -1, -1):
suf_min[i] = min(A[i], suf_min[i+1])
suf_sum[i] = suf_sum[i+1] + A[i]
suf_ans[i] = max(suf_ans[i+1], suf_sum[i]-D[i])
# print(i, suf_ans[i])
if K >= 2:
print(max(0, sum(A) - min(*D[:-1]), suf_ans[0]))
exit(0)
if K == 0:
print(max(suf_ans[0], 0))
exit(0)
pre_min = D[0]
pre_sum = 0
ans = max(0, sum(A) - D[0] - suf_min[0])
for i in range(N-1):
pre_sum += A[i]
pre_min = min(pre_min, D[i])
ans = max(ans, pre_sum - pre_min + suf_ans[i+1], suf_ans[i+1])
print(max(0, ans))
```
Yes
| 70,922 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
self.os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
n, k = map(int, input().split())
a = list(map(int, input().split()))
d = list(map(int, input().split()))
if k >= 2:
m = min(d[: -1])
print(max(sum(a) - m, a[-1] - d[-1], 0))
elif k == 0:
rightans = [0] * n
cursum = 0
ans = 0
for i in range(n - 1, -1, -1):
cursum += a[i]
rightans[i] = max(cursum - d[i], 0)
print(max(rightans))
else:
leftd = int(1e9)
leftsum = 0
rightans = [0] * n
cursum = 0
ans = 0
for i in range(n - 1, -1, -1):
cursum += a[i]
rightans[i] = max(cursum - d[i], 0)
for i in range(n - 1, 0, -1):
rightans[i - 1] = max(rightans[i - 1], rightans[i])
for i in range(n - 1):
leftd = min(leftd, d[i])
leftsum += a[i]
curans = max(leftsum - leftd, 0) + rightans[i + 1]
ans = max(ans, curans)
cursum = 0
rightmin = int(1e9)
for i in range(n - 1, -1, -1):
cursum += a[i]
ans = max(ans, cursum - rightmin - d[i])
rightmin = min(rightmin, a[i])
print(ans)
```
Yes
| 70,923 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
import sys
n, k = list(map(int, input().split(' ')))
activate = list(map(int, input().split(' ')))
deactivate = list(map(int, input().split(' ')))
presum = [0 for _ in range(n+2)]
for i in range(1, n+1):
presum[i] = presum[i-1] + activate[i-1]
ret = 0
if k == 0:
for i in range(1, n+1):
ret = max(ret, presum[n] - presum[i-1] - deactivate[i-1])
elif k == 1:
for i in range(1, n):
ret = max(ret, presum[n-1] - deactivate[i-1])
if deactivate[n-1] < activate[n-1]:
ret += (activate[n-1] - deactivate[n-1])
deac = sorted(deactivate[1:n-1])
ac = sorted(activate[1:n-1])
ret = max(ret, presum[n] - deac[0] - deac[1])
ret = max(ret, presum[n] - deactivate[0] - ac[0])
ret = max(ret, presum[n] - deactivate[0] - deac[0])
for i in range(2, n+1):
ret = max(ret, presum[n] - presum[i-1] - deactivate[i-1])
else:
for i in range(1, n):
ret = max(ret, presum[n] - deactivate[i-1])
ret = max(ret, activate[n-1] - deactivate[n-1])
print(ret)
```
Yes
| 70,924 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
d = list(map(int, input().split()))
if k == 0:
best = 0
curr = sum(a)
for i in range(n):
best = max(best, curr - d[i])
curr -= a[i]
print(best)
elif k == 1:
best = sum(a[:-1]) - min(d[:-1])
other = sum(a)
other -= sorted(d)[0]
other -= sorted(d)[1]
curr = sum(a)
for i in range(n):
if i:
best = max(best, curr - d[i])
curr -= a[i]
o2 = sum(a) - a[1] - d[0]
print(max((best,other,0, o2)))
else:
print(max((sum(a) - min(d[:-1]),0,a[-1] - d[-1])))
```
No
| 70,925 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
d = list(map(int, input().split()))
if k >= 2:
m = min(a)
print(max(sum(a) - m, 0))
elif k == 0:
ans = False
for i, (ai, di) in enumerate(zip(a, d)):
if ai >= di:
ans = True
break
if ans:
print(sum(a[j] for j in range(i, n)) - d[i])
else:
print(0)
else:
ans = False
for i, (ai, di) in enumerate(zip(a, d)):
if ai >= di:
ans = True
break
if ans:
ans = sum(a[j] for j in range(i, n)) - d[i]
else:
ans = 0
m = min(a[: -1])
ans = max(ans, sum(a[: -1]) - m, 0)
print(ans)
```
No
| 70,926 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
# by the authority of GOD author: manhar singh sachdev #
import os,sys
from io import BytesIO,IOBase
def main():
n,k = map(int,input().split())
a = list(map(int,input().split()))
d = list(map(int,input().split()))
mini = [a[-2]]
for i in range(n-3,0,-1):
mini.append(min(mini[-1],a[i]))
mini.reverse()
mini.extend([10**10,10**10])
ans,ans1,x,y = 0,0,sum(a),sum(a)
for i in range(n):
ans = max(ans,x-d[i])
ans1 = max(ans1,y-a[-1]-d[i],x-d[i]-mini[i])
x -= a[i]
if k >= 2:
print(max(0,sum(a)-min(d[:-1]),a[-1]-d[-1]))
elif k:
print(ans1)
else:
print(ans)
#Fast IO Region
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == '__main__':
main()
```
No
| 70,927 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mr. Chanek is currently participating in a science fair that is popular in town. He finds an exciting puzzle in the fair and wants to solve it.
There are N atoms numbered from 1 to N. These atoms are especially quirky. Initially, each atom is in normal state. Each atom can be in an excited. Exciting atom i requires D_i energy. When atom i is excited, it will give A_i energy. You can excite any number of atoms (including zero).
These atoms also form a peculiar one-way bond. For each i, (1 β€ i < N), if atom i is excited, atom E_i will also be excited at no cost. Initially, E_i = i+1. Note that atom N cannot form a bond to any atom.
Mr. Chanek must change exactly K bonds. Exactly K times, Mr. Chanek chooses an atom i, (1 β€ i < N) and changes E_i to a different value other than i and the current E_i. Note that an atom's bond can remain unchanged or changed more than once. Help Mr. Chanek determine the maximum energy that he can achieve!
note: You must first change exactly K bonds before you can start exciting atoms.
Input
The first line contains two integers N K (4 β€ N β€ 10^5, 0 β€ K < N), the number of atoms, and the number of bonds that must be changed.
The second line contains N integers A_i (1 β€ A_i β€ 10^6), which denotes the energy given by atom i when on excited state.
The third line contains N integers D_i (1 β€ D_i β€ 10^6), which denotes the energy needed to excite atom i.
Output
A line with an integer that denotes the maximum number of energy that Mr. Chanek can get.
Example
Input
6 1
5 6 7 8 10 2
3 5 6 7 1 10
Output
35
Note
An optimal solution to change E_5 to 1 and then excite atom 5 with energy 1. It will cause atoms 1, 2, 3, 4, 5 be excited. The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10) - 1 = 35.
Another possible way is to change E_3 to 1 and then exciting atom 3 (which will excite atom 1, 2, 3) and exciting atom 4 (which will excite atom 4, 5, 6). The total energy gained by Mr. Chanek is (5 + 6 + 7 + 8 + 10 + 2) - (6 + 7) = 25 which is not optimal.
Submitted Solution:
```
N, K = map(int, input().split())
A = list(map(int, input().split()))
D = list(map(int, input().split()))
suf_sum = A[N-1]
suf_ans = [None]*N
suf_ans[N-1] = max(A[N-1] - D[N-1], 0)
for i in range(N-2, -1, -1):
suf_sum += A[i]
suf_ans[i] = max(suf_ans[i+1], suf_sum-D[i])
# print(i, suf_ans[i])
if K >= 2:
print(max(0, sum(A) - min(*D[:-1]), suf_ans[0]))
exit(0)
if K == 0:
print(max(suf_ans[0], 0))
exit(0)
pre_min = D[0]
pre_sum = 0
ans = 0
for i in range(N-1):
pre_sum += A[i]
pre_min = min(pre_min, D[i])
ans = max(ans, pre_sum - pre_min + suf_ans[i+1])
print(max(0, ans))
```
No
| 70,928 | [
0.2315673828125,
0.17626953125,
-0.26708984375,
0.546875,
-0.60400390625,
-0.53271484375,
-0.53515625,
-0.0253753662109375,
-0.0005054473876953125,
0.5732421875,
0.84130859375,
-0.337158203125,
0.346435546875,
-1.12890625,
-0.349609375,
0.09478759765625,
-0.70703125,
-0.96044921875... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.
This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good.
Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.
Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.
Input
The only line contains four integers n, m, a, b (1 β€ n, m β€ 109, 1 β€ a β€ b β€ n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.
Output
Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.
Examples
Input
11 4 3 9
Output
3
Input
20 5 2 20
Output
2
Note
The images below illustrate statement tests.
The first test:
<image>
In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.
The second test:
<image>
In this test we can first select all folders in the first row (2, 3, 4, 5), then β all other ones.
Submitted Solution:
```
n, m, a, b = map(int, input().split())
a -= 1
b -= 1
ans = 0
if a % m != 0 or b - a < m:
ans += 1
if (b - a - m + a % m) // m > 0:
ans += 1
if b % m != m - 1:
ans += 1
print(ans)
```
No
| 71,363 | [
0.389892578125,
0.1112060546875,
0.211669921875,
0.1729736328125,
-0.7353515625,
-0.466552734375,
-0.57568359375,
0.45703125,
-0.06671142578125,
0.96240234375,
0.595703125,
-0.32568359375,
0.26806640625,
-0.470947265625,
-0.4150390625,
0.1727294921875,
-0.313720703125,
-0.907226562... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.
This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good.
Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.
Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.
Input
The only line contains four integers n, m, a, b (1 β€ n, m β€ 109, 1 β€ a β€ b β€ n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.
Output
Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.
Examples
Input
11 4 3 9
Output
3
Input
20 5 2 20
Output
2
Note
The images below illustrate statement tests.
The first test:
<image>
In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.
The second test:
<image>
In this test we can first select all folders in the first row (2, 3, 4, 5), then β all other ones.
Submitted Solution:
```
readints=lambda:map(int, input().strip('\n').split())
n,m,a,b=readints()
a-=1
b-=1 # 0-index
ra=a//m
rb=b//m
ia=a%m
ib=b%m
if ra==rb or (a==0 and b==n-1): # same row
print(1)
else:
mid=rb-1-ra
if ia==0 and ib==m-1:
print(1)
elif ia==0 and ib!=m-1:
print(2)
elif ib==m-1:
print(2)
elif (a-1)==ib:
print(2)
else:
if mid:
print(3)
else:
print(2)
```
No
| 71,364 | [
0.389892578125,
0.1112060546875,
0.211669921875,
0.1729736328125,
-0.7353515625,
-0.466552734375,
-0.57568359375,
0.45703125,
-0.06671142578125,
0.96240234375,
0.595703125,
-0.32568359375,
0.26806640625,
-0.470947265625,
-0.4150390625,
0.1727294921875,
-0.313720703125,
-0.907226562... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.
This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good.
Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.
Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.
Input
The only line contains four integers n, m, a, b (1 β€ n, m β€ 109, 1 β€ a β€ b β€ n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.
Output
Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.
Examples
Input
11 4 3 9
Output
3
Input
20 5 2 20
Output
2
Note
The images below illustrate statement tests.
The first test:
<image>
In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.
The second test:
<image>
In this test we can first select all folders in the first row (2, 3, 4, 5), then β all other ones.
Submitted Solution:
```
import sys
from array import array # noqa: F401
def input():
return sys.stdin.buffer.readline().decode('utf-8')
n, m, a, b = map(int, input().split())
a, b = a - 1, b - 1
if a // m == b // m:
print(1)
elif a % m == 0 and b % m == m - 1:
print(1)
elif b % m + 1 == a % m:
print(2)
elif a // m + 1 == b // m:
print(2)
else:
ans = 1 + (a % m != 0) + (b % m != m - 1)
print(ans)
```
No
| 71,365 | [
0.389892578125,
0.1112060546875,
0.211669921875,
0.1729736328125,
-0.7353515625,
-0.466552734375,
-0.57568359375,
0.45703125,
-0.06671142578125,
0.96240234375,
0.595703125,
-0.32568359375,
0.26806640625,
-0.470947265625,
-0.4150390625,
0.1727294921875,
-0.313720703125,
-0.907226562... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.
This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good.
Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.
Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.
Input
The only line contains four integers n, m, a, b (1 β€ n, m β€ 109, 1 β€ a β€ b β€ n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.
Output
Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.
Examples
Input
11 4 3 9
Output
3
Input
20 5 2 20
Output
2
Note
The images below illustrate statement tests.
The first test:
<image>
In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.
The second test:
<image>
In this test we can first select all folders in the first row (2, 3, 4, 5), then β all other ones.
Submitted Solution:
```
readints=lambda:map(int, input().strip('\n').split())
n,m,a,b=readints()
a-=1
b-=1 # 0-index
ra=a//m
rb=b//m
ia=a%m
ib=b%m
if ra==rb: # same row
print(1)
else:
mid=rb-1-ra
if ia==0 and ib==m-1:
print(1)
elif ia==0 and ib!=m-1:
print(2)
elif ia!=0 and ib==m-1:
print(2)
elif (a-1)==ib:
print(2)
else:
if mid:
print(3)
else:
print(2)
```
No
| 71,366 | [
0.389892578125,
0.1112060546875,
0.211669921875,
0.1729736328125,
-0.7353515625,
-0.466552734375,
-0.57568359375,
0.45703125,
-0.06671142578125,
0.96240234375,
0.595703125,
-0.32568359375,
0.26806640625,
-0.470947265625,
-0.4150390625,
0.1727294921875,
-0.313720703125,
-0.907226562... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Tags: data structures, geometry, implementation, math
Correct Solution:
```
coord = []
coef = {}
a = b = 0
v = {}
coef_a = {}
n = int(input())
for i in range(n):
coord.append(list(map(float, input().split())))
for i in range(n):
x1, y1 = coord[i]
for j in range(i+1,n):
x2, y2 = coord[j]
if x2 - x1: # Ax + By + C, B != 0 (not vert)
a = (y2-y1)/(x2-x1)
b = (y1*x2-y2*x1)/(x2-x1)
coef[(a,b)] = coef.get((a,b),0)+1
coef_a[a] = coef_a.get(a,0)+1
if coef[(a,b)] > 1:
coef[(a,b)] -= 1 # del the same lines
coef_a[a] -= 1
else:
v[x2] = 1
v_nmbr = sum(v.values())
coe = list(coef_a.values())
for i in range(len(coe)):
coe[i] = coe[i]*(coe[i]-1)//2
l_par = sum(coe)
l_nmbr = len(coef) + v_nmbr
ans = l_nmbr*(l_nmbr-1)//2 - v_nmbr*(v_nmbr-1)//2 - l_par
print(ans)
```
| 71,713 | [
0.312744140625,
0.11431884765625,
0.1375732421875,
0.249755859375,
-0.2056884765625,
-0.64208984375,
-0.2266845703125,
0.138671875,
0.63818359375,
0.89697265625,
0.76513671875,
-0.032562255859375,
0.06494140625,
-0.53759765625,
-0.388671875,
0.1484375,
-0.67822265625,
-0.6806640625... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Tags: data structures, geometry, implementation, math
Correct Solution:
```
#Bhargey Mehta (Sophomore)
#DA-IICT, Gandhinagar
import sys, math, queue
#sys.stdin = open("input.txt", "r")
MOD = 10**9+7
n = int(input())
p = []
for i in range(n):
x, y = map(int, input().split())
p.append((x, y))
d = {}
for i in range(n):
x1, y1 = p[i]
for j in range(i+1, n):
x2, y2 = p[j]
if x1 != x2:
m = (y2-y1)/(x2-x1)
c = (y1*x2-x1*y2)/(x2-x1)
else:
m = 10**10
c = x1
if m in d:
if c in d[m]:
d[m][c] += 1
else:
d[m][c] = 1
else:
d[m] = {c: 1}
p = []
for m in d:
p.append(len(d[m]))
s = sum(p)
ans = 0
for x in p:
ans += x*(s-x)
print(ans//2)
```
| 71,715 | [
0.312744140625,
0.14306640625,
0.12225341796875,
0.303955078125,
-0.2425537109375,
-0.6298828125,
-0.28125,
0.1375732421875,
0.55810546875,
0.99267578125,
0.76708984375,
-0.00876617431640625,
0.06689453125,
-0.521484375,
-0.42431640625,
0.2271728515625,
-0.64794921875,
-0.699707031... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Tags: data structures, geometry, implementation, math
Correct Solution:
```
import sys
input=sys.stdin.readline
from math import gcd
n=int(input())
p=[list(map(int,input().split())) for i in range(n)]
lines=[]
for i in range(n):
x1,y1=p[i]
for j in range(i+1,n):
x2,y2=p[j]
# a*x-b*y=c
a=y1-y2
b=x1-x2
c=y1*x2-x1*y2
if a<0 or (a==0 and b<0):
a=-a;b=-b;c=-c
g=gcd(a,gcd(b,c))
a//=g;b//=g;c//=g
lines.append((a,b,c))
lines=list(set(lines)) # remove duplicate
m=len(lines)
lines.sort(key=lambda x:x[1]/max(x[0],10**(-10)))
cnt=1
ans=m*(m-1)//2
for i in range(m-1):
a1,b1,c1=lines[i]
a2,b2,c2=lines[i+1]
if a1*b2-a2*b1==0:
cnt+=1
else:
ans-=cnt*(cnt-1)//2
cnt=1
ans-=cnt*(cnt-1)//2
print(ans)
```
| 71,716 | [
0.296142578125,
0.117431640625,
0.1412353515625,
0.2783203125,
-0.1739501953125,
-0.6220703125,
-0.2308349609375,
0.08441162109375,
0.57666015625,
0.93505859375,
0.72265625,
-0.0516357421875,
0.10870361328125,
-0.56396484375,
-0.38818359375,
0.1593017578125,
-0.65771484375,
-0.6992... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Tags: data structures, geometry, implementation, math
Correct Solution:
```
from sys import stdin,stdout
import math
from itertools import accumulate
def getabc(x1,y1,x2,y2):
t1=x2-x1;t2=y2-y1;t3=y1*x2-y2*x1
if t1<0:
t1=t1*(-1);t2=t2*(-1);t3=t3*(-1)
t4=math.gcd(math.gcd(t1,t2),t3)
return t1//t4,t2//t4,t3//t4
n=int(stdin.readline())
x=[];y=[]
for i in range(n):
xi,yi=stdin.readline().strip().split(' ')
x.append(int(xi));y.append(int(yi))
d={}
there={}
for i in range(len(x)):
for j in range(i+1,len(x)):
num=y[i]-y[j]
den=x[i]-x[j]
if num==0:
key='yintercept'+str(y[i])
if key not in d:
d[key]=1
elif den==0:
key='xintercept'+str(x[i])
if key not in d:
d[key]=1
else:
a,b,c=getabc(x[i],y[i],x[j],y[j])
key=str(a)+' '+str(b)+' '+str(c)
keys=str(a)+' '+str(b)
if key not in there:
if keys in d:
d[keys]+=1
else:
d[keys]=1
there[key]=1
ansarr=[0,0] # [lines parallel to y-axis , lines parallel to x axis]
for i in d:
if i[0]=='x':
ansarr[0]+=1
elif i[0]=='y':
ansarr[1]+=1
else:
ansarr.append(d[i])
ans=0;
tarr=sum(ansarr)
for i in range(len(ansarr)):
ans+=(tarr-ansarr[i])*ansarr[i]
stdout.write(str(ans//2)+'\n')
```
| 71,718 | [
0.282958984375,
0.1578369140625,
0.124267578125,
0.260498046875,
-0.1787109375,
-0.64453125,
-0.30517578125,
0.056121826171875,
0.60791015625,
0.8837890625,
0.68896484375,
-0.0994873046875,
0.092041015625,
-0.54736328125,
-0.3642578125,
0.130615234375,
-0.66259765625,
-0.7094726562... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Tags: data structures, geometry, implementation, math
Correct Solution:
```
from functools import reduce
from math import gcd
import collections
gcdm = lambda *args: reduce(gcd, args, 0)
def pointsToLine2d(p1, p2):
if p1 == p2:
return (0, 0, 0)
_p1, _p2 = sorted((p1, p2))
g = gcdm(*filter(lambda x: x != 0, (_p2[1] - _p1[1], _p1[0] - _p2[0], _p1[1] * _p2[0] - _p1[0] * _p2[1])))
return ((_p2[1] - _p1[1]) // g, (_p1[0] - _p2[0]) // g, (_p1[1] * _p2[0] - _p1[0] * _p2[1]) // g)
def main():
from sys import stdin, stdout
def read():
return stdin.readline().rstrip('\n')
def read_array(sep=None, maxsplit=-1):
return read().split(sep, maxsplit)
def read_int():
return int(read())
def read_int_array(sep=None, maxsplit=-1):
return [int(a) for a in read_array(sep, maxsplit)]
def write(*args, **kwargs):
sep = kwargs.get('sep', ' ')
end = kwargs.get('end', '\n')
stdout.write(sep.join(str(a) for a in args) + end)
def write_array(array, **kwargs):
sep = kwargs.get('sep', ' ')
end = kwargs.get('end', '\n')
stdout.write(sep.join(str(a) for a in array) + end)
n = read_int()
p = []
for _ in range(n):
p.append(read_int_array())
lines = set()
for i in range(n):
for j in range(i+1, n):
lines.add(pointsToLine2d(p[i], p[j]))
k = len(lines)
ax_bx = collections.defaultdict(int)
out = 0
for a, b, _ in lines:
ax_bx[a, b] += 1
for x in ax_bx.values():
out += (k - x) * x
write(out // 2)
main()
```
| 71,719 | [
0.26904296875,
0.16015625,
0.199462890625,
0.2626953125,
-0.17822265625,
-0.6025390625,
-0.24072265625,
0.025390625,
0.58251953125,
0.9423828125,
0.724609375,
-0.1619873046875,
0.03253173828125,
-0.55419921875,
-0.388427734375,
0.1900634765625,
-0.7236328125,
-0.7109375,
-0.37939... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
from math import *
class slopeC:
def __init__(self):
self.chil = set()
n = int(input())
slopes = {}
L = []
for i in range(n):
x, y = map(int, input().split())
for l in L:
if x != l[0]:
slope = (y - l[1]) / (x - l[0])
else:
slope = inf
s1 = str(l[0]) + '-' + str(l[1])
s2 = str(x) + '-' + str(y)
if slope not in slopes:
slopes[slope] = [slopeC()]
slopes[slope][0].chil.add(s1)
slopes[slope][0].chil.add(s2)
else:
f = 0
for child in slopes[slope]:
if s1 in child.chil:
f = 1
child.chil.add(s2)
break
if f == 0:
slopes[slope] += [slopeC()]
slopes[slope][0].chil.add(s1)
slopes[slope][0].chil.add(s2)
L += [[x, y]]
A = []
P = [0]
for s in slopes:
A += [(len(slopes[s]))]
P += [P[-1] + A[-1]]
ans = 0
for i, v in enumerate(A):
ans += A[i] * (P[-1] - P[i+1])
print(ans)
```
Yes
| 71,720 | [
0.35302734375,
0.300048828125,
0.05609130859375,
0.19189453125,
-0.279052734375,
-0.46630859375,
-0.300537109375,
0.193359375,
0.509765625,
0.88427734375,
0.74609375,
-0.036468505859375,
0.1236572265625,
-0.552734375,
-0.4443359375,
0.150146484375,
-0.6826171875,
-0.74267578125,
... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
from collections import Counter
from sys import exit
N = int(input())
if N == 2:
print(0)
exit()
inf = 10**9+7
inf2 = 10**18
def gcdl(A):
if len(A) == 0:
return -1
if len(A) == 1:
return 0
g = gcd(A[0], A[1])
for a in A[2:]:
g = gcd(a, g)
return g
def gcd(a,b):
if b == 0:
return a
return gcd(b,a%b)
Point = []
ans = 0
for _ in range(N):
Point.append(list(map(int, input().split())))
S = Counter()
T = set()
for i in range(N):
x1 , y1 = Point[i]
for j in range(N):
if i == j:
continue
x2 , y2 = Point[j]
a = y1 - y2
b = -(x1 - x2)
c = x2*y1 - x1*y2
g = gcdl([a, b, c])
a //= g
b //= g
c //= g
if a < 0:
a *= -1
b *= -1
c *= -1
k = a*inf+b*inf2+c
if k not in T:
T.add(a*inf+b*inf2+c)
if x1 == x2:
S[-1] += 1
else:
y = y1 - y2
x = x1 - x2
g = gcd(y, x)
y //= g
x //= g
if y < 0:
y *= -1
x *= -1
S[y*inf+x] += 1
L = len(T)
ans = L*(L-1)//2
for s in S.values():
ans -= s*(s-1)//2
print(ans)
```
Yes
| 71,721 | [
0.369873046875,
0.278564453125,
0.028350830078125,
0.1650390625,
-0.27099609375,
-0.51123046875,
-0.273681640625,
0.209716796875,
0.53125,
0.92138671875,
0.7705078125,
-0.01375579833984375,
0.0860595703125,
-0.533203125,
-0.410888671875,
0.1553955078125,
-0.6220703125,
-0.640136718... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
from math import gcd
n = int(input())
P = [[int(x) for x in input().split()] for _ in range(n)]
L = []
def addLine(x,y,dx,dy):
if dx < 0:
dx *= -1
dy *= -1
elif dx == 0:
if dy < 0:
dy *= -1
g = gcd(dx,dy)
dx //= g
dy //= g
x += dx * (10**9)
y += dy * (10**9)
if dx:
k = x//dx
else:
k = y//dy
x -= k*dx
y -= k*dy
L.append((x,y,dx,dy))
for i in range(n):
for j in range(i+1,n):
xi,yi = P[i]
xj,yj = P[j]
dx,dy = xi-xj,yi-yj
addLine(xi,yi,dx,dy)
from collections import defaultdict as dd, deque
L = list(set(L))
res = 0
C = dd(int)
for x,y,dx,dy in L:
C[dx,dy] += 1
ss = sum(C.values())
for x in C.values():
res += (ss-x)*x
#for i in range(len(L)):
# for j in range(i+1, len(L)):
# x1,y1,dx1,dy1 = L[i]
# x2,y2,dx2,dy2 = L[j]
# if dx1 != dx2 or dy1 != dy2:
# #print(L[i])
# #print(L[j])
# #print('---')
# res += 1
print(res//2)
```
Yes
| 71,722 | [
0.323974609375,
0.262939453125,
0.09228515625,
0.193115234375,
-0.262939453125,
-0.491943359375,
-0.281494140625,
0.20703125,
0.51953125,
0.9169921875,
0.7724609375,
-0.0233001708984375,
0.06744384765625,
-0.53076171875,
-0.41357421875,
0.165283203125,
-0.6298828125,
-0.66162109375... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
from functools import reduce
from math import gcd
import collections
gcdm = lambda *args: reduce(gcd, args, 0)
def pointsToLine2d(p1, p2):
if p1 == p2:
return 0, 0, 0
p1, p2 = sorted((p1, p2))
a, b, c = p2[1] - p1[1], p1[0] - p2[0], p1[1] * p2[0] - p1[0] * p2[1]
g = gcdm(*filter(lambda x: x != 0, (a, b, c)))
return a // g, b // g, c // g
def main():
from sys import stdin, stdout
def read():
return stdin.readline().rstrip('\n')
def read_array(sep=None, maxsplit=-1):
return read().split(sep, maxsplit)
def read_int():
return int(read())
def read_int_array(sep=None, maxsplit=-1):
return [int(a) for a in read_array(sep, maxsplit)]
def write(*args, **kwargs):
sep = kwargs.get('sep', ' ')
end = kwargs.get('end', '\n')
stdout.write(sep.join(str(a) for a in args) + end)
def write_array(array, **kwargs):
sep = kwargs.get('sep', ' ')
end = kwargs.get('end', '\n')
stdout.write(sep.join(str(a) for a in array) + end)
n = read_int()
p = []
for _ in range(n):
p.append(read_int_array())
lines = set()
for i in range(n):
for j in range(i+1, n):
lines.add(pointsToLine2d(p[i], p[j]))
k = len(lines)
ax_bx = collections.defaultdict(int)
out = 0
for a, b, _ in lines:
ax_bx[a, b] += 1
for x in ax_bx.values():
out += (k - x) * x
write(out // 2)
main()
```
Yes
| 71,723 | [
0.283203125,
0.212890625,
0.142333984375,
0.20361328125,
-0.28076171875,
-0.456787109375,
-0.29150390625,
0.11529541015625,
0.5390625,
0.94140625,
0.74169921875,
-0.154052734375,
0.038665771484375,
-0.5146484375,
-0.40966796875,
0.203125,
-0.68359375,
-0.669921875,
-0.36767578125... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
lines = set()
points = []
num = int(input())
for i in range(num):
points.append([int(j) for j in input().split()])
for i in range(num):
for j in range(i):
dx = (points[j][0] - points[i][0])
if dx == 0:
lines.add((11932912953213, points[i][0]))
else:
m = (points[j][1] - points[i][1])/dx
lines.add((int((11000000000)*m), int((1100000000000)*(points[i][1] - m * points[i][0]))))
ms = {}
for l in lines:
if l[0] in ms:
ms[l[0]] += 1
else:
ms[l[0]] = 1
total = 0
#print(lines)
#print(ms)
#print(type(ms.values()))
t = list(ms.values())
s = sum(t)
for a in t:
total += a * (s-a)
print(total//2)
```
No
| 71,724 | [
0.33251953125,
0.28564453125,
0.053619384765625,
0.184814453125,
-0.3193359375,
-0.5126953125,
-0.298828125,
0.2459716796875,
0.51708984375,
0.92431640625,
0.77001953125,
0.0099945068359375,
0.073486328125,
-0.5029296875,
-0.414794921875,
0.171630859375,
-0.6435546875,
-0.680175781... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
from collections import *
def li():return [int(i) for i in input().split()]
def val():return int(input())
n = val()
l = []
for i in range(n):l.append(li())
d = defaultdict(int)
tot = 1
tottillnow = 0
visited = set()
for i in range(n):
for j in range(i):
tottillnow += 1
try:
slope = (l[i][1] - l[j][1])/(l[i][0] - l[j][0])
except:
slope = 'inf'
if slope == 'inf':
intercept = l[j][0]
else:
intercept = l[j][0]*slope - l[j][1]
if tuple([slope,intercept]) not in visited:
d[slope] += 1
visited.add(tuple([slope,intercept]))
tot = sum(d.values())
ans = 0
for i in d:
ans += (tot - d[i])*(d[i])
print(ans//2)
```
No
| 71,725 | [
0.35107421875,
0.284912109375,
0.052978515625,
0.17822265625,
-0.27587890625,
-0.48876953125,
-0.29052734375,
0.194091796875,
0.51611328125,
0.908203125,
0.744140625,
-0.0109100341796875,
0.05303955078125,
-0.50146484375,
-0.4189453125,
0.1527099609375,
-0.61767578125,
-0.666992187... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
lines = set()
points = []
num = int(input())
for i in range(num):
points.append([int(j) for j in input().split()])
for i in range(num):
for j in range(i):
dx = (points[j][0] - points[i][0])
if dx == 0:
lines.add((11932912953213, points[i][0]))
else:
m = (points[j][1] - points[i][1])/dx
lines.add((int((11000000000)*m), int((11000000000)*(points[i][1] - m * points[i][0]))))
ms = {}
for l in lines:
if l[0] in ms:
ms[l[0]] += 1
else:
ms[l[0]] = 1
total = 0
#print(lines)
#print(ms)
#print(type(ms.values()))
t = list(ms.values())
s = sum(t)
for a in t:
total += a * (s-a)
print(total//2)
```
No
| 71,726 | [
0.33251953125,
0.28564453125,
0.053619384765625,
0.184814453125,
-0.3193359375,
-0.5126953125,
-0.298828125,
0.2459716796875,
0.51708984375,
0.92431640625,
0.77001953125,
0.0099945068359375,
0.073486328125,
-0.5029296875,
-0.414794921875,
0.171630859375,
-0.6435546875,
-0.680175781... | 3 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is same as the previous one, but has larger constraints.
It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.
At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates (x_i, y_i). Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.
Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?
Input
The first line contains a single integer n (2 β€ n β€ 1000) β the number of electric poles.
Each of the following n lines contains two integers x_i, y_i (-10^4 β€ x_i, y_i β€ 10^4) β the coordinates of the poles.
It is guaranteed that all of these n points are distinct.
Output
Print a single integer β the number of pairs of wires that are intersecting.
Examples
Input
4
0 0
1 1
0 3
1 2
Output
14
Input
4
0 0
0 2
0 4
2 0
Output
6
Input
3
-1 -1
1 0
3 1
Output
0
Note
In the first example:
<image>
In the second example:
<image>
Note that the three poles (0, 0), (0, 2) and (0, 4) are connected by a single wire.
In the third example:
<image>
Submitted Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
from math import gcd, ceil
def pre(s):
n = len(s)
pi = [0] * n
for i in range(1, n):
j = pi[i - 1]
while j and s[i] != s[j]:
j = pi[j - 1]
if s[i] == s[j]:
j += 1
pi[i] = j
return pi
def prod(a):
ans = 1
for each in a:
ans = (ans * each)
return ans
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
pts = []
for _ in range(int(input()) if True else 1):
x, y = map(int, input().split())
pts += [[x,y]]
ps = []
pss = set()
from fractions import Fraction
for i in range(len(pts)-1):
for j in range(i+1, len(pts)):
x1, y1, x2, y2 = pts[i][0], pts[i][1], pts[j][0], pts[j][1]
#ax+by+c=0
a,b,c=y1-y2, x2-x1, x1*y2-x2*y1
g = gcd(a,b)
a, b = a//g, b//g
c = str(Fraction(c, g))
xx = str(a) + ","+str(b)+","+str(c)
if xx not in pss:
pss.add(xx)
ps += [[a,b,c]]
ans = len(ps) * (len(ps) - 1) // 2
di={}
for i in ps:
xx = str(i[0])+","+str(i[1])
if xx in di:
di[xx] += 1
else:
di[xx] = 1
for i in di:
ans -= di[i] * (di[i] - 1) // 2
print(ans)
```
No
| 71,727 | [
0.3681640625,
0.30078125,
0.0201568603515625,
0.2032470703125,
-0.31298828125,
-0.499267578125,
-0.3291015625,
0.279296875,
0.46875,
0.892578125,
0.759765625,
0.01493072509765625,
0.0616455078125,
-0.50830078125,
-0.4091796875,
0.176025390625,
-0.59228515625,
-0.68017578125,
-0.3... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Being tired of participating in too many Codeforces rounds, Gildong decided to take some rest in a park. He sat down on a bench, and soon he found two rabbits hopping around. One of the rabbits was taller than the other.
He noticed that the two rabbits were hopping towards each other. The positions of the two rabbits can be represented as integer coordinates on a horizontal line. The taller rabbit is currently on position x, and the shorter rabbit is currently on position y (x < y). Every second, each rabbit hops to another position. The taller rabbit hops to the positive direction by a, and the shorter rabbit hops to the negative direction by b.
<image>
For example, let's say x=0, y=10, a=2, and b=3. At the 1-st second, each rabbit will be at position 2 and 7. At the 2-nd second, both rabbits will be at position 4.
Gildong is now wondering: Will the two rabbits be at the same position at the same moment? If so, how long will it take? Let's find a moment in time (in seconds) after which the rabbits will be at the same point.
Input
Each test contains one or more test cases. The first line contains the number of test cases t (1 β€ t β€ 1000).
Each test case contains exactly one line. The line consists of four integers x, y, a, b (0 β€ x < y β€ 10^9, 1 β€ a,b β€ 10^9) β the current position of the taller rabbit, the current position of the shorter rabbit, the hopping distance of the taller rabbit, and the hopping distance of the shorter rabbit, respectively.
Output
For each test case, print the single integer: number of seconds the two rabbits will take to be at the same position.
If the two rabbits will never be at the same position simultaneously, print -1.
Example
Input
5
0 10 2 3
0 10 3 3
900000000 1000000000 1 9999999
1 2 1 1
1 3 1 1
Output
2
-1
10
-1
1
Note
The first case is explained in the description.
In the second case, each rabbit will be at position 3 and 7 respectively at the 1-st second. But in the 2-nd second they will be at 6 and 4 respectively, and we can see that they will never be at the same position since the distance between the two rabbits will only increase afterward.
Tags: math
Correct Solution:
```
for i in range (int(input())):
x,y,a,b=[int(x) for x in input().split()]
k=(y-x)%(a+b)
j=(y-x)//(a+b)
if k==0:
print(j)
else:
print(-1)
```
| 71,789 | [
0.25390625,
0.431396484375,
-0.061309814453125,
0.333984375,
-0.36376953125,
-0.69384765625,
-0.27099609375,
0.2000732421875,
0.27294921875,
1.1201171875,
0.464111328125,
-0.2457275390625,
-0.10015869140625,
-0.81201171875,
-0.163818359375,
0.1282958984375,
-0.5048828125,
-0.915527... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Being tired of participating in too many Codeforces rounds, Gildong decided to take some rest in a park. He sat down on a bench, and soon he found two rabbits hopping around. One of the rabbits was taller than the other.
He noticed that the two rabbits were hopping towards each other. The positions of the two rabbits can be represented as integer coordinates on a horizontal line. The taller rabbit is currently on position x, and the shorter rabbit is currently on position y (x < y). Every second, each rabbit hops to another position. The taller rabbit hops to the positive direction by a, and the shorter rabbit hops to the negative direction by b.
<image>
For example, let's say x=0, y=10, a=2, and b=3. At the 1-st second, each rabbit will be at position 2 and 7. At the 2-nd second, both rabbits will be at position 4.
Gildong is now wondering: Will the two rabbits be at the same position at the same moment? If so, how long will it take? Let's find a moment in time (in seconds) after which the rabbits will be at the same point.
Input
Each test contains one or more test cases. The first line contains the number of test cases t (1 β€ t β€ 1000).
Each test case contains exactly one line. The line consists of four integers x, y, a, b (0 β€ x < y β€ 10^9, 1 β€ a,b β€ 10^9) β the current position of the taller rabbit, the current position of the shorter rabbit, the hopping distance of the taller rabbit, and the hopping distance of the shorter rabbit, respectively.
Output
For each test case, print the single integer: number of seconds the two rabbits will take to be at the same position.
If the two rabbits will never be at the same position simultaneously, print -1.
Example
Input
5
0 10 2 3
0 10 3 3
900000000 1000000000 1 9999999
1 2 1 1
1 3 1 1
Output
2
-1
10
-1
1
Note
The first case is explained in the description.
In the second case, each rabbit will be at position 3 and 7 respectively at the 1-st second. But in the 2-nd second they will be at 6 and 4 respectively, and we can see that they will never be at the same position since the distance between the two rabbits will only increase afterward.
Tags: math
Correct Solution:
```
#Ashish Sagar
import math
q=int(input())
#q=1
for _ in range(q):
x,y,a,b=map(int,input().split())
if (y-x)%(a+b)==0:
print((y-x)//(a+b))
else:
print(-1)
```
| 71,790 | [
0.25390625,
0.431396484375,
-0.061309814453125,
0.333984375,
-0.36376953125,
-0.69384765625,
-0.27099609375,
0.2000732421875,
0.27294921875,
1.1201171875,
0.464111328125,
-0.2457275390625,
-0.10015869140625,
-0.81201171875,
-0.163818359375,
0.1282958984375,
-0.5048828125,
-0.915527... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Being tired of participating in too many Codeforces rounds, Gildong decided to take some rest in a park. He sat down on a bench, and soon he found two rabbits hopping around. One of the rabbits was taller than the other.
He noticed that the two rabbits were hopping towards each other. The positions of the two rabbits can be represented as integer coordinates on a horizontal line. The taller rabbit is currently on position x, and the shorter rabbit is currently on position y (x < y). Every second, each rabbit hops to another position. The taller rabbit hops to the positive direction by a, and the shorter rabbit hops to the negative direction by b.
<image>
For example, let's say x=0, y=10, a=2, and b=3. At the 1-st second, each rabbit will be at position 2 and 7. At the 2-nd second, both rabbits will be at position 4.
Gildong is now wondering: Will the two rabbits be at the same position at the same moment? If so, how long will it take? Let's find a moment in time (in seconds) after which the rabbits will be at the same point.
Input
Each test contains one or more test cases. The first line contains the number of test cases t (1 β€ t β€ 1000).
Each test case contains exactly one line. The line consists of four integers x, y, a, b (0 β€ x < y β€ 10^9, 1 β€ a,b β€ 10^9) β the current position of the taller rabbit, the current position of the shorter rabbit, the hopping distance of the taller rabbit, and the hopping distance of the shorter rabbit, respectively.
Output
For each test case, print the single integer: number of seconds the two rabbits will take to be at the same position.
If the two rabbits will never be at the same position simultaneously, print -1.
Example
Input
5
0 10 2 3
0 10 3 3
900000000 1000000000 1 9999999
1 2 1 1
1 3 1 1
Output
2
-1
10
-1
1
Note
The first case is explained in the description.
In the second case, each rabbit will be at position 3 and 7 respectively at the 1-st second. But in the 2-nd second they will be at 6 and 4 respectively, and we can see that they will never be at the same position since the distance between the two rabbits will only increase afterward.
Tags: math
Correct Solution:
```
for i in range(int(input())):
x,y,a,b=list(map(int,input().split()))
if ((y-x)%(a+b))==0:
print((y-x)//(a+b))
else:
print(-1)
```
| 71,791 | [
0.25390625,
0.431396484375,
-0.061309814453125,
0.333984375,
-0.36376953125,
-0.69384765625,
-0.27099609375,
0.2000732421875,
0.27294921875,
1.1201171875,
0.464111328125,
-0.2457275390625,
-0.10015869140625,
-0.81201171875,
-0.163818359375,
0.1282958984375,
-0.5048828125,
-0.915527... | 3 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Being tired of participating in too many Codeforces rounds, Gildong decided to take some rest in a park. He sat down on a bench, and soon he found two rabbits hopping around. One of the rabbits was taller than the other.
He noticed that the two rabbits were hopping towards each other. The positions of the two rabbits can be represented as integer coordinates on a horizontal line. The taller rabbit is currently on position x, and the shorter rabbit is currently on position y (x < y). Every second, each rabbit hops to another position. The taller rabbit hops to the positive direction by a, and the shorter rabbit hops to the negative direction by b.
<image>
For example, let's say x=0, y=10, a=2, and b=3. At the 1-st second, each rabbit will be at position 2 and 7. At the 2-nd second, both rabbits will be at position 4.
Gildong is now wondering: Will the two rabbits be at the same position at the same moment? If so, how long will it take? Let's find a moment in time (in seconds) after which the rabbits will be at the same point.
Input
Each test contains one or more test cases. The first line contains the number of test cases t (1 β€ t β€ 1000).
Each test case contains exactly one line. The line consists of four integers x, y, a, b (0 β€ x < y β€ 10^9, 1 β€ a,b β€ 10^9) β the current position of the taller rabbit, the current position of the shorter rabbit, the hopping distance of the taller rabbit, and the hopping distance of the shorter rabbit, respectively.
Output
For each test case, print the single integer: number of seconds the two rabbits will take to be at the same position.
If the two rabbits will never be at the same position simultaneously, print -1.
Example
Input
5
0 10 2 3
0 10 3 3
900000000 1000000000 1 9999999
1 2 1 1
1 3 1 1
Output
2
-1
10
-1
1
Note
The first case is explained in the description.
In the second case, each rabbit will be at position 3 and 7 respectively at the 1-st second. But in the 2-nd second they will be at 6 and 4 respectively, and we can see that they will never be at the same position since the distance between the two rabbits will only increase afterward.
Tags: math
Correct Solution:
```
t = int(input())
for i in range(t):
x,y,a,b = map(int, input().split())
if (y-x) % (a+b) == 0:
print( int((y-x)/(a+b)) )
else:
print(-1)
```
| 71,792 | [
0.25390625,
0.431396484375,
-0.061309814453125,
0.333984375,
-0.36376953125,
-0.69384765625,
-0.27099609375,
0.2000732421875,
0.27294921875,
1.1201171875,
0.464111328125,
-0.2457275390625,
-0.10015869140625,
-0.81201171875,
-0.163818359375,
0.1282958984375,
-0.5048828125,
-0.915527... | 3 |
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