message stringlengths 2 44.5k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = ki·x + bi. It was necessary to determine whether there is at least one point of intersection of two of these lines, that lays strictly inside the strip between x1 < x2. In other words, is it true that there are 1 ≤ i < j ≤ n and x', y', such that:
* y' = ki * x' + bi, that is, point (x', y') belongs to the line number i;
* y' = kj * x' + bj, that is, point (x', y') belongs to the line number j;
* x1 < x' < x2, that is, point (x', y') lies inside the strip bounded by x1 < x2.
You can't leave Anton in trouble, can you? Write a program that solves the given task.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x1 and x2 ( - 1 000 000 ≤ x1 < x2 ≤ 1 000 000) defining the strip inside which you need to find a point of intersection of at least two lines.
The following n lines contain integers ki, bi ( - 1 000 000 ≤ ki, bi ≤ 1 000 000) — the descriptions of the lines. It is guaranteed that all lines are pairwise distinct, that is, for any two i ≠ j it is true that either ki ≠ kj, or bi ≠ bj.
Output
Print "Yes" (without quotes), if there is at least one intersection of two distinct lines, located strictly inside the strip. Otherwise print "No" (without quotes).
Examples
Input
4
1 2
1 2
1 0
0 1
0 2
Output
NO
Input
2
1 3
1 0
-1 3
Output
YES
Input
2
1 3
1 0
0 2
Output
YES
Input
2
1 3
1 0
0 3
Output
NO
Note
In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.
<image>
Submitted Solution:
```
n = int(input())
x1, x2 = [int(x) for x in input().split(' ')]
YSSorted = []
for i in range(n):
k, b = [int(x) for x in input().split(' ')]
y1 = k*x1 + b
y2 = k*x2 + b
YSSorted.append((y2, y1))
YSSorted.sort(reverse=True)
def solve(YSSorted):
minY2 = YSSorted[0][0]
for y2, y1 in YSSorted:
if y2 > minY2:
return 'Yes'
minY2 = min(minY2, y2)
return 'No'
print(solve(YSSorted))
``` | instruction | 0 | 40,808 | 23 | 81,616 |
No | output | 1 | 40,808 | 23 | 81,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = ki·x + bi. It was necessary to determine whether there is at least one point of intersection of two of these lines, that lays strictly inside the strip between x1 < x2. In other words, is it true that there are 1 ≤ i < j ≤ n and x', y', such that:
* y' = ki * x' + bi, that is, point (x', y') belongs to the line number i;
* y' = kj * x' + bj, that is, point (x', y') belongs to the line number j;
* x1 < x' < x2, that is, point (x', y') lies inside the strip bounded by x1 < x2.
You can't leave Anton in trouble, can you? Write a program that solves the given task.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x1 and x2 ( - 1 000 000 ≤ x1 < x2 ≤ 1 000 000) defining the strip inside which you need to find a point of intersection of at least two lines.
The following n lines contain integers ki, bi ( - 1 000 000 ≤ ki, bi ≤ 1 000 000) — the descriptions of the lines. It is guaranteed that all lines are pairwise distinct, that is, for any two i ≠ j it is true that either ki ≠ kj, or bi ≠ bj.
Output
Print "Yes" (without quotes), if there is at least one intersection of two distinct lines, located strictly inside the strip. Otherwise print "No" (without quotes).
Examples
Input
4
1 2
1 2
1 0
0 1
0 2
Output
NO
Input
2
1 3
1 0
-1 3
Output
YES
Input
2
1 3
1 0
0 2
Output
YES
Input
2
1 3
1 0
0 3
Output
NO
Note
In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.
<image>
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
n = int(input())
x1,x2 = map(int,input().split())
Y = []
KB = []
for i in range(n):
k,b = map(int,input().split())
y1 = k*x1 + b
y2 = k*x2 + b
Y.append((min(y1,y2),max(y1,y2),i))
KB.append((k,b))
Y.sort()
prev1,prev2,prev = Y[0][0],Y[0][1],Y[0][2]
prev_k,prev_b = KB[prev]
for y1, y2, idx in Y[1:]:
k,b = KB[idx]
if prev_k - k == 0:
continue
inter = (b - prev_b)/(prev_k - k)
if x1 < inter < x2:
break
else:
print('NO')
quit()
print('YES')
``` | instruction | 0 | 40,809 | 23 | 81,618 |
No | output | 1 | 40,809 | 23 | 81,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = ki·x + bi. It was necessary to determine whether there is at least one point of intersection of two of these lines, that lays strictly inside the strip between x1 < x2. In other words, is it true that there are 1 ≤ i < j ≤ n and x', y', such that:
* y' = ki * x' + bi, that is, point (x', y') belongs to the line number i;
* y' = kj * x' + bj, that is, point (x', y') belongs to the line number j;
* x1 < x' < x2, that is, point (x', y') lies inside the strip bounded by x1 < x2.
You can't leave Anton in trouble, can you? Write a program that solves the given task.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x1 and x2 ( - 1 000 000 ≤ x1 < x2 ≤ 1 000 000) defining the strip inside which you need to find a point of intersection of at least two lines.
The following n lines contain integers ki, bi ( - 1 000 000 ≤ ki, bi ≤ 1 000 000) — the descriptions of the lines. It is guaranteed that all lines are pairwise distinct, that is, for any two i ≠ j it is true that either ki ≠ kj, or bi ≠ bj.
Output
Print "Yes" (without quotes), if there is at least one intersection of two distinct lines, located strictly inside the strip. Otherwise print "No" (without quotes).
Examples
Input
4
1 2
1 2
1 0
0 1
0 2
Output
NO
Input
2
1 3
1 0
-1 3
Output
YES
Input
2
1 3
1 0
0 2
Output
YES
Input
2
1 3
1 0
0 3
Output
NO
Note
In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.
<image>
Submitted Solution:
```
intersect = False
numOfLines = int(input())
xOnexTwo = input().split(" ")
xOnexTwo[0] = int(xOnexTwo[0])
xOnexTwo[1] = int(xOnexTwo[1])
lines = []
for i in range(numOfLines):
tempLine = []
tempLine = input().split(" ")
tempLine[0] = int(tempLine[0])
tempLine[1] = int(tempLine[1])
lines.append(tempLine)
#process info
def compare(line1, line2, lower, upper):
line1Low = line1[0]*lower + line1[1]
line2Low = line2[0]*lower + line2[1]
line1High = line1[0]*upper + line1[1]
line2High = line2[0]*upper + line2[1]
if line1Low < line2Low and line1High > line2Low:
return True
elif line1Low > line2Low and line1High < line2High:
return True
elif line1Low == line2Low and line1High == line2High:
return True
else:
return False
for i in range(len(lines)):
for j in range(len(lines)):
if i == j:
pass
else:
intersect = compare(lines[i],lines[j], xOnexTwo[0], xOnexTwo[1])
if intersect:
print("YES")
break
if intersect:
break
if intersect == False:
print("NO")
``` | instruction | 0 | 40,810 | 23 | 81,620 |
No | output | 1 | 40,810 | 23 | 81,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = ki·x + bi. It was necessary to determine whether there is at least one point of intersection of two of these lines, that lays strictly inside the strip between x1 < x2. In other words, is it true that there are 1 ≤ i < j ≤ n and x', y', such that:
* y' = ki * x' + bi, that is, point (x', y') belongs to the line number i;
* y' = kj * x' + bj, that is, point (x', y') belongs to the line number j;
* x1 < x' < x2, that is, point (x', y') lies inside the strip bounded by x1 < x2.
You can't leave Anton in trouble, can you? Write a program that solves the given task.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 100 000) — the number of lines in the task given to Anton. The second line contains integers x1 and x2 ( - 1 000 000 ≤ x1 < x2 ≤ 1 000 000) defining the strip inside which you need to find a point of intersection of at least two lines.
The following n lines contain integers ki, bi ( - 1 000 000 ≤ ki, bi ≤ 1 000 000) — the descriptions of the lines. It is guaranteed that all lines are pairwise distinct, that is, for any two i ≠ j it is true that either ki ≠ kj, or bi ≠ bj.
Output
Print "Yes" (without quotes), if there is at least one intersection of two distinct lines, located strictly inside the strip. Otherwise print "No" (without quotes).
Examples
Input
4
1 2
1 2
1 0
0 1
0 2
Output
NO
Input
2
1 3
1 0
-1 3
Output
YES
Input
2
1 3
1 0
0 2
Output
YES
Input
2
1 3
1 0
0 3
Output
NO
Note
In the first sample there are intersections located on the border of the strip, but there are no intersections located strictly inside it.
<image>
Submitted Solution:
```
def main():
N = int(input())
X1, X2 = [int(i) for i in input().split()]
X1 += 0.1
X2 -= 0.1
retas = []
for n in range(N):
retas.append([int(i) for i in input().split()])
B1 = {}
B2 = {}
for n in range(N):
k = retas[n][0]
b = retas[n][1]
B1[k*X1 + b] = n
B2[k*X2 + b] = n
L1 = list(B1.keys())
L2 = list(B2.keys())
L1.sort()
L2.sort()
flag = True
for n in range(N):
if B1[L1[n]] != B2[L2[n]]:
flag = False
break
if not flag:
print("YES")
else:
print("NO")
main()
# 1508530408701
``` | instruction | 0 | 40,811 | 23 | 81,622 |
No | output | 1 | 40,811 | 23 | 81,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently Luba bought a monitor. Monitor is a rectangular matrix of size n × m. But then she started to notice that some pixels cease to work properly. Luba thinks that the monitor will become broken the first moment when it contains a square k × k consisting entirely of broken pixels. She knows that q pixels are already broken, and for each of them she knows the moment when it stopped working. Help Luba to determine when the monitor became broken (or tell that it's still not broken even after all q pixels stopped working).
Input
The first line contains four integer numbers n, m, k, q (1 ≤ n, m ≤ 500, 1 ≤ k ≤ min(n, m), 0 ≤ q ≤ n·m) — the length and width of the monitor, the size of a rectangle such that the monitor is broken if there is a broken rectangle with this size, and the number of broken pixels.
Each of next q lines contain three integer numbers xi, yi, ti (1 ≤ xi ≤ n, 1 ≤ yi ≤ m, 0 ≤ t ≤ 109) — coordinates of i-th broken pixel (its row and column in matrix) and the moment it stopped working. Each pixel is listed at most once.
We consider that pixel is already broken at moment ti.
Output
Print one number — the minimum moment the monitor became broken, or "-1" if it's still not broken after these q pixels stopped working.
Examples
Input
2 3 2 5
2 1 8
2 2 8
1 2 1
1 3 4
2 3 2
Output
8
Input
3 3 2 5
1 2 2
2 2 1
2 3 5
3 2 10
2 1 100
Output
-1
Submitted Solution:
```
n,m,k,q=list(map(int,input().split()))
low,high=float('inf'),-1
qry=list()
for _ in range(q):
a,b,c=list(map(int,input().split()))
low=min(low,c)
high=max(high,c)
qry.append([a,b,c])
arr=[[0]*(m) for _ in range(n)]
for i in range(0,q):
arr[qry[i][0]-1][qry[i][1]-1]=qry[i][2]
#print(arr)
def func(t):
precal=[[0]*(m+1) for _ in range(n+1)]
for i in range(1,n+1):
for j in range(1,m+1):
temp=1
if arr[i-1][j-1]>t or arr[i-1][j-1]==0:
temp=0
precal[i][j]=precal[i-1][j]+precal[i][j-1]+temp-precal[i-1][j-1]
for i in range(1,n-k+2):
for j in range(1,m-k+2):
s=precal[i+k-1][j+k-1]+precal[i-1][j-1]-precal[i+k-1][j-1]-precal[i-1][j+k-1]
# print(s,t)
if s>=k*k:
return True
return False
ans=-1
temp=low
#print(low,high)
while(low<=high):
mid=(low+high)//2
check=func(mid)
if check:
if mid==temp:
ans=mid
break
if func(mid-1):
high=mid-1
else:
ans=mid
break
else:
low=mid+1
print(ans)
``` | instruction | 0 | 40,906 | 23 | 81,812 |
No | output | 1 | 40,906 | 23 | 81,813 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,069 | 23 | 82,138 |
"Correct Solution:
```
def gcd(a,b):
if b == 0:
return a
return gcd(b,a%b)
def inpl(): return [int(i) for i in input().split()]
from collections import defaultdict
H = defaultdict(lambda: 0)
N = int(input())
dot = [()]*N
mod = 998244353
for i in range(N):
x, y = inpl()
dot[i] = (x, y)
for i in range(N):
for j in range(i+1,N):
x1, y1 = dot[i]
x2, y2 = dot[j]
A = y1 - y2
B = x2 - x1
C = y1*x2 - x1*y2
if A < 0:
A *= -1
B *= -1
C *= -1
gcdabc = gcd(gcd(A,B), C)
A //= gcdabc
B //= gcdabc
C //= gcdabc
H[(A, B, C)] += 1
ans = (2**N - N - 1 )%mod
for i in H.values():
i = int((1+(1+8*i)**(1/2))/2)
ans -= (2**i - i - 1)%mod
print(ans%mod)
``` | output | 1 | 41,069 | 23 | 82,139 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,070 | 23 | 82,140 |
"Correct Solution:
```
# E
from collections import Counter
N = int(input())
xy_list = [list(map(int, input().split())) for _ in range(N)]
M = 998244353
res = pow(2, N, M)
# 0 points
res -= 1
# 1 points
res -= N
# all lines
line_cnt = [0]*(N+1)
for i in range(N):
xi, yi = xy_list[i]
angle_list = []
for j in range(N):
xj, yj = xy_list[j]
if xj != xi:
angle_list.append((yj-yi)/(xj-xi))
elif yj != yi:
angle_list.append(10000.0)
# count points in same line
cnt_i = Counter(angle_list)
for k in cnt_i.values():
line_cnt[k+1] += 1
for i in range(2, N+1):
cnt = line_cnt[i] // i
res -= cnt*(pow(2, i, M)-i-1)
res = res % M
print(res)
``` | output | 1 | 41,070 | 23 | 82,141 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,071 | 23 | 82,142 |
"Correct Solution:
```
def main():
import sys
input = sys.stdin.readline
def same_line(p1, p2, p3):
c1 = complex(p1[0], p1[1])
c2 = complex(p2[0], p2[1])
c3 = complex(p3[0], p3[1])
a = c2 - c1
b = c3 - c1
if a.real * b.imag == a.imag * b.real:
return 1
else:
return 0
mod = 998244353
N = int(input())
if N <= 2:
print(0)
exit()
xy = []
for _ in range(N):
x, y = map(int, input().split())
xy.append((x, y))
ans = pow(2, N, mod) - N - 1
ans %= mod
used = [[0] * N for _ in range(N)]
for i in range(N-1):
for j in range(i+1, N):
if used[i][j]:
continue
tmp = [i, j]
cnt = 2
for k in range(N):
if k == i or k == j:
continue
if same_line(xy[i], xy[j], xy[k]):
cnt += 1
tmp.append(k)
ans -= pow(2, cnt, mod) - cnt - 1
ans %= mod
for a in range(len(tmp)):
for b in range(a+1, len(tmp)):
used[tmp[a]][tmp[b]] = 1
used[tmp[b]][tmp[a]] = 1
print(ans%mod)
if __name__ == '__main__':
main()
``` | output | 1 | 41,071 | 23 | 82,143 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,072 | 23 | 82,144 |
"Correct Solution:
```
from collections import *
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
def red(a, b, c):
if a == 0 and b < 0: b, c = -b, -c
if a < 0: a, b, c = -a, -b, -c
g = gcd(a, gcd(abs(b), abs(c)))
return a // g, b // g, c // g
def main():
md = 998244353
n = int(input())
xy = LLI(n)
cnt_online = {}
# 各２点を結ぶ直線をax+by+c=0の(a,b,c)で表し
# 各直線上にいくつの点があるかカウントする
for i in range(n):
x0, y0 = xy[i]
counted = set()
for j in range(i):
x1, y1 = xy[j]
a = y0 - y1
b = x1 - x0
c = -a * x0 - b * y0
a, b, c = red(a, b, c)
if (a, b, c) in counted: continue
counted.add((a, b, c))
cnt_online.setdefault((a, b, c), 1)
cnt_online[(a, b, c)] += 1
# print(cnt_online)
# 各直線上で、2点以上で多角形ができない点の選び方を数える
sum_online = 0
for plot_n in cnt_online.values():
sum_online += pow(2, plot_n, md) - 1 - plot_n
sum_online %= md
# すべての2点以上の選び方から、多角形ができないものを引く
ans = pow(2, n, md) - 1 - n - sum_online
print(ans % md)
main()
``` | output | 1 | 41,072 | 23 | 82,145 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,073 | 23 | 82,146 |
"Correct Solution:
```
from collections import Counter
from fractions import gcd
n = int(input())
xys = [tuple(map(int, input().split())) for _ in range(n)]
MOD = 998244353
excludes = 0
for i, (x1, y1) in enumerate(xys):
slopes = []
for x2, y2 in xys[i + 1:]:
dx, dy = x2 - x1, y2 - y1
if dx == 0:
slopes.append(1j)
elif dy == 0:
slopes.append(1)
else:
m = gcd(dx, dy)
slopes.append(dx // m + dy // m * 1j)
for c in Counter(slopes).values():
if c > 1:
excludes += 2 ** c - c - 1
excludes %= MOD
print((pow(2, n, MOD) - excludes - (n * (n - 1) // 2) - n - 1) % MOD)
``` | output | 1 | 41,073 | 23 | 82,147 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,074 | 23 | 82,148 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
from fractions import gcd
from collections import Counter
"""
適当に部分集合Xをとり、凸包 S として、Sに1点計上すればよい
これだと2^N点得られる
ただし、凸包の面積が0となる場合が例外
空集合、1点の場合と、線分の場合を除外する
"""
MOD = 998244353
N = int(input())
XY = [[int(x) for x in input().split()] for _ in range(N)]
answer = pow(2,N,MOD)
answer -= N + 1# 空、1点
for i,(x,y) in enumerate(XY):
# i を選び、i+1番目以上のうちいくつかを選んで線分とする
pts = []
for x1, y1 in XY[i+1:]:
dx, dy = x1-x, y1-y
g = gcd(dx, dy)
dx //= g
dy //= g
# 標準化
if dx < 0:
dx, dy = -dx, -dy
elif dx == 0:
dy = 1
pts.append((dx,dy))
c = Counter(pts)
for v in c.values():
answer -= pow(2,v,MOD) - 1
answer %= MOD
print(answer)
``` | output | 1 | 41,074 | 23 | 82,149 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,075 | 23 | 82,150 |
"Correct Solution:
```
#!/usr/bin/env python3
def main():
N = int(input())
points = []
for i in range(N):
points.append(list(map(int, input().split())))
x = [p[0] for p in points]
y = [p[1] for p in points]
M = 998244353
c = 1 + N + N * (N - 1) // 2
for i in range(N):
xi = x[i]
yi = y[i]
dx = [xj - xi for xj in x]
dy = [yj - yi for yj in y]
for j in range(i + 1, N):
xj = dx[j]
yj = dy[j]
cc = 1
for k in range(j + 1, N):
if xj * dy[k] - dx[k] * yj == 0:
cc *= 2
cc %= M
c += cc - 1
r = 1
for i in range(N):
r *= 2
r %= M
r -= c
r %= M
print(r)
if __name__ == '__main__':
main()
``` | output | 1 | 41,075 | 23 | 82,151 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0 | instruction | 0 | 41,076 | 23 | 82,152 |
"Correct Solution:
```
import math
mod = 998244353
n = int(input())
p = [list(map(int, input().split())) for i in range(n)]
pow2 = [1]
for i in range(n):
pow2.append(pow2[-1] * 2 % mod)
used = [[False] * n for i in range(n)]
ret = (pow2[n] - 1 - n - n * (n - 1) / 2) % mod
for i in range(n):
for j in range(i):
if used[i][j]:
continue
inline = [i, j]
for k in range(n):
if k == i or k == j:
continue
if (p[i][1] - p[k][1]) * (p[j][0] - p[k][0]) == (p[j][1] - p[k][1]) * (p[i][0] - p[k][0]):
inline.append(k)
for k in range(len(inline)):
for l in range(len(inline)):
used[inline[k]][inline[l]] = True
v = len(inline)
ret = (ret + mod - pow2[v] + 1 + v + v * (v - 1) // 2) % mod
print(int(ret))
``` | output | 1 | 41,076 | 23 | 82,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
import sys
from collections import defaultdict
# sys.stdin = open('e1.in')
def read_int_list():
return list(map(int, input().split()))
def read_int():
return int(input())
def read_str_list():
return input().split()
def read_str():
return input()
def gcd(a, b):
if b == 0:
return a
return gcd(b, a % b)
def solve():
def collinear(x0, y0, x1, y1):
return x0 * y1 == x1 * y0
def aligned(i, j, k):
return collinear(x[j] - x[i], y[j] - y[i], x[k] - x[i], y[k] - y[i])
n = read_int()
mod = 998244353
res = pow(2, n, mod) - n - 1
x, y = zip(*[read_int_list() for i in range(n)])
lines = defaultdict(set)
for i in range(n):
for j in range(i + 1, n):
a = y[i] - y[j]
b = x[j] - x[i]
g = gcd(a, b)
a //= g
b //= g
if a < 0 or (a == 0 and b < 0):
a, b = -a, -b
c = -(a * x[i] + b * y[i])
lines[(a, b, c)].add(i)
lines[(a, b, c)].add(j)
for k, v in lines.items():
m = len(v)
res -= pow(2, m, mod) - m - 1
res %= mod
return res
def main():
res = solve()
print(res)
if __name__ == '__main__':
main()
``` | instruction | 0 | 41,077 | 23 | 82,154 |
Yes | output | 1 | 41,077 | 23 | 82,155 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
# seishin.py
N = int(input())
P = [list(map(int, input().split())) for i in range(N)]
MOD = 998244353
ans = pow(2, N, MOD) - 1 - N
u = set()
for i in range(N):
xi, yi = P[i]
for j in range(i+1, N):
xj, yj = P[j]
if (i, j) in u:
continue
cnt = 0
Q = {i, j}
for k in range(N):
xk, yk = P[k]
if (xj - xi)*(yk - yi) == (xk - xi)*(yj - yi):
cnt += 1
Q.add(k)
for p in Q:
for q in Q:
u.add((p, q))
ans -= pow(2, cnt, MOD) - cnt - 1
print(ans % MOD)
``` | instruction | 0 | 41,078 | 23 | 82,156 |
Yes | output | 1 | 41,078 | 23 | 82,157 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
from collections import Counter
if __name__ == '__main__':
N = int(input())
xy_list = [list(map(int, input().split())) for _ in range(N)]
modulo_num = 998244353
duplicate_list = [0] * (N + 1)
for i in range(N):
xi, yi = xy_list[i]
gradient_list = []
for j in range(N):
xj, yj = xy_list[j]
if xi != xj:
gradient_list.append((yj - yi) / (xj - xi))
elif yi != yj:
gradient_list.append(100000)
counter = Counter(gradient_list)
for k in counter.values():
duplicate_list[k + 1] += 1
ans = pow(2, N, modulo_num)
ans -= 1
ans -= N
for i in range(2, N + 1):
cnt = duplicate_list[i] // i
ans -= cnt * (pow(2, i, modulo_num) - i - 1)
ans = ans % modulo_num
print(ans)
``` | instruction | 0 | 41,079 | 23 | 82,158 |
Yes | output | 1 | 41,079 | 23 | 82,159 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
from fractions import Fraction
from collections import defaultdict
from itertools import combinations
class Combination:
"""
O(n)の前計算を1回行うことで，O(1)でnCr mod mを求められる
n_max = 10**6のとき前処理は約950ms (PyPyなら約340ms, 10**7で約1800ms)
使用例：
comb = Combination(1000000)
print(comb(5, 3)) # 10
"""
def __init__(self, n_max, mod=10**9+7):
self.mod = mod
self.modinv = self.make_modinv_list(n_max)
self.fac, self.facinv = self.make_factorial_list(n_max)
def __call__(self, n, r):
return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod
def make_factorial_list(self, n):
# 階乗のリストと階乗のmod逆元のリストを返す O(n)
# self.make_modinv_list()が先に実行されている必要がある
fac = [1]
facinv = [1]
for i in range(1, n+1):
fac.append(fac[i-1] * i % self.mod)
facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
return fac, facinv
def make_modinv_list(self, n):
# 0からnまでのmod逆元のリストを返す O(n)
modinv = [0] * (n+1)
modinv[1] = 1
for i in range(2, n+1):
modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
return modinv
N = int(input())
XY = [list(map(int, input().split())) for i in range(N)]
D = defaultdict(int)
for (x1, y1), (x2, y2) in combinations(XY, 2):
if x1 != x2:
a = Fraction(y2-y1, x2-x1)
b = Fraction(y1) - a * Fraction(x1)
D[(a, b)] += 1
else:
D[(None, x1)] += 1
mod = 998244353
comb = Combination(N+1, mod)
A = [0] * (N+1)
coA = [0] * (N+1)
ans = 0
for i in range(3, N+1):
ans += comb(N, i)
ans %= mod
for i in range(3, N+1):
for j in range(i-2):
A[i] += (i-2-j)*(1<<j)
coA[i] = coA[i-1]+A[i]
for (a, b), n in D.items():
if n==1:
continue
n = int((n<<1)**0.5)+1
ans -= coA[n]
ans %= mod
print(ans)
``` | instruction | 0 | 41,080 | 23 | 82,160 |
Yes | output | 1 | 41,080 | 23 | 82,161 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
def same_line(p1, p2, p3):
eps = 10**-8
c1 = complex(p1[0], p1[1])
c2 = complex(p2[0], p2[1])
c3 = complex(p3[0], p3[1])
d = (c2-c1) / (c3-c1)
if abs(d.imag) < eps:
return 1
else:
return 0
mod = 998244353
N = int(input())
if N <= 2:
print(0)
xy = []
for _ in range(N):
x, y = map(int, input().split())
xy.append((x, y))
ans = pow(2, N, mod) - N - 1
used = [[0] * N for _ in range(N)]
for i in range(N-1):
for j in range(i+1, N):
if used[i][j]:
continue
tmp = [i, j]
cnt = 2
for k in range(N):
if k == i or k == j:
continue
if same_line(xy[i], xy[j], xy[k]):
cnt += 1
tmp.append(k)
ans -= pow(2, cnt, mod) - cnt - 1
ans %= mod
for a in range(len(tmp)):
for b in range(a+1, len(tmp)):
used[tmp[a]][tmp[b]] = 1
used[tmp[b]][tmp[a]] = 1
print(ans%mod)
if __name__ == '__main__':
main()
``` | instruction | 0 | 41,081 | 23 | 82,162 |
No | output | 1 | 41,081 | 23 | 82,163 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
import math
n = int(input())
dat = [list(map(int, input().split())) for i in range(n)]
dic = {}
mod = 998244353
mp = [(2**i) % mod for i in range(n + 1)]
ret = (mp[n] - 1 - n * (n + 1) / 2) % mod
for i in range(n):
for j in range(i):
a = 0
b = 0
if dat[i][0] == dat[j][0]:
a = 10**9
b = dat[i][0]
else:
a = (dat[i][1] - dat[j][1]) / (dat[i][0] - dat[j][0])
b = dat[i][1] - dat[i][0] * a
if (a, b) in dic:
dic[(a, b)] += 1
else:
dic[(a, b)] = 1
for v in dic.values():
x = int((math.sqrt(8 * v + 1) + 1) / 2)
ret = (ret + mod - mp[x] + 1 + x * (x + 1) / 2) % mod
print(int(ret))
``` | instruction | 0 | 41,082 | 23 | 82,164 |
No | output | 1 | 41,082 | 23 | 82,165 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
import math
import itertools
def read_data():
try:
LOCAL_FLAG
import codecs
import os
lines = []
file_path = os.path.join(os.path.dirname(__file__), 'arc082-e.dat')
with codecs.open(file_path, 'r', 'utf-8') as f:
lines.append(f.readline().rstrip("\r\n"))
N = int(lines[0])
for i in range(N):
lines.append(f.readline().rstrip("\r\n"))
except NameError:
lines = []
lines.append(input())
N = int(lines[0])
for i in range(N):
lines.append(input())
return lines
def isIncluded(ref_points, ref):
min_y = ref_points[0]['y']
min_index = 0
for i in range(1, len(ref_points)):
if(min_y > ref_points[i]['y']):
min_y = ref_points[i]['y']
min_index = i
points = []
p = {}
for i in range(len(ref_points)):
data = {}
data['x'] = ref_points[i]['x'] - ref_points[min_index]['x']
data['y'] = ref_points[i]['y'] - ref_points[min_index]['y']
data['rad'] = math.atan2(data['y'], data['x'])
points.append(data)
p['x'] = ref['x'] - ref_points[min_index]['x']
p['y'] = ref['y'] - ref_points[min_index]['y']
points = sorted(points, key=lambda x: x['rad'])
lines = []
v1 = {}
v2 = {}
Included = True
lines = ((0,1), (1,2), (2,0))
for n in range(3):
v1['x'] = points[lines[n][1]]['x'] - points[lines[n][0]]['x']
v1['y'] = points[lines[n][1]]['y'] - points[lines[n][0]]['y']
v2['x'] = p['x'] - points[lines[n][1]]['x']
v2['y'] = p['y'] - points[lines[n][1]]['y']
cross = v1['x']*v2['y'] - v2['x']*v1['y']
# print(v1, v2)
# print(cross)
if(cross < 0):
return False
if(Included):
return True
else:
return False
def isConvex(xy, points):
lines = []
v1 = {}
v2 = {}
N = len(points)
for n in range(N-1):
lines.append((points[n], points[n+1]))
lines.append((points[n+1], points[0]))
lines.append(lines[0])
for n in range(N):
v1['x'] = xy[lines[n][1]]['x'] - xy[lines[n][0]]['x']
v1['y'] = xy[lines[n][1]]['y'] - xy[lines[n][0]]['y']
v2['x'] = xy[lines[n+1][1]]['x'] - xy[lines[n+1][0]]['x']
v2['y'] = xy[lines[n+1][1]]['y'] - xy[lines[n+1][0]]['y']
cross = v1['x']*v2['y'] - v2['x']*v1['y']
if(cross <= 0):
return False
return True
def sort_by_rad(xy, points):
min_y = xy[points[0]]['y']
min_index = 0
for i in range(1, len(points)):
if(min_y > xy[points[i]]['y']):
min_y = xy[points[i]]['y']
min_index = i
new_points = []
for i in range(len(points)):
data = {}
data['x'] = xy[points[i]]['x'] - xy[points[min_index]]['x']
data['y'] = xy[points[i]]['y'] - xy[points[min_index]]['y']
data['rad'] = math.atan2(data['y'], data['x'])
data['index'] = points[i]
new_points.append(data)
sort_points = sorted(new_points, key=lambda x: x['rad'])
results = []
for i in range(len(points)):
results.append(sort_points[i]['index'])
return results
def E_ConvexScore():
raw_data = read_data()
xy = []
N = int(raw_data[0])
key_list = ["x", "y"]
min_xy = dict(zip(key_list, list(map(int, raw_data[1].split()))))
max_xy = dict(zip(key_list, list(map(int, raw_data[1].split()))))
index_min = 0
for i in range(N):
xy.append(dict(zip(key_list, list(map(int, raw_data[i+1].split())))))
xy[i]['rad'] = math.atan2(xy[i]['y'], xy[i]['x'])
xy[i]['d'] = xy[i]['y'] + xy[i]['x']
xy_d = sorted(xy, key=lambda x: x['d'])
xy_rad = sorted(xy_d, key=lambda x: x['rad'])
xy = xy_rad
included = {}
total_rank = 0
for points in itertools.combinations(range(N), 3):
new_points = sort_by_rad(xy, points)
# print(new_points)
if(not isConvex(xy, new_points)):
included[points] = set([])
continue
count = 0
index_included = []
for i in range(points[0]+1, points[2]):
if(i in points):
continue
elif(isIncluded(list([xy[points[0]], xy[points[1]], xy[points[2]]]), xy[i])):
count += 1
index_included.append(i)
included[points] = set(index_included)
# print(count)
total_rank += pow(2, count)
# print(included)
for i in range(4, N+1):
for points in itertools.combinations(range(N), i):
new_points = sort_by_rad(xy, points)
if(not isConvex(xy, new_points)):
continue
# print(new_points)
count_set = set([])
for j in range(i-2):
triangle = (new_points[0], new_points[j+1], new_points[j+2])
count_set = count_set ^ included[triangle]
# print(count_set)
total_rank += pow(2, len(count_set))
print(total_rank)
E_ConvexScore()
``` | instruction | 0 | 41,083 | 23 | 82,166 |
No | output | 1 | 41,083 | 23 | 82,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.
cddb0c267926c2add885ca153c47ad8a.png
For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.
Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.
However, since the sum can be extremely large, print the sum modulo 998244353.
Constraints
* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of all the scores modulo 998244353.
Examples
Input
4
0 0
0 1
1 0
1 1
Output
5
Input
5
0 0
0 1
0 2
0 3
1 1
Output
11
Input
1
3141 2718
Output
0
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
def same_line(p1, p2, p3):
eps = 10**-8
c1 = complex(p1[0], p1[1])
c2 = complex(p2[0], p2[1])
c3 = complex(p3[0], p3[1])
d = (c2-c1) / (c3-c1)
if abs(d.imag) < eps:
return 1
else:
return 0
mod = 998244353
N = int(input())
xy = []
for _ in range(N):
x, y = map(int, input().split())
xy.append((x, y))
ans = pow(2, N, mod) - N - 1
used = [[0] * N for _ in range(N)]
for i in range(N-1):
for j in range(i+1, N):
if used[i][j]:
continue
tmp = [i, j]
cnt = 2
for k in range(N):
if k == i or k == j:
continue
if same_line(xy[i], xy[j], xy[k]):
cnt += 1
tmp.append(k)
ans -= pow(2, cnt, mod) - cnt - 1
ans %= mod
for a in range(len(tmp)):
for b in range(a+1, len(tmp)):
used[tmp[a]][tmp[b]] = 1
used[tmp[b]][tmp[a]] = 1
print(ans)
if __name__ == '__main__':
main()
``` | instruction | 0 | 41,084 | 23 | 82,168 |
No | output | 1 | 41,084 | 23 | 82,169 |
Provide a correct Python 3 solution for this coding contest problem.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2 | instruction | 0 | 41,119 | 23 | 82,238 |
"Correct Solution:
```
from math import sin, pi
def calc(n):
s = a = 0
V = []
for i in range(n-1):
v = int(input())
s += v
a += sin(v*pi/180)
V.append(v)
V.append(360-s)
a += sin((360-s)*pi/180)
return a, sorted(V)
while 1:
m = int(input())
if m == 0:
break
a1, V1 = calc(m)
n = int(input())
a2, V2 = calc(n)
if V1 == V2 or a1 == a2:
print(0)
elif a1 < a2:
print(2)
else:
print(1)
``` | output | 1 | 41,119 | 23 | 82,239 |
Provide a correct Python 3 solution for this coding contest problem.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2 | instruction | 0 | 41,120 | 23 | 82,240 |
"Correct Solution:
```
import math
ONE_BIGGER_TWO = 1
TWO_BIGGER_ONE = 2
SAME = 0
def calculate_area(input_list):
last = 360 - sum(input_list)
input_list.append(last)
radian_list = [math.radians(item) for item in input_list]
sin_list = [math.sin(item) for item in radian_list]
area = math.fsum(sin_list)
return area
while True:
input_count = int(input())
if input_count == 0:
break
input_list1 = [int(input()) for _ in range(input_count - 1)]
area1 = calculate_area(input_list1)
input_count = int(input())
input_list2 = [int(input()) for _ in range(input_count - 1)]
area2 = calculate_area(input_list2)
if math.isclose(area1, area2):
print(SAME)
elif area1 > area2:
print(ONE_BIGGER_TWO)
else:
print(TWO_BIGGER_ONE)
``` | output | 1 | 41,120 | 23 | 82,241 |
Provide a correct Python 3 solution for this coding contest problem.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2 | instruction | 0 | 41,121 | 23 | 82,242 |
"Correct Solution:
```
# AOJ 0166: Area of Polygon
# Python3 2018.6.18 bal4u
import math
M = 0.00872664625997164788461845384244
EPS = 1e-8
a = [0]*2
s = [0.0]*2
while True:
eof = False
for i in range(2):
s[i] = a[i] = 0;
n = int(input())
if n == 0:
eof = True
break
for j in range(1, n):
v = int(input())
a[i] += v
s[i] += math.sin(M*v)*math.cos(M*v)
v = 360-a[i]
s[i] += math.sin(M*v)*math.cos(M*v)
if eof: break
if abs(s[1]-s[0]) <= EPS: print(0)
elif s[1] >= s[0]: print(2)
else: print(1);
``` | output | 1 | 41,121 | 23 | 82,243 |
Provide a correct Python 3 solution for this coding contest problem.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2 | instruction | 0 | 41,122 | 23 | 82,244 |
"Correct Solution:
```
from math import *
def area(x):
ret=0.
theta = 360.
for i in range(x-1):
tmp=float(input())
theta-=tmp
tmp=tmp*pi/180.
ret+=(sin(tmp/2)*cos(tmp/2))
theta=pi*theta/180.
ret+=sin(theta/2)*cos(theta/2);
return ret;
while 1:
m=int(input())
if m==0:break
a=area(m)
b=area(int(input()))
print(0 if a==b else (1 if a>b else 2))
``` | output | 1 | 41,122 | 23 | 82,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2
Submitted Solution:
```
import math
ONE_BIGGER_TWO = 1
TWO_BIGGER_ONE = 2
SAME = 0
def calculate_area(input_list):
last = 360 - sum(input_list)
input_list.append(last)
radian_list = [math.radians(item) for item in input_list]
sin_list = [math.sin(item) for item in radian_list]
area = sum(sin_list)
return area
while True:
input_count = int(input())
if input_count == 0:
break
input_list1 = [int(input()) for _ in range(input_count - 1)]
area1 = calculate_area(input_list1)
input_count = int(input())
input_list2 = [int(input()) for _ in range(input_count - 1)]
area2 = calculate_area(input_list2)
if area1 == area2:
print(SAME)
elif area1 > area2:
print(ONE_BIGGER_TWO)
else:
print(TWO_BIGGER_ONE)
``` | instruction | 0 | 41,123 | 23 | 82,246 |
No | output | 1 | 41,123 | 23 | 82,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2
Submitted Solution:
```
from sys import float_info
from math import sin, radians
ONE_BIGGER_TWO = 1
TWO_BIGGER_ONE = 2
SAME = 0
def calculate_area(input_list):
radian_list = [radians(item) for item in input_list]
sin_list = [sin(item) for item in radian_list]
area = sum(sin_list)
return area
while True:
input_count = int(input())
if input_count == 0:
break
input_list1 = [int(input()) for _ in range(input_count - 1)]
area1 = calculate_area(input_list1)
input_count = int(input())
input_list2 = [int(input()) for _ in range(input_count - 1)]
area2 = calculate_area(input_list2)
if area1 - area2 < float_info.epsilon:
print(SAME)
elif area1 > area2:
print(ONE_BIGGER_TWO)
else:
print(TWO_BIGGER_ONE)
``` | instruction | 0 | 41,124 | 23 | 82,248 |
No | output | 1 | 41,124 | 23 | 82,249 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2
Submitted Solution:
```
from math import sin, radians
ONE_BIGGER_TWO = 1
TWO_BIGGER_ONE = 2
SAME = 0
def calculate_area(input_list):
radian_list = [radians(item) for item in input_list]
sin_list = [sin(item) for item in radian_list]
area = sum(sin_list)
return area
while True:
input_count = int(input())
if input_count == 0:
break
input_list1 = [int(input()) for _ in range(input_count - 1)]
area1 = calculate_area(input_list1)
input_count = int(input())
input_list2 = [int(input()) for _ in range(input_count - 1)]
area2 = calculate_area(input_list2)
if area1 == area2:
print(SAME)
elif area1 > area2:
print(ONE_BIGGER_TWO)
else:
print(TWO_BIGGER_ONE)
``` | instruction | 0 | 41,125 | 23 | 82,250 |
No | output | 1 | 41,125 | 23 | 82,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.
Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of the first polygon is large, 2 (half-width number) when the area of the second polygon is large, and when the areas are the same, Please output 0 (half-width number).
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1
The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..
The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.
The number of datasets does not exceed 200.
Output
Outputs the magnitude relationship (half-width numbers) for each data set on one line.
Example
Input
4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0
Output
0
1
2
Submitted Solution:
```
import math
"""
import decimal
quantizeで1つずつ丸めていく?
"""
ONE_BIGGER_TWO = 1
TWO_BIGGER_ONE = 2
SAME = 0
def calculate_area(input_list):
radian_list = [math.radians(item) for item in input_list]
sin_list = [math.sin(item) for item in radian_list]
area = math.fsum(sin_list)
return area
while True:
input_count = int(input())
if input_count == 0:
break
input_list1 = [int(input()) for _ in range(input_count - 1)]
area1 = calculate_area(input_list1)
input_count = int(input())
input_list2 = [int(input()) for _ in range(input_count - 1)]
area2 = calculate_area(input_list2)
if math.isclose(area1, area2):
print(SAME)
elif area1 > area2:
print(ONE_BIGGER_TWO)
else:
print(TWO_BIGGER_ONE)
``` | instruction | 0 | 41,126 | 23 | 82,252 |
No | output | 1 | 41,126 | 23 | 82,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
The JOI building is a combination of regular hexagons with a side of 1 meter as shown in the figure. As Christmas is approaching, JOI decided to decorate the walls of the building with illuminations. However, since it is useless to illuminate the parts that cannot be seen from the outside, we decided to decorate only the walls that can be reached from the outside without passing through the building.
<image>
Figure: Example of JOI building layout
The figure above is an example of the layout of JOI's buildings as seen from above. The numbers in the regular hexagon represent the coordinates. A gray regular hexagon represents a place with a building, and a white regular hexagon represents a place without a building. In this example, the part indicated by the solid red line is the wall surface to be decorated with illumination, and the total length of the wall surface is 64 meters.
Given a map showing the layout of JOI's buildings, create a program to find the total length of the walls to decorate. However, the outside of the map can be freely moved, and it is not possible to pass between adjacent buildings.
input
Two integers W and H (1 ≤ W ≤ 100, 1 ≤ H ≤ 100) are written on the first line of the input file, separated by blanks. The following line H describes the layout of the JOI building. On the first line of i + (1 ≤ i ≤ H), W integers are written separated by blanks, and the jth (1 ≤ j ≤ W) integer is a regular hexagon with coordinates (j, i). It is 1 when there is a building in, and 0 when there is no building. Also, the input data given always has one or more buildings.
The map is described by the following rules.
* The westernmost regular hexagon in the northernmost row of the map is the coordinates (1, 1).
* The eastern adjacent regular hexagon adjacent to the regular hexagon with coordinates (x, y) is the coordinates (x + 1, y).
* When y is odd, the coordinates of the southwestern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
* When y is even, the coordinates of the southeastern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
output
Output the total length of the walls to be decorated with illuminations in one line.
Input / output example
Input example 1
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1 1
0 1 1 0 1 0 1 0
Output example 1
64
Input / output example 1 corresponds to the example in the problem statement, and the total length of the wall surface decorated with illumination is 64 meters.
Input example 2
8 5
0 1 1 1 0 1 1 1
0 1 0 0 1 1 0 0
1 0 0 1 1 1 1 1 1
0 1 0 1 1 0 1 0
0 1 1 0 1 1 0 0
Output example 2
56
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1
0 1 1 0 1 0 1 0
Output
64
Submitted Solution:
```
WALL = 100
w, h = map(int,input().split())
lst = [[WALL] + list(map(int,input().split())) + [WALL] for i in range(h)]
lst.insert(0, [WALL] * (w + 2))
lst.append([WALL] * (w + 2))
visited = [[0] * (w + 2) for _ in range(h + 2)]
hold = []
def search(x, y):
if lst[x][y] == WALL:
visited[x][y] = 3
return 3
if lst[x][y] == 1:
visited[x][y] = 2
return 2
visited[x][y] = 1
hold.append((x, y))
if not x % 2:
pairs = [(x - 1, y - 1), (x - 1, y), (x, y - 1), (x, y + 1), (x + 1, y - 1), (x + 1, y)]
else:
pairs = [(x - 1, y), (x - 1, y + 1), (x, y - 1), (x, y + 1), (x + 1, y), (x + 1, y + 1)]
ret = 0
for t in pairs:
tx, ty = t[0], t[1]
a = 0
if not visited[tx][ty]:
a = search(tx, ty)
elif visited[x][y] == 3:
a = 3
elif visited[x][y] == 2:
a = 2
if a > ret:
ret = a
return ret
for x in range(1, h + 1):
for y in range(1, w + 1):
if not visited[x][y] and not lst[x][y]:
stat = search(x, y)
for point in hold:
visited[point[0]][point[1]] = stat
hold.clear()
ans = 0
for x in range(1, h + 1):
for y in range(1, w + 1):
if lst[x][y]:
if not x % 2:
pairs = [(x - 1, y - 1), (x - 1, y), (x, y - 1), (x, y + 1), (x + 1, y - 1), (x + 1, y)]
else:
pairs = [(x - 1, y), (x - 1, y + 1), (x, y - 1), (x, y + 1), (x + 1, y), (x + 1, y + 1)]
for t in pairs:
tx, ty = t[0], t[1]
if visited[tx][ty] in [0,3]:
ans += 1
print(ans)
``` | instruction | 0 | 41,139 | 23 | 82,278 |
No | output | 1 | 41,139 | 23 | 82,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
The JOI building is a combination of regular hexagons with a side of 1 meter as shown in the figure. As Christmas is approaching, JOI decided to decorate the walls of the building with illuminations. However, since it is useless to illuminate the parts that cannot be seen from the outside, we decided to decorate only the walls that can be reached from the outside without passing through the building.
<image>
Figure: Example of JOI building layout
The figure above is an example of the layout of JOI's buildings as seen from above. The numbers in the regular hexagon represent the coordinates. A gray regular hexagon represents a place with a building, and a white regular hexagon represents a place without a building. In this example, the part indicated by the solid red line is the wall surface to be decorated with illumination, and the total length of the wall surface is 64 meters.
Given a map showing the layout of JOI's buildings, create a program to find the total length of the walls to decorate. However, the outside of the map can be freely moved, and it is not possible to pass between adjacent buildings.
input
Two integers W and H (1 ≤ W ≤ 100, 1 ≤ H ≤ 100) are written on the first line of the input file, separated by blanks. The following line H describes the layout of the JOI building. On the first line of i + (1 ≤ i ≤ H), W integers are written separated by blanks, and the jth (1 ≤ j ≤ W) integer is a regular hexagon with coordinates (j, i). It is 1 when there is a building in, and 0 when there is no building. Also, the input data given always has one or more buildings.
The map is described by the following rules.
* The westernmost regular hexagon in the northernmost row of the map is the coordinates (1, 1).
* The eastern adjacent regular hexagon adjacent to the regular hexagon with coordinates (x, y) is the coordinates (x + 1, y).
* When y is odd, the coordinates of the southwestern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
* When y is even, the coordinates of the southeastern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
output
Output the total length of the walls to be decorated with illuminations in one line.
Input / output example
Input example 1
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1 1
0 1 1 0 1 0 1 0
Output example 1
64
Input / output example 1 corresponds to the example in the problem statement, and the total length of the wall surface decorated with illumination is 64 meters.
Input example 2
8 5
0 1 1 1 0 1 1 1
0 1 0 0 1 1 0 0
1 0 0 1 1 1 1 1 1
0 1 0 1 1 0 1 0
0 1 1 0 1 1 0 0
Output example 2
56
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1
0 1 1 0 1 0 1 0
Output
64
Submitted Solution:
```
W, H = map(int, input().split())
m = [list(map(int, input().split())) for i in range(H)]
dx = [[1, 1, 1, 0, -1, 0], [0, 1, 0, -1, -1, -1]]
dy = [-1, 0, 1, 1, 0, -1]
def dfs(x, y):
if m[y][x] != 0:
return
m[y][x] = 2
for xx, yy in zip(dx[y % 2], dy):
tx, ty = x + xx, y + yy
if 0 <= tx < W and 0 <= ty < H:
dfs(tx, ty)
for x in range(W):
dfs(x, 0)
dfs(x, H - 1)
for y in range(H):
dfs(0, y)
dfs(W - 1, y)
from itertools import product
n = 0
for x, y in product(range(W), range(H)):
if m[y][x] != 1:
continue
fn = n
for xx, yy in zip(dx[y % 2], dy):
tx, ty = x + xx, y + yy
if 0 <= tx < W and 0 <= ty < H:
if m[ty][tx] == 2:
n += 1
else:
n += 1
print(n)
``` | instruction | 0 | 41,140 | 23 | 82,280 |
No | output | 1 | 41,140 | 23 | 82,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
The JOI building is a combination of regular hexagons with a side of 1 meter as shown in the figure. As Christmas is approaching, JOI decided to decorate the walls of the building with illuminations. However, since it is useless to illuminate the parts that cannot be seen from the outside, we decided to decorate only the walls that can be reached from the outside without passing through the building.
<image>
Figure: Example of JOI building layout
The figure above is an example of the layout of JOI's buildings as seen from above. The numbers in the regular hexagon represent the coordinates. A gray regular hexagon represents a place with a building, and a white regular hexagon represents a place without a building. In this example, the part indicated by the solid red line is the wall surface to be decorated with illumination, and the total length of the wall surface is 64 meters.
Given a map showing the layout of JOI's buildings, create a program to find the total length of the walls to decorate. However, the outside of the map can be freely moved, and it is not possible to pass between adjacent buildings.
input
Two integers W and H (1 ≤ W ≤ 100, 1 ≤ H ≤ 100) are written on the first line of the input file, separated by blanks. The following line H describes the layout of the JOI building. On the first line of i + (1 ≤ i ≤ H), W integers are written separated by blanks, and the jth (1 ≤ j ≤ W) integer is a regular hexagon with coordinates (j, i). It is 1 when there is a building in, and 0 when there is no building. Also, the input data given always has one or more buildings.
The map is described by the following rules.
* The westernmost regular hexagon in the northernmost row of the map is the coordinates (1, 1).
* The eastern adjacent regular hexagon adjacent to the regular hexagon with coordinates (x, y) is the coordinates (x + 1, y).
* When y is odd, the coordinates of the southwestern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
* When y is even, the coordinates of the southeastern regular hexagon adjacent to the regular hexagon of coordinates (x, y) are (x, y + 1).
output
Output the total length of the walls to be decorated with illuminations in one line.
Input / output example
Input example 1
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1 1
0 1 1 0 1 0 1 0
Output example 1
64
Input / output example 1 corresponds to the example in the problem statement, and the total length of the wall surface decorated with illumination is 64 meters.
Input example 2
8 5
0 1 1 1 0 1 1 1
0 1 0 0 1 1 0 0
1 0 0 1 1 1 1 1 1
0 1 0 1 1 0 1 0
0 1 1 0 1 1 0 0
Output example 2
56
The question text and the data used for the automatic referee are the question text and the test data for scoring, which are created and published by the Japan Committee for Information Olympics.
Example
Input
8 4
0 1 0 1 0 1 1 1
0 1 1 0 0 1 0 0
1 0 1 0 1 1 1 1
0 1 1 0 1 0 1 0
Output
64
Submitted Solution:
```
def solve():
from collections import deque
from copy import deepcopy
W, H = map(int, input().split())
a = [[0]*(W+2)] + [list(map(int, ("0 "+input()+" 0").split())) for _ in [0]*H] + [[0]*(W+2)]
result = 0
visited = deepcopy(a)
dq = deque([(0, 0)])
append, popleft = dq.append, dq.popleft
while dq:
x, y = popleft()
neighbour = [(-1, 0), (1, 0)] + ([(-1, -1), (0, -1), (-1, 1), (0, 1)] if y%2 == 0 else [(0, -1), (1, -1), (0, 1), (1, 1)])
for dx, dy in neighbour:
nx, ny = dx+x, dy+y
if 0 <= nx < W+2 and 0 <= ny < H+2:
result += a[ny][nx]
for dx, dy in ((-1, 0), (1, 0), (0, -1), (0, 1)):
nx, ny = x+dx, y+dy
if 0 <= nx < W+2 and 0 <= ny < H+2 and visited[ny][nx] == 0:
visited[ny][nx] = 1
append((nx, ny))
print(result)
if __name__ == "__main__":
solve()
``` | instruction | 0 | 41,141 | 23 | 82,282 |
No | output | 1 | 41,141 | 23 | 82,283 |
Provide a correct Python 3 solution for this coding contest problem.
Yoko’s math homework today was to calculate areas of polygons in the xy-plane. Vertices are all aligned to grid points (i.e. they have integer coordinates).
Your job is to help Yoko, not good either at math or at computer programming, get her home- work done. A polygon is given by listing the coordinates of its vertices. Your program should approximate its area by counting the number of unit squares (whose vertices are also grid points) intersecting the polygon. Precisely, a unit square “intersects the polygon” if and only if the in- tersection of the two has non-zero area. In the figure below, dashed horizontal and vertical lines are grid lines, and solid lines are edges of the polygon. Shaded unit squares are considered inter- secting the polygon. Your program should output 55 for this polygon (as you see, the number of shaded unit squares is 55).
<image>
Figure 1: A polygon and unit squares intersecting it
Input
The input file describes polygons one after another, followed by a terminating line that only contains a single zero.
A description of a polygon begins with a line containing a single integer, m (≥ 3), that gives the number of its vertices. It is followed by m lines, each containing two integers x and y, the coordinates of a vertex. The x and y are separated by a single space. The i-th of these m lines gives the coordinates of the i-th vertex (i = 1, ... , m). For each i = 1, ... , m - 1, the i-th vertex and the (i + 1)-th vertex are connected by an edge. The m-th vertex and the first vertex are also connected by an edge (i.e., the curve is closed). Edges intersect only at vertices. No three edges share a single vertex (i.e., the curve is simple). The number of polygons is no more than 100. For each polygon, the number of vertices (m) is no more than 100. All coordinates x and y satisfy -2000 ≤ x ≤ 2000 and -2000 ≤ y ≤ 2000.
Output
The output should consist of as many lines as the number of polygons. The k-th output line should print an integer which is the area of the k-th polygon, approximated in the way described above. No other characters, including whitespaces, should be printed.
Example
Input
4
5 -3
1 0
1 7
-7 -1
3
5 5
18 5
5 10
3
-5 -5
-5 -10
-18 -10
5
0 0
20 2
11 1
21 2
2 0
0
Output
55
41
41
23 | instruction | 0 | 41,142 | 23 | 82,284 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
write = sys.stdout.write
def solve():
N = int(readline())
if N == 0:
return False
P = [list(map(int, readline().split())) for i in range(N)]
L = 2000
Q = [[] for i in range(2*L+1)]
LS = []
for i in range(N):
x0, y0 = P[i-1]; x1, y1 = P[i]
if y0 != y1:
Q[y0].append(i); Q[y1].append(i)
LS.append((P[i-1], P[i]) if y0 < y1 else (P[i], P[i-1]))
U = [0]*N
s = set()
ans = 0
for y in range(-L, L):
for i in Q[y]:
if U[i]:
s.remove(i)
else:
s.add(i)
U[i] = 1
*js, = s
def f(i):
(x0, y0), (x1, y1) = LS[i]
dx = x1 - x0; dy = y1 - y0
if dx < 0:
return (x0 + dx*((y+1) - y0)/dy, x0 + (dx*(y - y0) + dy-1)//dy)
return (x0 + dx*(y - y0)/dy, x0 + (dx*((y+1) - y0) + dy-1)//dy)
js.sort(key = f)
l = r = -5000
for k, i in enumerate(js):
(x0, y0), (x1, y1) = LS[i]
dx = x1 - x0; dy = y1 - y0
if k & 1:
if dx >= 0:
x = x0 + (dx*((y+1) - y0) + dy-1) // dy
else:
x = x0 + (dx*(y - y0) + dy-1) // dy
r = x
else:
if dx >= 0:
x = x0 + dx*(y - y0) // dy
else:
x = x0 + dx*((y+1) - y0) // dy
if r < x:
ans += r-l
l = x
ans += r-l
write("%d\n" % ans)
return True
while solve():
...
``` | output | 1 | 41,142 | 23 | 82,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,202 | 23 | 82,404 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
a = []
for i in range(1, m + 1):
a.append(i)
for j in range(n):
l, r = map(int, input().split())
for i in range(l - 1, r):
a[i] = 0
k = 0
for i in range(len(a)):
if a[i] != 0:
k += 1
print(k)
for i in range(len(a)):
if a[i] != 0:
print(a[i], end = ' ')
``` | output | 1 | 41,202 | 23 | 82,405 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,203 | 23 | 82,406 |
Tags: implementation
Correct Solution:
```
n,m=input().split()
l=[]
f=[]
for i in range (1,int(m)+1):
l.append(i)
for i in range (0,int(n)):
a,b=input().split()
for j in range (int(a),int(b)+1):
if j not in f:
f.append(j)
final=set(l)-set(f)
print(len(final))
for i in final:
print(i,end=" ")
``` | output | 1 | 41,203 | 23 | 82,407 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,204 | 23 | 82,408 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
dp = [0 for i in range(m+1)]
for n0 in range(n):
l, r = map(int, input().split())
for i in range(l, r+1):
dp[i] = 1
res = []
for i in range(1, m+1):
if dp[i] == 0:
res.append(i)
print(len(res))
for e in res:
print(e, end=" ")
print()
``` | output | 1 | 41,204 | 23 | 82,409 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,205 | 23 | 82,410 |
Tags: implementation
Correct Solution:
```
s = list(map(int, input().split()))
n, m = s[0], s[1]
cl = []
def check(x):
res = True
for r in cl:
if x>=r[0] and x<=r[1]:
res = False
break
return res
for i in range(n):
cl.append(list(map(int, input().split())))
res = []
for i in range(1, m+1):
if check(i): res.append(i)
print(len(res))
if len(res)!=0: print(*res)
``` | output | 1 | 41,205 | 23 | 82,411 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,206 | 23 | 82,412 |
Tags: implementation
Correct Solution:
```
l=list(map(int, input().split()))
I = []
for i in range(l[0]):
k = list(map(int, input().split()))
I.append(k)
def segment(l):
return [int(i) for i in range(l[0],l[1]+1)]
def count_absent_point(l,I):
main = []
count_absent = 0
absent_num =[]
for i in I:
for j in segment(i):
main.append(j)
Set = set(main)
for i in range(1,l[1]+1):
if i not in Set:
count_absent += 1
absent_num.append(i)
if count_absent!=0:
print(count_absent)
for i in absent_num:
print(i, end= " ")
else:
print(0)
count_absent_point(l,I)
``` | output | 1 | 41,206 | 23 | 82,413 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,207 | 23 | 82,414 |
Tags: implementation
Correct Solution:
```
### 1015A
(n, m) = (int(_) for _ in input().split(' '))
points = set(range(1,m+1))
for _ in range(0, n):
(l, r) = (int(_) for _ in input().split(' '))
points = points - set(range(l, r + 1))
print(len(points))
print(' '.join(str(p) for p in points))
``` | output | 1 | 41,207 | 23 | 82,415 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,208 | 23 | 82,416 |
Tags: implementation
Correct Solution:
```
from sys import stdin, stdout
# string input
n, m = (stdin.readline().split())
n, m = int(n), int(m)
arr = []
for x in range(n):
a, b = stdin.readline().split()
arr.append((int(a), int(b)))
arr = sorted(arr, key=lambda x: x[0])
x = 1
i = 0
count = 0
ans = []
while(x <= m and i < n):
if(x >= arr[i][0] and x <= arr[i][1]):
x+=1
elif( x > arr[i][1]):
i+=1
else:
count += 1
ans.append(x)
x+=1
for x in range(x, m+1):
count +=1
ans.append(x)
print(count)
for i in range(len(ans)):
print(ans[i], end=' ')
``` | output | 1 | 41,208 | 23 | 82,417 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment. | instruction | 0 | 41,209 | 23 | 82,418 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
sp = [1] * (m+1)
sp[0] = 0
for _ in range(n):
l, r = map(int, input().split())
for i in range(l, r+1):
sp[i] = 0
print(sp.count(1))
for i in range(m+1):
if sp[i] == 1:
print(i, end=" ")
``` | output | 1 | 41,209 | 23 | 82,419 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
nm = list(map(int,input().split()))
segment = [0 for x in range(nm[1])]
for i in range(nm[0]):
temp = list(map(int,input().split()))
segment[temp[0]-1:temp[1]:1] = [1 for x in range(temp[1]-temp[0]+1)]
answer = [str(i+1) for i in range(nm[1]) if segment[i]==0]
print(len(answer))
print(" ".join(answer))
``` | instruction | 0 | 41,210 | 23 | 82,420 |
Yes | output | 1 | 41,210 | 23 | 82,421 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
n_m=input().split()
n=int(n_m[0])
m=int(n_m[1])
every_point=[*range(1,m+1)]
for i in range(n):
l_r=input().split()
l=int(l_r[0])
r=int(l_r[1])
check_point=[*range(l,r+1)]
for point in check_point:
try:
every_point.remove(point)
except ValueError:
pass
print(len(every_point))
every_point=[str(every_point[w]) for w in range(len(every_point))]
every_point=" ".join(every_point)
print(every_point)
``` | instruction | 0 | 41,211 | 23 | 82,422 |
Yes | output | 1 | 41,211 | 23 | 82,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
n, m = list(map(int, input().split(' ')))
c = set(range(1, m+1))
for i in range(n):
li, ri = list(map(int, input().split(' ')))
c -= set(range(li, ri+1))
print(len(c))
if len(c) > 0:
print(*c)
``` | instruction | 0 | 41,212 | 23 | 82,424 |
Yes | output | 1 | 41,212 | 23 | 82,425 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
n,m=map(int,input().split())
ml=[]
count=0
for i in range(1,m+1):
ml.append(i)
lo=[]
for i in range(n):
l,r=map(int,input().split())
for j in range(l,r+1):
lo.append(j)
ml = [i for i in ml if i not in lo]
print(len(ml))
print(*ml)
``` | instruction | 0 | 41,213 | 23 | 82,426 |
Yes | output | 1 | 41,213 | 23 | 82,427 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
def answer():
a = input().split()
a = [int(x) for x in a]
n = a[0]
high = a[1]
i=1
c=[]
low=1
z=[low]
i=low
while i<=high:
z.append(i)
i+=1
d=[]
for x in z:
if x not in d:
d.append(x)
if len(d)==0:
print(0)
done=1
else:
for x in c:
i=min(x)
while i<=max(x):
if i in d: d.remove(i)
i+=1
print(len(d))
c_out=""
i=0
while i<len(d):
c_out+=str(d[i])
if i!=len(d)-1:
c_out+=" "
i+=1
print(c_out)
answer()
``` | instruction | 0 | 41,214 | 23 | 82,428 |
No | output | 1 | 41,214 | 23 | 82,429 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
q, w = map(int, input().split())
e = [0] * (200)
for i in range(q):
r, t = map(int, input().split())
if r == t:
e[t] = 1
else:
for j in range(r, t + 1):
e[j] = 1
v = 0
b = []
for i in range(1, w):
if e[i] == 0:
v += 1
b.append(i)
print(v)
print(*b)
``` | instruction | 0 | 41,215 | 23 | 82,430 |
No | output | 1 | 41,215 | 23 | 82,431 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
n,m = map(int,input().strip().split(" "))
List = []
start = 1
MyList = []
for _ in range(n):
MyList.append(list(map(int,input().strip().split(" "))))
MyList.sort()
for e in MyList:
for i in range(start,e[0]):
List.append(i)
start = e[1]+1
for i in range(start,m+1):
List.append(i)
print(len(List))
print(*List)
``` | instruction | 0 | 41,216 | 23 | 82,432 |
No | output | 1 | 41,216 | 23 | 82,433 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints.
Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.
Input
The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.
The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.
Output
In the first line print one integer k — the number of points that don't belong to any segment.
In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.
If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.
Examples
Input
3 5
2 2
1 2
5 5
Output
2
3 4
Input
1 7
1 7
Output
0
Note
In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.
In the second example all the points from 1 to 7 belong to the first segment.
Submitted Solution:
```
#n = int(input())
n,m = map(int,input().split())
#s = input()
#a = list(map(int,input().split()))
a = []
for i in range(n):
x,y = map(int,input().split())
a.append((x,y))
a.append((-1,0))
a.append((m,m+1))
a.sort()
a.sort(key=lambda x: x[1] if x[1]!=x[0] else x[0])
#print(a)
res = []
for i in range(1,len(a)):
if a[i][0]>a[i-1][1]:
res+=list(range(a[i-1][1]+1,a[i][0]))
res = list(sorted(list(set(res))))
print(len(res))
print(*res)
``` | instruction | 0 | 41,217 | 23 | 82,434 |
No | output | 1 | 41,217 | 23 | 82,435 |
Provide a correct Python 3 solution for this coding contest problem.
Given are a positive integer N and a sequence of length 2^N consisting of 0s and 1s: A_0,A_1,\ldots,A_{2^N-1}. Determine whether there exists a closed curve C that satisfies the condition below for all 2^N sets S \subseteq \\{0,1,\ldots,N-1 \\}. If the answer is yes, construct one such closed curve.
* Let x = \sum_{i \in S} 2^i and B_S be the set of points \\{ (i+0.5,0.5) | i \in S \\}.
* If there is a way to continuously move the closed curve C without touching B_S so that every point on the closed curve has a negative y-coordinate, A_x = 1.
* If there is no such way, A_x = 0.
For instruction on printing a closed curve, see Output below.
Constraints
* 1 \leq N \leq 8
* A_i = 0,1 \quad (0 \leq i \leq 2^N-1)
* A_0 = 1
Input
Input is given from Standard Input in the following format:
N
A_0A_1 \cdots A_{2^N-1}
Output
If there is no closed curve that satisfies the condition, print `Impossible`.
If such a closed curve exists, print `Possible` in the first line. Then, print one such curve in the following format:
L
x_0 y_0
x_1 y_1
:
x_L y_L
This represents the closed polyline that passes (x_0,y_0),(x_1,y_1),\ldots,(x_L,y_L) in this order.
Here, all of the following must be satisfied:
* 0 \leq x_i \leq N, 0 \leq y_i \leq 1, and x_i, y_i are integers. (0 \leq i \leq L)
* |x_i-x_{i+1}| + |y_i-y_{i+1}| = 1. (0 \leq i \leq L-1)
* (x_0,y_0) = (x_L,y_L).
Additionally, the length of the closed curve L must satisfy 0 \leq L \leq 250000.
It can be proved that, if there is a closed curve that satisfies the condition in Problem Statement, there is also a closed curve that can be expressed in this format.
Examples
Input
1
10
Output
Possible
4
0 0
0 1
1 1
1 0
0 0
Input
2
1000
Output
Possible
6
1 0
2 0
2 1
1 1
0 1
0 0
1 0
Input
2
1001
Output
Impossible
Input
1
11
Output
Possible
0
1 1 | instruction | 0 | 42,664 | 23 | 85,328 |
"Correct Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N = int(readline())
A = list(map(int,readline().rstrip().decode()))
minimal_sets = []
for n in range(1<<N):
s = n
is_min = (A[n] == 0)
while s:
s = (s - 1) & n
if A[n] == 1 and A[s] == 0:
print('Impossible')
exit()
if A[s] == 0:
is_min = False
if is_min:
minimal_sets.append(n)
def make(nums, x):
if not nums:
return [(x,0)]
path = []
if len(nums) == 1:
n = nums[0]
for i in range(x, n+1):
path.append((i,0))
path += [(n+1,0),(n+1,1),(n,1),(n,0)]
for i in range(n-1,x-1,-1):
path.append((i,0))
return path
n = nums[0]
for i in range(x, n+1):
path.append((i,0))
P = make(nums[1:], n+1)
path += P
path += [(n,0), (n,1), (n+1,1), (n+1, 0)]
path += P[::-1][1:]
path += [(n+1,1), (n,1), (n,0)]
for i in range(n-1,x-1,-1):
path += [(i,0)]
return path
path = [(0,0)]
for n in minimal_sets:
path += make([i for i in range(N) if n & (1<<i)], 0)[1:]
print('Possible')
print(len(path) - 1)
print('\n'.join('{} {}'.format(x,y) for x,y in path))
``` | output | 1 | 42,664 | 23 | 85,329 |
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