message stringlengths 2 48.6k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 318 108k | cluster float64 8 8 | __index_level_0__ int64 636 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a building with n rooms, numbered 1 to n.
We can move from any room to any other room in the building.
Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).
Initially, there was one person in each room in the building.
After that, we know that there were exactly k moves happened up to now.
We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?
Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 3 \leq n \leq 2 \times 10^5
* 2 \leq k \leq 10^9
Input
Input is given from Standard Input in the following format:
n k
Output
Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).
Examples
Input
3 2
Output
10
Input
200000 1000000000
Output
607923868
Input
15 6
Output
22583772
Submitted Solution:
```
n,k = map(int, input().split())
if k%2==0:
f=0
else:
f=1
def modinv(a, mod=10**9+7):
return pow(a, mod-2, mod)
def fact_m(n, modulus=10**9+7):
ans=1
if n <= modulus//2:
for i in range(1,n+1):
ans = (ans * i) % modulus
else:
for i in range(1,modulus-n):
ans = (ans * i) % modulus
ans = modinv(ans, modulus)
if n % 2 == 0:
ans = -1*ans + modulus
return ans % modulus
ans=0
for i in range(f,k+1,2):
zs=i
os=n-i
sm=fact_m(zs+os) / (fact_m(zs)*fact_m(os))
sm *= (zs+os)
sm %= 10**9+7
ans+=sm
print(ans)
``` | instruction | 0 | 67,019 | 8 | 134,038 |
No | output | 1 | 67,019 | 8 | 134,039 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a building with n rooms, numbered 1 to n.
We can move from any room to any other room in the building.
Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).
Initially, there was one person in each room in the building.
After that, we know that there were exactly k moves happened up to now.
We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?
Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 3 \leq n \leq 2 \times 10^5
* 2 \leq k \leq 10^9
Input
Input is given from Standard Input in the following format:
n k
Output
Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).
Examples
Input
3 2
Output
10
Input
200000 1000000000
Output
607923868
Input
15 6
Output
22583772
Submitted Solution:
```
n, k = map(int, input().split())
#割り算のやーつ
MOD = 1000000007
# 二項係数関連.
class COM():
def __init__(self, MAX, MOD):
self.MOD = MOD
self.MAX = MAX
self.fac = [1] * MAX
self.finv = [1] * MAX
inv = [1] * MAX
for i in range(2, MAX):
self.fac[i] = self.fac[i - 1] * i % MOD
inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
self.finv[i] = self.finv[i - 1] * inv[i] % MOD
def calc_COM(self, n, k):
if n < k:
return 0
if n < 0 or k < 0:
return 0
if self.MAX <= n:
return 0
return self.fac[n] * (self.finv[k] * self.finv[n - k] % self.MOD) % self.MOD
def calc_PER(self, n, k):
if n < k:
return 0
if n < 0 or k < 0:
return 0
if self.MAX <= n:
return 0
return self.fac[n] * self.finv[n - k] % self.MOD
def calc_FAC(self, n):
if self.MAX <= n:
return 0
return self.fac[n]
com = COM(n * 2, MOD)
if(k == 1):
# 0となる部屋と2となる部屋がそれぞれある.組み合わせ.
print((n * (n - 1)) % MOD)
elif(n-1 <= k):
# すべての組み合わせがあり得る.
print(com.calc_COM(n*2-1, n) % MOD)
else:
# 動けない人たちが現れる.
# ∴0人の部屋は必ずk以下.逆も成り立つ.
# この時、0人となる部屋をn-k(=r)以下で選び、そのそれぞれについて、rの部屋での移動パターンがどれだけあるかを求めればよい
ans = 1 # 0人となる部屋が0の場合.1通り.
for r in range(1, k + 1):
ans += (com.calc_COM(n, r) * com.calc_COM(n - 1, r)) % MOD
print(ans)
``` | instruction | 0 | 67,020 | 8 | 134,040 |
No | output | 1 | 67,020 | 8 | 134,041 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,069 | 8 | 134,138 |
"Correct Solution:
```
a,b = map(int,input().split())
print(((1+(b-a))*(b-a))//2-b)
``` | output | 1 | 67,069 | 8 | 134,139 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,070 | 8 | 134,140 |
"Correct Solution:
```
a,b=map(int,input().split())
print(sum(_ for _ in range(b-a+1))-b)
``` | output | 1 | 67,070 | 8 | 134,141 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,071 | 8 | 134,142 |
"Correct Solution:
```
a, b = map(int, input().split())
print(((b-a-1)*(b-a))//2-a)
``` | output | 1 | 67,071 | 8 | 134,143 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,072 | 8 | 134,144 |
"Correct Solution:
```
a, b = map(int, input().split())
d = b-a
print((d+1)*d//2 - b)
``` | output | 1 | 67,072 | 8 | 134,145 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,073 | 8 | 134,146 |
"Correct Solution:
```
a,b = map(int,input().split())
print((b-a+1)*(b-a)//2-b)
``` | output | 1 | 67,073 | 8 | 134,147 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,074 | 8 | 134,148 |
"Correct Solution:
```
a,b=map(int,input().split());a-=b;print(~-a*a//2-b)
``` | output | 1 | 67,074 | 8 | 134,149 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,075 | 8 | 134,150 |
"Correct Solution:
```
a,b=map(int,input().split())
k=b-a
print(-~k*k//2-b)
``` | output | 1 | 67,075 | 8 | 134,151 |
Provide a correct Python 3 solution for this coding contest problem.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1 | instruction | 0 | 67,076 | 8 | 134,152 |
"Correct Solution:
```
a,b = map(int,input().split())
c = b-a
s = (1+c)*c//2
print(s-b)
``` | output | 1 | 67,076 | 8 | 134,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a, b = map(int, input().split())
d = b-a
r = d*(d+1)//2-b
print(r)
``` | instruction | 0 | 67,077 | 8 | 134,154 |
Yes | output | 1 | 67,077 | 8 | 134,155 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a,b = map(int,input().split())
print(sum(range(b-a+1))-b)
``` | instruction | 0 | 67,078 | 8 | 134,156 |
Yes | output | 1 | 67,078 | 8 | 134,157 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a,b=map(int,input().split())
s=(1+b-a)*(b-a)//2
print(s-b)
``` | instruction | 0 | 67,079 | 8 | 134,158 |
Yes | output | 1 | 67,079 | 8 | 134,159 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a,b=map(int,input().split())
d=b-a
print((d*(d+1)//2)-b)
``` | instruction | 0 | 67,080 | 8 | 134,160 |
Yes | output | 1 | 67,080 | 8 | 134,161 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a, b = map(int, input())
n = b - a
original_b = n * (n + 1) // 2
print(original_b - b)
``` | instruction | 0 | 67,081 | 8 | 134,162 |
No | output | 1 | 67,081 | 8 | 134,163 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
[a,b] = list(map(int,input().split()))
tou = []
dam=0
for i in range(1,1000):
dam +=i
tou.append(dam)
for ans in range(1,10000):
west, east = a+ans, b+ans
for j in range(998):
if west==tou[j] and east==tou[j+1]:
# print("west,wast,j,ans", west,east,j,ans)
out=ans
break
print(out)
``` | instruction | 0 | 67,082 | 8 | 134,164 |
No | output | 1 | 67,082 | 8 | 134,165 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a,b=map(int,input().split())
l=[]
e=b-a
k=0
for i in range(999):
k+=i
l.append(k)
for j in range(998):
o=l[j+1]-l[j]
if(o==e):
print(l[j]-a)
else:
continue
``` | instruction | 0 | 67,083 | 8 | 134,166 |
No | output | 1 | 67,083 | 8 | 134,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In some village, there are 999 towers that are 1,(1+2),(1+2+3),...,(1+2+3+...+999) meters high from west to east, at intervals of 1 meter.
It had been snowing for a while before it finally stopped. For some two adjacent towers located 1 meter apart, we measured the lengths of the parts of those towers that are not covered with snow, and the results are a meters for the west tower, and b meters for the east tower.
Assuming that the depth of snow cover and the altitude are the same everywhere in the village, find the amount of the snow cover.
Assume also that the depth of the snow cover is always at least 1 meter.
Constraints
* 1 \leq a < b < 499500(=1+2+3+...+999)
* All values in input are integers.
* There is no input that contradicts the assumption.
Input
Input is given from Standard Input in the following format:
a b
Output
If the depth of the snow cover is x meters, print x as an integer.
Examples
Input
8 13
Output
2
Input
54 65
Output
1
Submitted Solution:
```
a,b=map(int,input().split())
diff=0
c=0
d=0
g=0
for i in range(1,1000):
num=(i*(i+1))//2
if(num>=a and num<=b and g==0):
c=num
g=1
if(num>=b):
d=num
break
print(c-a)
``` | instruction | 0 | 67,084 | 8 | 134,168 |
No | output | 1 | 67,084 | 8 | 134,169 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,195 | 8 | 134,390 |
"Correct Solution:
```
import sys
import math
datasets = []
ans = []
while 1:
n = int(input())
if n == 0:
break
datasets.append(n)
for n in datasets:
facts = []
for x in range(1, int((math.sqrt(2*n)))+1 ):
if 2*n%x == 0:
facts.append(x)
for x in reversed(facts):
y = 2*n // x
if (y-x)%2 == 1:
ans.append((x, y))
break
for i in range(len(datasets)):
x = ans[i][0]
y = ans[i][1]
print("{} {}".format((y-x+1)//2, x))
``` | output | 1 | 67,195 | 8 | 134,391 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,196 | 8 | 134,392 |
"Correct Solution:
```
while True:
b = int(input())
if b == 0:break
x = b * 2
for k in range(int(x ** (1 / 2)), 0, -1):
if x % k == 0:
if (-k + 1 + (x // k)) % 2 == 0:
a = (-k + 1 + x // k) // 2
if a > 0:
print(a, k)
break
``` | output | 1 | 67,196 | 8 | 134,393 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,197 | 8 | 134,394 |
"Correct Solution:
```
while True:
b = int(input())
if b == 0:
break
n = 1
ans = []
while True:
# print(n)
if n % 2 == 0:
if b % n != 0:
if b // n >= n // 2:
if (b / n * 10) % 5 == 0:
ans = [b // n - n // 2 + 1, n]
else:
break
else:
if b % n == 0:
if b // n - 1 >= (n - 1) // 2:
ans = [b // n - 1 - (n - 1) // 2 + 1, n]
else:
break
n += 1
# print(ans)
print(ans[0], ans[1])
``` | output | 1 | 67,197 | 8 | 134,395 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,198 | 8 | 134,396 |
"Correct Solution:
```
ans_list = []
while True:
b = int(input())
if b == 0:
break
h = 1
ans = -1
while h*(h-1)//2 <= b:
if (b- h*(h-1)//2) % h == 0:
n = (b- h*(h-1)//2) // h
if n >= 1:
ans = "{} {}".format(n, h)
h += 1
ans_list.append(ans)
for ans in ans_list:
print(ans)
``` | output | 1 | 67,198 | 8 | 134,397 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,199 | 8 | 134,398 |
"Correct Solution:
```
import math
def main(n):
for i in range(int((1 + math.sqrt(1 + 8 * n)) // 2) + 1, 0, -1):
if float.is_integer(n / i - (i - 1) / 2) and n / i - (i - 1) / 2 > 0:
print(int(n / i - (i - 1) / 2), i)
return
while 1:
n = int(input())
if n == 0:
break
main(n)
``` | output | 1 | 67,199 | 8 | 134,399 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,200 | 8 | 134,400 |
"Correct Solution:
```
ans = []
while 1:
b = int(input())
if b == 0:
break
x = 1
res = (1, 1)
while x*x <= b:
if b % x == 0:
y = b // x
if x % 2 == 1:
if y - x//2 >= 1:
res = max(res, (x, y - x//2))
if x//2 - y + 1 >= 1:
res = max(res, (2*y, x//2 - y + 1))
if y % 2 == 1:
if x - y//2 >= 1:
res = max(res, (y, x - y//2))
if y//2 - x + 1 >= 1:
res = max(res, (2*x, y//2 - x + 1))
x += 1
b, a = res
ans.append("%d %d" % (a, b))
print(*ans, sep='\n')
``` | output | 1 | 67,200 | 8 | 134,401 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,201 | 8 | 134,402 |
"Correct Solution:
```
import math
while True:
b = int(input())
if b == 0:
break
k_max = int(((-1 + math.sqrt(1 + 8 * b)) / 2))
for k in range(k_max, 0, -1):
if 2 * b % k == 0 and (2 * b / k + 1 - k) % 2 == 0:
n = int((2 * b / k + 1 - k) / 2)
print("{} {}".format(n, k))
break
``` | output | 1 | 67,201 | 8 | 134,403 |
Provide a correct Python 3 solution for this coding contest problem.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994 | instruction | 0 | 67,202 | 8 | 134,404 |
"Correct Solution:
```
import re
import sys
import math
import itertools
from sys import stdin
def main():
"""
解答をこちらに
"""
while 1:
b = int(input())
if b==0:
return
ans1 = b
ans2 = 1
for l in range(1, b+1):
p = (b - l *(l-1)/2 )/l
if p <1:
break
if p % 1==0:
ans1 = int(p)
ans2 = l
print(ans1, ans2)
if __name__ == "__main__":
main()
``` | output | 1 | 67,202 | 8 | 134,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
import math
def main(b):
if b == 0:
return False
for n in range(int(math.sqrt(2*b)), 0, -1):
if 2*b % n == 0:
a = (-n*n + n + 2 * b)/(2*n)
if a >= 1 and a.is_integer():
print(int(a), n)
return True
while main(int(input())):
pass
``` | instruction | 0 | 67,203 | 8 | 134,406 |
Yes | output | 1 | 67,203 | 8 | 134,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
#2005_c
"""
n = int(input())
k = list("mcxi")
for i in range(n):
d = {"m":0,"c":0,"x":0,"i":0}
a,b = input().split()
a = list(a)
b = list(b)
a.insert(0,1)
b.insert(0,1)
for j in range(1,len(a)):
if a[j] in k:
if a[j-1] in k:
d[a[j]] += 1
else:
d[a[j]] += int(a[j-1])
for j in range(1,len(b))[::-1]:
if b[j] in k:
if b[j-1] in k:
d[b[j]] += 1
else:
d[b[j]] += int(b[j-1])
if d[b[j]] >= 10:
l = b[j]
while d[l] >= 10:
d[l] -= 10
l = k[k.index(l)-1]
d[l] += 1
for j in k:
if d[j]:
if d[j] == 1:
print(j,end = "")
else:
print(str(d[j])+j,end = "")
print()
"""
#2017_c
"""
while 1:
h, w = map(int, input().split())
if h == w == 0:
break
s = [list(map(int, input().split())) for i in range(h)]
ans = 0
for u in range(h):
for d in range(u+2,h):
for l in range(w):
for r in range(l+2,w):
m = float("inf")
for i in range(u,d+1):
m = min(m,s[i][l],s[i][r])
for i in range(l,r+1):
m = min(m,s[u][i],s[d][i])
f = 1
su = 0
for i in range(u+1,d):
for j in range(l+1,r):
su += (m-s[i][j])
if s[i][j] >= m:
f = 0
break
if not f:
break
if f:
ans = max(ans,su)
print(ans)
"""
#2016_c
"""
while 1:
m,n = map(int, input().split())
if m == n == 0:
break
d = {}
ma = 7368791
for i in range(m,ma+1):
d[i] = 1
z = m
for i in range(n):
for j in range(z,ma+1):
if d[j]:
z = j
break
j = 1
while z*j <= ma:
d[z*j] = 0
j += 1
for j in range(z,ma+1):
if d[j]:
print(j)
break
"""
#2018_c
def factorize(n):
if n < 4:
return [1,n]
i = 2
l = [1]
while i**2 <= n:
if n%i == 0:
l.append(i)
if n//i != i:
l.append(n//i)
i += 1
l.append(n)
l.sort()
return l
while 1:
b = int(input())
if b == 0:
break
f = factorize(2*b)
for n in f[::-1]:
a = 1-n+(2*b)//n
if a >= 1 and a%2 == 0:
print(a//2,n)
break
``` | instruction | 0 | 67,204 | 8 | 134,408 |
Yes | output | 1 | 67,204 | 8 | 134,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
import sys
def resolve(buget,num):
return ((((2*buget)/num)-num+1)/2)
for buget in sys.stdin:
buget = int(buget)
if buget == 0 :
break
num = 1
answer_floor = 1
answer_num = 1
answer = 0
while (num*num)/2 < buget :
#num を増やしていって、aの解が整数になるかをチェックする
answer = resolve(buget,num)
if answer.is_integer():
answer_floor = answer
answer_num = num
num = num + 1
print(str(int(answer_floor)) + " " + str(answer_num))
``` | instruction | 0 | 67,205 | 8 | 134,410 |
Yes | output | 1 | 67,205 | 8 | 134,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
from math import sqrt
def solve(B):
ans = 0
for L in range(1,int(sqrt(1+8*B))+2):
# print(L)
a = (2*B+L*L-L)
b = (2*L)
if(a%b==0):
u = a//b
d = u - L + 1
if(1<=d<=u):
# print(":",d,u)
ans = L
ans_d = d
print(ans_d,ans)
def main():
while(True):
N=int(input())
if(N):
solve(N)
else:
break
if __name__ == "__main__":
main()
``` | instruction | 0 | 67,206 | 8 | 134,412 |
Yes | output | 1 | 67,206 | 8 | 134,413 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
while True:
money=int(input())
high = 1
low = 1
if money==0:
break
sum = low
while True:
if sum==money:
print (str(low)+" "+str(high-low+1))
break
elif sum>money:
low+=1
high=low+1
sum=high+low
if money==low:
print (str(low)+" 1" )
break
else:
high+=1
sum+=high
``` | instruction | 0 | 67,207 | 8 | 134,414 |
No | output | 1 | 67,207 | 8 | 134,415 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
while True:
money=int(input())
high = 1
low = 1
if money==0:
break
sum = low
while True:
if sum==money:
print (str(low)+" "+str(high-low+1))
break
elif sum>money:
low+=1
high=low+1
sum=high+low
if money==low:
print (str(low)+" 1" )
break
elif sum<money:
high+=1
sum+=high
``` | instruction | 0 | 67,208 | 8 | 134,416 |
No | output | 1 | 67,208 | 8 | 134,417 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
while True:
money=int(input())
high = 1
low = 1
if money==0:
break
sum = low
while True:
if sum==money:
print (str(low)+" "+str(high-low+1))
break
elif sum>money:
low+=1
high=low+1
sum=high+low
if money==low:
print (str(low)+" 1" )
break
else:
high+=1
assert isinstance(high, object)
sum+=high
``` | instruction | 0 | 67,209 | 8 | 134,418 |
No | output | 1 | 67,209 | 8 | 134,419 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Skyscraper "MinatoHarukas"
Mr. Port plans to start a new business renting one or more floors of the new skyscraper with one giga floors, MinatoHarukas. He wants to rent as many vertically adjacent floors as possible, because he wants to show advertisement on as many vertically adjacent windows as possible. The rent for one floor is proportional to the floor number, that is, the rent per month for the n-th floor is n times that of the first floor. Here, the ground floor is called the first floor in the American style, and basement floors are out of consideration for the renting. In order to help Mr. Port, you should write a program that computes the vertically adjacent floors satisfying his requirement and whose total rental cost per month is exactly equal to his budget.
For example, when his budget is 15 units, with one unit being the rent of the first floor, there are four possible rent plans, 1+2+3+4+5, 4+5+6, 7+8, and 15. For all of them, the sums are equal to 15. Of course in this example the rent of maximal number of the floors is that of 1+2+3+4+5, that is, the rent from the first floor to the fifth floor.
Input
The input consists of multiple datasets, each in the following format.
> b
>
A dataset consists of one line, the budget of Mr. Port b as multiples of the rent of the first floor. b is a positive integer satisfying 1 < b < 109.
The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 1000.
Output
For each dataset, output a single line containing two positive integers representing the plan with the maximal number of vertically adjacent floors with its rent price exactly equal to the budget of Mr. Port. The first should be the lowest floor number and the second should be the number of floors.
Sample Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output for the Sample Input
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Example
Input
15
16
2
3
9699690
223092870
847288609
900660121
987698769
999999999
0
Output
1 5
16 1
2 1
1 2
16 4389
129 20995
4112949 206
15006 30011
46887 17718
163837 5994
Submitted Solution:
```
while True:
money=int(input())
high = 1
low = 1
if money==0:
break
sum = low
while True:
if sum==money:
print (str(low)+" "+str(high-low+1))
break
elif sum>money:
low+=1
high=low+1
sum=high+low
if money==low:
print (str(low)+" "+str(low-low+1) )
break
elif sum<money:
high+=1
sum+=high
``` | instruction | 0 | 67,210 | 8 | 134,420 |
No | output | 1 | 67,210 | 8 | 134,421 |
Provide a correct Python 3 solution for this coding contest problem.
Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to gain dexterity that never mistypes by carefully stacking blocks. Since there are many building blocks, let's build a tall tower.
There are N blocks, and the i-th (1 ≤ i ≤ N) building blocks are in the shape of a rectangular parallelepiped of 1 x Ai x Bi. The side of length 1 is used in the depth direction, and the sides of lengths Ai and Bi are assigned one by one in the horizontal direction and one in the height direction. When building blocks, the upper building blocks must be exactly shorter in width than the lower building blocks. The blocks can be used in any order, and some blocks may not be used. Under these restrictions, I want to make the tallest tower that can be built.
Input
N
A1 B1
...
AN BN
Satisfy 1 ≤ N ≤ 1,000, 1 ≤ Ai, Bi ≤ 1,000,000. All input values are integers.
Output
Output the maximum height of the tower on one line.
Examples
Input
3
10 40
10 40
20 30
Output
80
Input
4
1 2
2 3
3 4
4 1
Output
11 | instruction | 0 | 67,211 | 8 | 134,422 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
class Edge():
def __init__(self,t,f,r,ca,co):
self.to = t
self.fron = f
self.rev = r
self.cap = ca
self.cost = co
class MinCostFlow():
size = 0
graph = []
def __init__(self, s):
self.size = s
self.graph = [[] for _ in range(s)]
def add_edge(self, f, t, ca, co):
self.graph[f].append(Edge(t, f, len(self.graph[t]), ca, co))
self.graph[t].append(Edge(f, t, len(self.graph[f])-1, 0, -co))
def min_path(self, s, t):
dist = [inf] * self.size
route = [None] * self.size
que = collections.deque()
inq = [False] * self.size
dist[s] = 0
que.append(s)
inq[s] = True
while que:
u = que.popleft()
inq[u] = False
for e in self.graph[u]:
if e.cap == 0:
continue
v = e.to
if dist[v] > dist[u] + e.cost:
dist[v] = dist[u] + e.cost
route[v] = e
if not inq[v]:
que.append(v)
inq[v] = True
if dist[t] == inf:
return inf
flow = inf
v = t
while v != s:
e = route[v]
if flow > e.cap:
flow = e.cap
v = e.fron
c = 0
v = t
while v != s:
e = route[v]
e.cap -= flow
self.graph[e.to][e.rev].cap += flow
c += e.cost * flow
v = e.fron
return dist[t]
def calc_min_cost_flow(self, s, t, flow):
total_cost = 0
for i in range(flow):
c = self.min_path(s, t)
if c == inf:
return c
total_cost += c
return total_cost
def main():
n = I()
mcf = MinCostFlow(4096)
s = 4094
t = 4095
for i in range(n):
mcf.add_edge(s, i, 1, 0)
mcf.add_edge(i, 4093, 1, 0)
a = []
b = []
ss = set()
for _ in range(n):
ai,bi = LI()
a.append(ai)
b.append(bi)
ss.add(ai)
ss.add(bi)
d = {}
for i,v in zip(range(len(ss)), sorted(ss)):
d[v] = i + n
mcf.add_edge(i+n, t, 1, 0)
mcf.add_edge(4093, t, inf, 0)
for i in range(n):
mcf.add_edge(i, d[a[i]], 1, -b[i])
mcf.add_edge(i, d[b[i]], 1, -a[i])
res = mcf.calc_min_cost_flow(s, t, n)
return -res
print(main())
``` | output | 1 | 67,211 | 8 | 134,423 |
Provide a correct Python 3 solution for this coding contest problem.
Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to gain dexterity that never mistypes by carefully stacking blocks. Since there are many building blocks, let's build a tall tower.
There are N blocks, and the i-th (1 ≤ i ≤ N) building blocks are in the shape of a rectangular parallelepiped of 1 x Ai x Bi. The side of length 1 is used in the depth direction, and the sides of lengths Ai and Bi are assigned one by one in the horizontal direction and one in the height direction. When building blocks, the upper building blocks must be exactly shorter in width than the lower building blocks. The blocks can be used in any order, and some blocks may not be used. Under these restrictions, I want to make the tallest tower that can be built.
Input
N
A1 B1
...
AN BN
Satisfy 1 ≤ N ≤ 1,000, 1 ≤ Ai, Bi ≤ 1,000,000. All input values are integers.
Output
Output the maximum height of the tower on one line.
Examples
Input
3
10 40
10 40
20 30
Output
80
Input
4
1 2
2 3
3 4
4 1
Output
11 | instruction | 0 | 67,212 | 8 | 134,424 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7
class MinCostFlow:
""" 最小費用流(ダイクストラ版)：O(F*E*logV) """
INF = 10 ** 18
def __init__(self, N):
self.N = N
self.G = [[] for i in range(N)]
def add_edge(self, fr, to, cap, cost):
G = self.G
G[fr].append([to, cap, cost, len(G[to])])
G[to].append([fr, 0, -cost, len(G[fr])-1])
def flow(self, s, t, f):
from heapq import heappush, heappop
N = self.N; G = self.G
INF = MinCostFlow.INF
res = 0
H = [0] * N
prv_v = [0] * N
prv_e = [0] * N
while f:
dist = [INF] * N
dist[s] = 0
que = [(0, s)]
while que:
c, v = heappop(que)
if dist[v] < c:
continue
for i, (to, cap, cost, _) in enumerate(G[v]):
if cap > 0 and dist[to] > dist[v] + cost + H[v] - H[to]:
dist[to] = r = dist[v] + cost + H[v] - H[to]
prv_v[to] = v; prv_e[to] = i
heappush(que, (r, to))
if dist[t] == INF:
return INF
for i in range(N):
H[i] += dist[i]
d = f; v = t
while v != s:
d = min(d, G[prv_v[v]][prv_e[v]][1])
v = prv_v[v]
f -= d
res += d * H[t]
v = t
while v != s:
e = G[prv_v[v]][prv_e[v]]
e[1] -= d
G[v][e[3]][1] += d
v = prv_v[v]
return res
def compress(S):
""" 座標圧縮 """
zipped, unzipped = {}, {}
for i, a in enumerate(sorted(S)):
zipped[a] = i
unzipped[i] = a
return zipped, unzipped
N = INT()
S = set()
AB = []
for i in range(N):
a, b = MAP()
AB.append((a, b))
S.add(a)
S.add(b)
zipped, unzipped = compress(S)
M = len(zipped)
mcf = MinCostFlow(N+M+2)
s = N + M
t = N + M + 1
# 負コストを避けるための調整用
MAX = 10 ** 6
# 積み木iをどう使うか
for i, (a, b) in enumerate(AB):
# 始点 -> 各積み木
mcf.add_edge(s, i, 1, 0)
# 積み木iを幅a,高さbに使う
mcf.add_edge(i, N+zipped[a], 1, MAX-b)
# 積み木iを幅b,高さaに使う
mcf.add_edge(i, N+zipped[b], 1, MAX-a)
# 積み木を使わない場合の辺
mcf.add_edge(s, t, N, MAX)
for i in range(M):
# ある幅 -> 終点
mcf.add_edge(N+i, t, 1, 0)
res = MAX * N - mcf.flow(s, t, N)
print(res)
``` | output | 1 | 67,212 | 8 | 134,425 |
Provide a correct Python 3 solution for this coding contest problem.
Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to gain dexterity that never mistypes by carefully stacking blocks. Since there are many building blocks, let's build a tall tower.
There are N blocks, and the i-th (1 ≤ i ≤ N) building blocks are in the shape of a rectangular parallelepiped of 1 x Ai x Bi. The side of length 1 is used in the depth direction, and the sides of lengths Ai and Bi are assigned one by one in the horizontal direction and one in the height direction. When building blocks, the upper building blocks must be exactly shorter in width than the lower building blocks. The blocks can be used in any order, and some blocks may not be used. Under these restrictions, I want to make the tallest tower that can be built.
Input
N
A1 B1
...
AN BN
Satisfy 1 ≤ N ≤ 1,000, 1 ≤ Ai, Bi ≤ 1,000,000. All input values are integers.
Output
Output the maximum height of the tower on one line.
Examples
Input
3
10 40
10 40
20 30
Output
80
Input
4
1 2
2 3
3 4
4 1
Output
11 | instruction | 0 | 67,213 | 8 | 134,426 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
write = sys.stdout.write
from heapq import heappush, heappop
class MinCostFlow:
INF = 10**18
def __init__(self, N):
self.N = N
self.G = [[] for i in range(N)]
def add_edge(self, fr, to, cap, cost):
forward = [to, cap, cost, None]
backward = forward[3] = [fr, 0, -cost, forward]
self.G[fr].append(forward)
self.G[to].append(backward)
def flow(self, s, t, f):
N = self.N; G = self.G
INF = MinCostFlow.INF
res = 0
H = [0]*N
prv_v = [0]*N
prv_e = [None]*N
d0 = [INF]*N
dist = [INF]*N
while f:
dist[:] = d0
dist[s] = 0
que = [(0, s)]
while que:
c, v = heappop(que)
if dist[v] < c:
continue
r0 = dist[v] + H[v]
for e in G[v]:
w, cap, cost, _ = e
if cap > 0 and r0 + cost - H[w] < dist[w]:
dist[w] = r = r0 + cost - H[w]
prv_v[w] = v; prv_e[w] = e
heappush(que, (r, w))
if dist[t] == INF:
return None
for i in range(N):
H[i] += dist[i]
d = f; v = t
while v != s:
d = min(d, prv_e[v][1])
v = prv_v[v]
f -= d
res += d * H[t]
v = t
while v != s:
e = prv_e[v]
e[1] -= d
e[3][1] += d
v = prv_v[v]
return res
def solve():
N = int(readline())
P = [list(map(int, readline().split())) for i in range(N)]
s = set()
for a, b in P:
s.add(a); s.add(b)
S = sorted(s)
M = len(S)
mp = {e: i for i, e in enumerate(S)}
mcf = MinCostFlow(N+M+2)
for i in range(M):
mcf.add_edge(N+i, N+M+1, 1, 0)
for i, (a, b) in enumerate(P):
mcf.add_edge(N+M, i, 1, 0)
mcf.add_edge(i, N+M+1, 1, 0)
mcf.add_edge(i, N+mp[a], 1, -b)
mcf.add_edge(i, N+mp[b], 1, -a)
write("%d\n" % -mcf.flow(N+M, N+M+1, N))
solve()
``` | output | 1 | 67,213 | 8 | 134,427 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
a1=[]
n1=int(input())
n=0
for i in range(n1):
a,b=map(int,input().split())
n=int(abs(b-a)/5)
if abs(b-a)%5!=0:
if abs(b-a)%5 <=2:
n=n+1
else:
n=n+2
a1.append(n)
for i in range(n1):
print(a1[i])
``` | instruction | 0 | 67,397 | 8 | 134,794 |
Yes | output | 1 | 67,397 | 8 | 134,795 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
x=int(input())
for i in range(x):
x,y=map(int,input().split())
c=abs(x-y)
a=c//5
b=(c-(a*5))//2
d=(c-(a*5))%2
print(a+b+d)
``` | instruction | 0 | 67,398 | 8 | 134,796 |
Yes | output | 1 | 67,398 | 8 | 134,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
n = int(input())
for i in range(n):
count = 0
a, b = map(int, input().split(' '))
c = abs(a-b)
temp = int(c / 5)
count += temp
c -= temp * 5
temp = int(c / 2)
count += temp
c -= temp * 2
temp = int(c / 1)
count += temp
c -= temp * 1
print(abs(count))
``` | instruction | 0 | 67,399 | 8 | 134,798 |
Yes | output | 1 | 67,399 | 8 | 134,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
n=int(input())
for i in range(n):
r,s=map(int,input().split())
t=abs(r-s)
p=t//5
y=t%5
o=y//2
u=y%2
v=u//1
x=u%1
print(p+v+x+o)
``` | instruction | 0 | 67,400 | 8 | 134,800 |
Yes | output | 1 | 67,400 | 8 | 134,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
import math
from collections import *
from functools import reduce
import sys
input = sys.stdin.readline
def factors(n):
return set(reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def li():return [int(i) for i in input().rstrip('\n').split(' ')]
def st():return input().rstrip('\n')
def val():return int(input())
for _ in range(val()):
a, b = li()
tot = 0
ans = abs(a - b)
if a<b:
s = [[a,0]]
if a:
s.append([a-1,1])
if a>1:
s.append([a-2,1])
s.append([a+1,1])
s.append([a+2,1])
for i in s:
if abs(b - i[0])%5 == 0:
ans = min(ans,(b - i[0])//5 + i[1])
if abs(b - i[0])%2 == 0:
ans = min(ans,(b - i[0])//2 + i[1])
else:
s = [[a,0]]
s.append([a-1,1])
s.append([a-2,1])
s.append([a+1,1])
s.append([a+2,1])
for i in s:
if i[0] >= 0:
if not (i[0] - b)%5:ans = min(ans,(i[0] - b)//5 + i[1])
if not (i[0] - b)%2:ans = min(ans,(i[0] - b)//2 + i[1])
print(ans)
``` | instruction | 0 | 67,401 | 8 | 134,802 |
No | output | 1 | 67,401 | 8 | 134,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob watches TV every day. He always sets the volume of his TV to b. However, today he is angry to find out someone has changed the volume to a. Of course, Bob has a remote control that can change the volume.
There are six buttons (-5, -2, -1, +1, +2, +5) on the control, which in one press can either increase or decrease the current volume by 1, 2, or 5. The volume can be arbitrarily large, but can never be negative. In other words, Bob cannot press the button if it causes the volume to be lower than 0.
As Bob is so angry, he wants to change the volume to b using as few button presses as possible. However, he forgets how to do such simple calculations, so he asks you for help. Write a program that given a and b, finds the minimum number of presses to change the TV volume from a to b.
Input
Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 1 000). Then the descriptions of the test cases follow.
Each test case consists of one line containing two integers a and b (0 ≤ a, b ≤ 10^{9}) — the current volume and Bob's desired volume, respectively.
Output
For each test case, output a single integer — the minimum number of presses to change the TV volume from a to b. If Bob does not need to change the volume (i.e. a=b), then print 0.
Example
Input
3
4 0
5 14
3 9
Output
2
3
2
Note
In the first example, Bob can press the -2 button twice to reach 0. Note that Bob can not press -5 when the volume is 4 since it will make the volume negative.
In the second example, one of the optimal ways for Bob is to press the +5 twice, then press -1 once.
In the last example, Bob can press the +5 once, then press +1.
Submitted Solution:
```
for _ in range(int(input())):
a, b = map(int,input().split())
dif = abs(b-a)
ans = dif % 5
if ans == 4 or ans == 3:
print(ans//5 + 2)
elif ans == 2 or ans == 1:
print(ans//5 + 1)
else:
print(ans//5)
``` | instruction | 0 | 67,403 | 8 | 134,806 |
No | output | 1 | 67,403 | 8 | 134,807 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,410 | 8 | 134,820 |
Tags: data structures, geometry, greedy
Correct Solution:
```
import sys
input = sys.stdin.buffer.readline
def main():
n = int(input())
a = list(map(int,input().split()))
stack = []
for i in a:
nnew = 1
while stack and stack[-1][0] >= i/nnew:
val,num = stack.pop()
i += val*num
nnew += num
stack.append((i/nnew,nnew))
if len(stack) == n:
print(*a,sep="\n")
exit()
for val,num in stack:
opt = str(round(val,9))+"\n"
sys.stdout.write(opt*num)
main()
``` | output | 1 | 67,410 | 8 | 134,821 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,411 | 8 | 134,822 |
Tags: data structures, geometry, greedy
Correct Solution:
```
N = int(input())
l = list(map(int, input().strip().split()))
q = [(0, 0)] * N
idx = 0
for x in reversed(l):
xn = x
xd = 1
while idx:
n, d = q[idx - 1]
if xn * d < n * xd:
break
q[idx - 1] = (0, 0)
xn += n
xd += d
idx -= 1
q[idx] = (xn, xd)
idx += 1
for xn, xd in reversed(q):
if not xd:
continue
s = f"{xn / xd:.10f}"
for _ in range(xd):
print(s)
``` | output | 1 | 67,411 | 8 | 134,823 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,412 | 8 | 134,824 |
Tags: data structures, geometry, greedy
Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
# sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7
N = INT()
A = LIST()
stack = [(A[0], 1)]
for i, a in enumerate(A[1:], 1):
stack.append((a, 1))
while len(stack) >= 2 and stack[-2][0] > stack[-1][0]:
a1, cnt1 = stack.pop()
a2, cnt2 = stack.pop()
merged = (a1*cnt1+a2*cnt2) / (cnt1+cnt2)
stack.append((merged, cnt1+cnt2))
ans = []
for a, cnt in stack:
print((str(a) + '\n') * cnt, end='')
``` | output | 1 | 67,412 | 8 | 134,825 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,413 | 8 | 134,826 |
Tags: data structures, geometry, greedy
Correct Solution:
```
import sys
input = sys.stdin.readline
n=int(input())
A=tuple(map(int,input().split()))
W=[]
for a in A:
W.append((a,1))
while len(W)>=2 and W[-2][0]*W[-1][1]>W[-1][0]*W[-2][1]:
x,y=W.pop()
z,w=W.pop()
W.append((x+z,y+w))
for x,y in W:
sys.stdout.write((str(x/y)+"\n")*y)
``` | output | 1 | 67,413 | 8 | 134,827 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,414 | 8 | 134,828 |
Tags: data structures, geometry, greedy
Correct Solution:
```
def main():
from sys import stdin,stdout
ans = []
stdin.readline()
for ai in map(int, map(int, stdin.readline().split())):
cnt=1
while ans and ai*ans[-1][0]<=ans[-1][1]*cnt:
c, r = ans.pop()
ai+=r
cnt+=c
ans.append((cnt, ai))
for i, res in ans:
m = str(res/i)
stdout.write((m+"\n")*i)
main()
``` | output | 1 | 67,414 | 8 | 134,829 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,415 | 8 | 134,830 |
Tags: data structures, geometry, greedy
Correct Solution:
```
#!/usr/bin/python3
# @Author : indiewar
import os
import sys
from io import BytesIO, IOBase
def main():
n = int(input())
a = list(map(int,input().split()))
le = [1 for i in range(n+1)]
sum = [0 for i in range(n+1)]
tmp = 1
for i in range(n):
sum[tmp] = 1.0 * a[i]
le[tmp] = 1
while tmp > 1 and sum[tmp] < sum[tmp-1]:
sum[tmp - 1] = (sum[tmp]*le[tmp] + sum[tmp-1]*le[tmp-1])/(le[tmp]+le[tmp-1])
le[tmp-1] += le[tmp]
tmp-=1
tmp += 1
ans = ""
for i in range(1,tmp):
for j in range(le[i]):
print(sum[i],end=" ")
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | output | 1 | 67,415 | 8 | 134,831 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence. | instruction | 0 | 67,416 | 8 | 134,832 |
Tags: data structures, geometry, greedy
Correct Solution:
```
import io
import os
from collections import Counter, defaultdict, deque
def solve(N, A):
# Bruteforce just to see if logic is right. Will TLE
for i in range(N):
best = (A[i], i, i + 1)
for j in range(i + 1, N + 1):
avg = sum(A[i:j]) / (j - i)
best = min(best, (avg, i, j))
if best[0] < A[i]:
avg, i, j = best
A[i:j] = [avg] * (j - i)
return "\n".join(map(str, A))
def solve(N, A):
# Answer is always monotonically increasing (suppose not, then you can average the decrease to get something lexicographically smaller)
# Track the monotonically increasing heights and number of consecutive columns with that that height
# For each new value seen, merge with a block with same height maintaining monotonic property
# Amortized linear. Total number of appends is N. Total number of pops is limited by appends.
blocks = [(0, 0)]
def combine(block1, block2):
h1, w1 = block1
h2, w2 = block2
total = h1 * w1 + h2 * w2
w = w1 + w2
return (total / w, w)
for x in A:
block = (x, 1)
while True:
combinedBlock = combine(blocks[-1], block)
if combinedBlock[0] <= blocks[-1][0]:
blocks.pop()
block = combinedBlock
else:
blocks.append(block)
break
# It seems like if you try to do map(str, ...) on a list of 10^6 floats it will TLE
ans = []
for h, w in blocks:
val = str(h)
ans.extend([val] * w)
return "\n".join(ans)
if __name__ == "__main__":
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
(N,) = [int(x) for x in input().split()]
A = [int(x) for x in input().split()]
ans = solve(N, A)
print(ans)
``` | output | 1 | 67,416 | 8 | 134,833 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.