message stringlengths 2 30.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 237 109k | cluster float64 10 10 | __index_level_0__ int64 474 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,872 | 10 | 203,744 |
"Correct Solution:
```
n = int(input())
if( n in {4,7,8,11,12,14,15,16} or n >= 18):
print('Yes')
else:
print('No')
``` | output | 1 | 101,872 | 10 | 203,745 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,873 | 10 | 203,746 |
"Correct Solution:
```
a=int(input())
print("Yes" if [4*x+7*y for x in range(101) for y in range(101)].count(a) else "No")
``` | output | 1 | 101,873 | 10 | 203,747 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,874 | 10 | 203,748 |
"Correct Solution:
```
x=int(input());print("No" if x<4 or 4<x<7 or 8<x<11 or x==13 or x==17 else "Yes")
``` | output | 1 | 101,874 | 10 | 203,749 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,875 | 10 | 203,750 |
"Correct Solution:
```
N = int(input())
for i in range(N//4+1):
if (N-4*i) % 7 == 0:
print("Yes")
exit()
print("No")
``` | output | 1 | 101,875 | 10 | 203,751 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,876 | 10 | 203,752 |
"Correct Solution:
```
N = int(input())
ans = "No"
for i in range(0,1+(N//7)):
if (N - 7*i)%4==0:
ans = "Yes"
break
print(ans)
``` | output | 1 | 101,876 | 10 | 203,753 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,877 | 10 | 203,754 |
"Correct Solution:
```
n = int(input())
print("Yes" if len([1 for i in range(100//4) for j in range(100//7) if i*4+j*7==n])>0 else "No")
``` | output | 1 | 101,877 | 10 | 203,755 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,878 | 10 | 203,756 |
"Correct Solution:
```
n=int(input())
if n<4 :
print("No")
elif n in {5, 6, 9, 10, 13, 17, 23}:
print("No")
else :
print("Yes")
``` | output | 1 | 101,878 | 10 | 203,757 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No | instruction | 0 | 101,879 | 10 | 203,758 |
"Correct Solution:
```
n = int(input())
ng = [1,2,3,5,6,9,10,13,17]
if n in ng:
print('No')
else:
print('Yes')
``` | output | 1 | 101,879 | 10 | 203,759 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N = int(input())
M = [4*i+7*j for i in range(30) for j in range(20)]
if N in M:
print("Yes")
else:
print("No")
``` | instruction | 0 | 101,880 | 10 | 203,760 |
Yes | output | 1 | 101,880 | 10 | 203,761 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N=int(input())
a=[4*x+7*y for x in range(200) for y in range(200)]
ans="Yes" if N in a else "No"
print(ans)
``` | instruction | 0 | 101,881 | 10 | 203,762 |
Yes | output | 1 | 101,881 | 10 | 203,763 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n=int(input())
if n <= 3 or n==5 or n==6 or n==9 or n==10 or n==13 or n==17:
print("No")
else:
print("Yes")
``` | instruction | 0 | 101,882 | 10 | 203,764 |
Yes | output | 1 | 101,882 | 10 | 203,765 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n=int(input())
b=[]
for i in range(15):
for j in range(12):
b.append(i*4+j*7)
print("NYoe s"[n in b::2])
``` | instruction | 0 | 101,883 | 10 | 203,766 |
Yes | output | 1 | 101,883 | 10 | 203,767 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n = int(input())
if n % 4 != 0 and n % 7 != 0 and n % 11 != 0:
print('Yes')
else:
print('No')
``` | instruction | 0 | 101,884 | 10 | 203,768 |
No | output | 1 | 101,884 | 10 | 203,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
if (N % 7) % 4 == 0 or (N % 4) % 7 == 0:
print("Yes")
else:
print("No")
``` | instruction | 0 | 101,885 | 10 | 203,770 |
No | output | 1 | 101,885 | 10 | 203,771 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N = int(input())
#4*a + 7*b == N ???
counter = 0
for a in range(N//4):
for b in range(N//7):
if 4*a + 7*b == N:
counter += 1
print(counter)
``` | instruction | 0 | 101,886 | 10 | 203,772 |
No | output | 1 | 101,886 | 10 | 203,773 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll MOD = 1e9 + 7;
const ll LINF = LLONG_MAX;
const int INF = INT_MAX;
int main() {
int n;
cin >> n;
for (int i = (0); i < (int)(30); i++) {
if ((n - 4 * i) % 7 == 0) {
cout << "Yes" << endl;
return 0;
}
if (i * 4 > n) break;
}
cout << "No" << endl;
}
``` | instruction | 0 | 101,887 | 10 | 203,774 |
No | output | 1 | 101,887 | 10 | 203,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price — c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10 000) — the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, …, c_n (x ≤ c_i ≤ 10 000; ∑{c_i} ≤ 10 000) — the prices of n relics.
Output
Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
n,x = [int(i) for i in input().split()]
c = [int(i) for i in input().split()]
res = 0
for i in range(n):
for j in range(n):
res += min(c[j],(2*n-i)/(2*n-2*i) * x)
res /= n
print(res)
``` | instruction | 0 | 102,136 | 10 | 204,272 |
No | output | 1 | 102,136 | 10 | 204,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price — c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10 000) — the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, …, c_n (x ≤ c_i ≤ 10 000; ∑{c_i} ≤ 10 000) — the prices of n relics.
Output
Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 50
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print(ans)
``` | instruction | 0 | 102,137 | 10 | 204,274 |
No | output | 1 | 102,137 | 10 | 204,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price — c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10 000) — the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, …, c_n (x ≤ c_i ≤ 10 000; ∑{c_i} ≤ 10 000) — the prices of n relics.
Output
Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 100
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print('%.100f'%ans)
``` | instruction | 0 | 102,138 | 10 | 204,276 |
No | output | 1 | 102,138 | 10 | 204,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.
Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.
Relics can be bought using an in-game currency called shards. Each relic has its own price — c_i shards for the i-th relic. A player can buy a relic using one of the following options:
* Pay c_i shards to buy the i-th relic;
* Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player.
Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.
Input
The first line contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10 000) — the number of relics and the cost to receive a random relic.
The second line consists of n integers c_1, c_2, …, c_n (x ≤ c_i ≤ 10 000; ∑{c_i} ≤ 10 000) — the prices of n relics.
Output
Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.
The absolute or relative error should not exceed 10^{-9}.
Examples
Input
2 20
25 100
Output
47.50000000000000000
Input
4 30
60 50 60 80
Output
171.25000000000000000
Note
In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios.
The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.
In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.
Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.
Submitted Solution:
```
from decimal import *
line = input()
content = line.split(" ")
n = int(content[0])
x = int(content[1])
c = [0 for _ in range(n)]
line = input()
content = line.split(" ")
for i in range(n):
c[i] = int(content[i])
getcontext().prec = 10000
ans = Decimal(0)
for i in range(n):
for j in range(n):
k = j
tmp = Decimal(x) + Decimal(k) * Decimal(x) / Decimal(2 * n - 2 * k)
if (2 * n - k) * x > c[i] * (2 * n - 2 * k):
ans += Decimal(c[i])
else:
ans += tmp
ans = ans / Decimal(n)
print('%.100f'%ans)
``` | instruction | 0 | 102,139 | 10 | 204,278 |
No | output | 1 | 102,139 | 10 | 204,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,221 | 10 | 204,442 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
t=1
for _ in range(t):
n=int(input())
l=[int(j) for j in input().split()]
l.sort()
c,cnt=0,0
k=[0]*n
for i in range(n//2):
k[c]=l[n//2+i]
c+=1
k[c]=l[i]
c+=1
if n%2!=0:
k[n-1]=l[n-1]
for i in range(1,n-1):
if k[i-1]>k[i] and k[i+1]>k[i]:
cnt+=1
print(cnt)
print(*k)
``` | output | 1 | 102,221 | 10 | 204,443 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,222 | 10 | 204,444 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n = int(input())
p = [int(x) for x in input().split()]
p.sort()
a = [None] * n
k = 0
if n % 2 == 1:
for i in range(1, n, 2):
a[i] = p[k]
k += 1
for i in range(0, n, 2):
a[i] = p[k]
k += 1
else:
for i in range(1, n, 2):
a[i] = p[k]
k += 1
for i in range(0, n, 2):
a[i] = p[k]
k += 1
ct = 0
for i in range(1, n - 1):
if a[i] < a[i - 1] and a[i] < a[i + 1]:
ct += 1
print(ct)
for e in a:
print(e, end=' ')
print()
``` | output | 1 | 102,222 | 10 | 204,445 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,223 | 10 | 204,446 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
lena=(len(l))
l.sort()
left=l[:lena//2]
right=l[lena//2:]
left.sort();right.sort()
answer=[]
count=0
for i in range(len(right)):
answer.append(right[i])
if i<len(left):
answer.append(left[i])
if answer[-1]<answer[-2] and i<len(right)-1:
count+=1
print(count)
print(*answer)
``` | output | 1 | 102,223 | 10 | 204,447 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,224 | 10 | 204,448 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
#3 1 3 2 3 3 6 7
#1 2 3 3 3 6 3 7
#1 3 3 3 2 6 3 7
#3 3 1 3 2 6 3 7
#maximum possible valleys = math.ceil(len / 2) - 1
#first maxPossibleValleys of sorted array
#min = 1,2,3
#max = 3,3,3,6,7
#iterate through max and put in elements from min if they work
#if some mins haven't been place, just put them at end of max
#return max and a count of the spots found
import math
N = int(input())
arr = [int(i) for i in input().split(' ')]
def win(arr):
if len(arr) <= 2:
print(0)
print(' '.join([str(i) for i in arr]))
return
arr.sort()
maxPossible = math.ceil(len(arr) / 2) - 1
minArr = arr[:maxPossible]
maxArr = arr[maxPossible:]
j = 0
ans = [maxArr[0]]
count = 0
for i in range(1,len(maxArr)):
if minArr[j] < maxArr[i-1] and minArr[j] < maxArr[i]:
count += 1
ans.append(minArr[j])
j += 1
ans.append(maxArr[i])
if j == len(minArr):
ans += maxArr[i+1:]
break
if j < len(minArr):
ans += minArr[j:]
print(count)
print(' '.join([str(i) for i in ans]))
win(arr)
``` | output | 1 | 102,224 | 10 | 204,449 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,225 | 10 | 204,450 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
import sys,math
n=int(input())
prc=list(map(int,sys.stdin.readline().strip().split()))
prc.sort(reverse=True)
if prc[0]==prc[-1] or len(prc)<3:
print(0)
sys.stdout.write(' '.join(map(str,prc))+'\n')
else:
new_prc=[]
for i in range(math.ceil(n/2)):
new_prc.append(prc[i])
if len(new_prc)<n:
new_prc.append(-1)
if prc[math.ceil(n/2)-1]==prc[math.ceil(n/2)]:
u_bound,l_bound=math.ceil(n/2)-1,math.ceil(n/2)
while u_bound>0 and prc[u_bound-1]==prc[u_bound]:
u_bound-=1
while l_bound<n and prc[l_bound]==prc[l_bound+1]:
l_bound+=1
# print(u_bound,l_bound)
j=math.ceil(n/2)
for i in range(1,2*(u_bound-1),2):
new_prc[i]=prc[j]
j+=1
# print(new_prc)
j=-1
for i in range(2*u_bound-1 if u_bound!=0 else 1,n,2):
new_prc[i]=prc[j]
j-=1
# print(new_prc)
else:
j=math.ceil(n/2)
for i in range(1,n,2):
new_prc[i]=prc[j]
j+=1
count=0
for i in range(1,n if n%2==1 else n-1,2):
if new_prc[i-1]>new_prc[i] and new_prc[i+1]>new_prc[i]:
count+=1
print(count)
sys.stdout.write(' '.join(map(str,new_prc))+'\n')
``` | output | 1 | 102,225 | 10 | 204,451 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,226 | 10 | 204,452 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
import threading
from bisect import bisect_right
from math import gcd,log
from collections import Counter
from pprint import pprint
# arr=[1]
# i=1
# while i <100:
# arr.append(2*arr[-1]+2**(i+1))
# i=2*i+1
# print(arr)
def main():
n=int(input())
arr=list(map(int,input().split()))
a=arr.copy()
a.sort(reverse=True)
ind=0
for i in range(0,n,2):
arr[i]=a[ind]
ind+=1
for i in range(1,n,2):
arr[i]=a[ind]
ind+=1
cnt=0
nahi=-1
ind=-1
for i in range(n):
if i!=0 and i!=n-1 and i%2:
if arr[i]<arr[i+1] and arr[i]<arr[i-1]:
cnt+=1
elif (nahi==-1):
nahi=arr[i]
ind=i
if n%2==0 and nahi!=-1 and arr[ind]!=arr[-1]:
arr[-1],arr[ind]=arr[ind],arr[-1]
cnt+=1
print(cnt)
print(*arr)
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__":
for _ in range(1):
main()
``` | output | 1 | 102,226 | 10 | 204,453 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,227 | 10 | 204,454 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
# from itertools import combinations_with_replacement
# for com in combinations_with_replacement(range(1,N+1),N):
# A = list(com)
A.sort()
B = [0]*N
for i in range(1,N,2):
B[i] = A[i//2]
Astart = N//2
Bstart = N-2 if N%2==0 else N-1
rem = []
while Astart<N and A[Astart]==B[Bstart-1]:
rem.append(A[Astart])
Astart += 1
for i in range(Bstart,-1,-2):
if Astart>=N:
B[i] = rem.pop()
else:
B[i] = A[Astart]
Astart += 1
ans = 0
for i in range(1,N-1,2):
if B[i-1]>B[i]<B[i+1]:
ans += 1
# if sorted(B)!=A:
# print(False)
# print(A)
print(ans)
print(*B)
``` | output | 1 | 102,227 | 10 | 204,455 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each. | instruction | 0 | 102,228 | 10 | 204,456 |
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n = int(input())
l=sorted(list(map(int,input().split())))
x=[]
if n<=2 :
print(0)
print(*l)
elif n%2==0 :
a=l[:n//2]
b=l[n//2:]
ans=0
for i in range(n//2):
x.append(b[i])
x.append(a[i])
for j in range(1,n-1,2):
if x[j]<x[j+1] and x[j]<x[j-1] :
ans+=1
print(ans)
print(*x)
else:
a=l[:n//2]
b=l[n//2:]
ans=0
for i in range(n//2):
x.append(b[i])
x.append(a[i])
x.append(b[-1])
for j in range(1,n,2):
if (x[j]<x[j+1]) and (x[j]<x[j-1]) :
ans+=1
print(ans)
print(*x)
``` | output | 1 | 102,228 | 10 | 204,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
# from collections import defaultdict, Counter, deque
# from heapq import heappop, heappush, heapify
# from functools import lru_cache, reduce
# import bisect
# from itertools import permutations, combinations, combinations_with_replacement
def f():
n = int(input())
arr = list(map(int, input().split()))
arr.sort()
newarr = []
for i in range(n//2):
newarr.append(arr[i+n//2])
newarr.append(arr[i])
if n % 2:
newarr.append(arr[n-1])
total = 0
i = 1
while i+1 < n:
if newarr[i-1] > newarr[i] and newarr[i] < newarr[i+1]:
total += 1
i += 2
newarr = list(map(str, newarr))
newarr = " ".join(newarr)
print(total)
print(newarr)
f()
# Test cases
'''
7
1 3 2 2 4 5 4
8
3 3 3 3 3 3 2 2
6
1 1 1 1 1 1
'''
``` | instruction | 0 | 102,229 | 10 | 204,458 |
Yes | output | 1 | 102,229 | 10 | 204,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
def solve(n, ices):
ices = sorted(ices)
former, latter = ices[:n//2], ices[n//2:]
res = 0
res_ice = []
for i in range((n-1)//2):
res_ice.append(latter[i])
res_ice.append(former[i])
if former[i] < latter[i]:
res += 1
res_ice.append(latter[-1])
if n % 2 == 0:
res_ice.append(former[-1])
return res, " ".join(list(map(str, res_ice)))
def main():
n = int(input())
ices = list(map(int, input().split()))
res1, res2 = solve(n, ices)
print(res1)
print(res2)
main()
``` | instruction | 0 | 102,230 | 10 | 204,460 |
Yes | output | 1 | 102,230 | 10 | 204,461 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
a.sort(reverse=True)
x=n//2
b=a[:x]
c=a[x:]
c.reverse()
b.reverse()
z=[]
for i in range(x):
z.append(b[i])
z.append(c[i])
c[i]=0
for i in range(len(c)):
if c[i]!=0:
z.append(c[i])
ans2=0
for i in range(1,n-1,2):
if z[i]<z[i-1] and z[i]<z[i+1]:
ans2+=1
b=[]
x=n//2
pos=x
if (2*x)!=n:
pos=x+1
for i in range(x):
b.append(a[i])
b.append(a[i+pos])
if (2*x)!=n:
b.append(a[x])
c=[]
for i in range(x):
c.append(a[i])
c.append(a[-i])
if (2*x)!=n:
c.append(a[x])
ans=0
for i in range(1,n-1,2):
if b[i]<b[i-1] and b[i]<b[i+1]:
ans+=1
tmp=0
for i in range(1,n-1,2):
if c[i]<c[i-1] and c[i]<c[i+1]:
tmp+=1
if max(ans,tmp,ans2)==ans:
print(ans)
print(*b)
elif max(ans,tmp,ans2)==tmp:
print(tmp)
print(*c)
else:
print(ans2)
print(*z)
``` | instruction | 0 | 102,231 | 10 | 204,462 |
Yes | output | 1 | 102,231 | 10 | 204,463 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n=int(input())
l=list(sorted(map(int,input().split())))
left= l[0:n//2]
right = l[n//2:n]
arr=[-1 for x in range(n)]
count=0
flag= True
j=0
k=0
for i in range(n):
if flag==True:
arr[i]=right[j]
j+=1
flag=False
elif flag==False:
arr[i]=left[k]
k+=1
flag=True
for a in range(1,n-1):
if arr[a]<arr[a-1] and arr[a]< arr[a+1]:
count+=1
print(count)
print(*arr)
``` | instruction | 0 | 102,232 | 10 | 204,464 |
Yes | output | 1 | 102,232 | 10 | 204,465 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
z,zz=input,lambda:list(map(int,z().split()))
zzz=lambda:[int(i) for i in stdin.readline().split()]
szz,graph,mod,szzz=lambda:sorted(zz()),{},10**9+7,lambda:sorted(zzz())
from string import *
from re import *
from collections import *
from queue import *
from sys import *
from collections import *
from math import *
from heapq import *
from itertools import *
from bisect import *
from collections import Counter as cc
from math import factorial as f
from bisect import bisect as bs
from bisect import bisect_left as bsl
from itertools import accumulate as ac
from itertools import permutations as permu
def lcd(xnum1,xnum2):return (xnum1*xnum2//gcd(xnum1,xnum2))
def prime(x):
p=ceil(x**.5)+1
for i in range(2,p):
if (x%i==0 and x!=2) or x==0:return 0
return 1
def dfs(u,visit,graph):
visit[u]=True
for i in graph[u]:
if not visit[i]:
dfs(i,visit,graph)
###########################---Test-Case---#################################
"""
"""
###########################---START-CODING---##############################
num=1
#num=int(z())
for _ in range( num ):
n=int(z())
arr=szzz()
l=0
r=n-1
lst=[]
while l<r:
lst.append(arr[r])
lst.append(arr[l])
r-=1
l+=1
if n%2==1:
lst.append(arr[l])
ans=0
for i in range(1,n-1):
if lst[i-1]>lst[i] and lst[i+1]>lst[i]:
ans+=1
print(ans)
print(*lst)
``` | instruction | 0 | 102,233 | 10 | 204,466 |
No | output | 1 | 102,233 | 10 | 204,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n = int(input())
d = [int(i) for i in input().split()]
if n < 3 or d[0] * n == sum(d):
print(0)
exit()
d.sort()
mxd = [max(d[i], d[i+1]) for i in range(n-1)]
hi = (n-3) // 2
lo = 0
while lo < hi:
mid = (lo + hi+1) // 2
kk = n - mid - 2
# print(mid, [(mxd[kk+i], d[i]) for i in range(mid+1)])
if sum(mxd[kk+i] > d[i] for i in range(mid+1)) == mid + 1:
lo = mid
else:
hi = mid - 1
print(lo+1)
# ans = [d[0]]
ans = []
for i in range(lo+1):
ans.append(d[n-lo-2+i])
ans.append(d[i])
ans.append(d[-1])
print(' '.join(map(str, ans)))
``` | instruction | 0 | 102,234 | 10 | 204,468 |
No | output | 1 | 102,234 | 10 | 204,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
import sys,math
n=int(input())
prc=list(map(int,sys.stdin.readline().strip().split()))
prc.sort(reverse=True)
if prc[0]==prc[-1] or len(prc)<3:
print(0)
sys.stdout.write(' '.join(map(str,prc))+'\n')
else:
new_prc=[]
for i in range(math.ceil(n/2)):
new_prc.append(prc[i])
if len(new_prc)<n:
new_prc.append(prc[math.ceil(n/2)+i])
count=0
for i in range(1,n-1,2):
if new_prc[i]<new_prc[i-1] and new_prc[i]<new_prc[i+1]:
count+=1
print(count)
sys.stdout.write(' '.join(map(str,new_prc))+'\n')
``` | instruction | 0 | 102,235 | 10 | 204,470 |
No | output | 1 | 102,235 | 10 | 204,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
big = 0
small = (N+1)//2
B = [0]*N
cnt = 0
while cnt<N:
B[cnt] = A[big]
big += 1
cnt += 1
if cnt==N:
break
B[cnt] = A[small]
small += 1
cnt += 1
ans = 0
for i in range(1,N-1,2):
if B[i-1]>B[i]<B[i+1]:
ans += 1
print(ans)
print(*B)
``` | instruction | 0 | 102,236 | 10 | 204,472 |
No | output | 1 | 102,236 | 10 | 204,473 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,240 | 10 | 206,480 |
Tags: implementation
Correct Solution:
```
import sys
def check_first(n, m, a):
ans = 0
while n > 0:
n-=1
ans+=a
return ans
def check_second(n, m, a, b):
ans = 0
if b < a:
while n > 0:
n-=m
ans+=b
return ans
else:
while n > 0:
if n - m >= 0:
n-=m
ans+=b
else:
n-=1
ans+=a
return ans
def main():
n, m, a, b = map(int, sys.stdin.readline().split())
if m > n and n!=1:
sys.stdout.write(f'{b}')
else:
sys.stdout.write(f'{min(check_first(n,m,a), check_second(n,m,a,b))}')
if __name__ == '__main__':
main()
``` | output | 1 | 103,240 | 10 | 206,481 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,241 | 10 | 206,482 |
Tags: implementation
Correct Solution:
```
n,m,a,b = map(int,input().split())
per_ride_single = a
per_ride_multiple = b/m
if per_ride_single<=per_ride_multiple:
rides = n*per_ride_single
else:
left_rides = n%m
rides =int(n/m)*b + min(left_rides*per_ride_single,b)
print(rides)
``` | output | 1 | 103,241 | 10 | 206,483 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,242 | 10 | 206,484 |
Tags: implementation
Correct Solution:
```
import math
n_trips, n_card, cost_trip, cost_card = [int(s) for s in input().split()]
if cost_card / n_card >= cost_trip:
print(n_trips * cost_trip)
else:
min_cost = min(math.ceil(n_trips / n_card) * cost_card,
n_trips // n_card * cost_card + (n_trips - n_trips // n_card * n_card) * cost_trip)
print(min_cost)
``` | output | 1 | 103,242 | 10 | 206,485 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,243 | 10 | 206,486 |
Tags: implementation
Correct Solution:
```
w = input().split(' ')
n = int(w[0])
m = int(w[1])
a = int(w[2])
b = int(w[3])
s = 0
if (b/m) > a:
print(a*n)
else:
while n >= m:
n -= m
s += b
if a*n < b:
s += a*n
else:
s += b
print(s)
``` | output | 1 | 103,243 | 10 | 206,487 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,244 | 10 | 206,488 |
Tags: implementation
Correct Solution:
```
n,m,a,b=map(int, input().split(' '))
if(m*a<=b):
print(n*a)
else:
ans=0
ans+=(n//m)*b+min((n%m)*a,b)
print(ans)
``` | output | 1 | 103,244 | 10 | 206,489 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,245 | 10 | 206,490 |
Tags: implementation
Correct Solution:
```
# coding=utf-8
if __name__ == '__main__':
n, m, a, b = str(input()).split()
n = int(n)
m = int(m)
a = int(a)
b = int(b)
if n % m == 0:
print(min(int(n * a), int(n / m) * b))
else:
print(min(int(n * a), int(n / m + 1) * b, int(n / m) * b + (n - int(n / m) * m) * a))
``` | output | 1 | 103,245 | 10 | 206,491 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,246 | 10 | 206,492 |
Tags: implementation
Correct Solution:
```
nmab=input().split()
n,m,a,b=int(nmab[0]),int(nmab[1]),int(nmab[2]),int(nmab[3])
cc=(n//m)*b+(n%m)*a
scc=(n//m+1)*b
sc=n*a
for i in range(3):
if cc<=sc and cc<scc:
print(cc)
break
if scc<=cc and scc<=sc:
print(scc)
break
else:
print(sc)
break
``` | output | 1 | 103,246 | 10 | 206,493 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets. | instruction | 0 | 103,247 | 10 | 206,494 |
Tags: implementation
Correct Solution:
```
n, m, a, b = input().split()
n, m, a, b = [int (x) for x in [n, m, a, b]]
if m * a > b:
print (min ((n // m * b + (n % m) * a), (n // m + 1) * b))
else:
print (n * a)
``` | output | 1 | 103,247 | 10 | 206,495 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
s=input()
x=list()
x=s.split()
n,m,a,b=int(x[0]),int(x[1]),int(x[2]),int(x[3])
p=b/m
if p<a:
print(int(n/m)*b+min((n%m)*a,b))
else:
print(n*a)
``` | instruction | 0 | 103,248 | 10 | 206,496 |
Yes | output | 1 | 103,248 | 10 | 206,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
from math import ceil
n,m,a,b=map(int,input().split())
x=[n*a,(ceil(n/m))*b,(n//m)*b+(n%m)*a,(n//m)*b+(n%m)*b]
print(min(x))
``` | instruction | 0 | 103,249 | 10 | 206,498 |
Yes | output | 1 | 103,249 | 10 | 206,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
#Consistency is the key.
#code by: amrit2000
from sys import stdin,stdout
import math
input=stdin.readline
def print(x='',y='',end='\n'):
if y=='':
stdout.write(str(x)+end)
else:
stdout.write(str(x)+' '+str(y)+end)
def solve():
n,m,a,b=map(int,input().split())
if b//m<a:
print((n//m)*b +min(math.ceil((n-m*(n//m))/m)*b,(n-m*(n//m))*a))
else:
print(n*a)
tt=1
#tt=int(input())
for __ in range(tt):
solve()
``` | instruction | 0 | 103,250 | 10 | 206,500 |
Yes | output | 1 | 103,250 | 10 | 206,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
def arr_inp():
return [int(x) for x in stdin.readline().split()]
from sys import stdin
from math import ceil
n, m, a, b = arr_inp()
print(min((n // m) * b + (n % m) * a, ceil(n / m) * b, a * n))
``` | instruction | 0 | 103,251 | 10 | 206,502 |
Yes | output | 1 | 103,251 | 10 | 206,503 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
# input consists of n, m, a, b
args = [int(a) for a in input().strip().split()]
num_rides, num_special_rides, one_ticket_price, special_ticket_price = args
# if the special tickets cost more per ride...
if one_ticket_price <= special_ticket_price / num_special_rides:
print(one_ticket_price * num_rides)
# if special tickets don't cost more...
# find out how many special tickets you can actually buy...
# and calculate if you should buy another special_ticket for the remainder
else:
print("here")
special_bought, remainder = divmod(num_rides, num_special_rides)
total_spent = special_bought * special_ticket_price
# check if you should buy another special_ticket
if remainder * one_ticket_price > special_ticket_price:
total_spent += remainder * one_ticket_price
else:
total_spent += special_ticket_price
print(total_spent)
``` | instruction | 0 | 103,252 | 10 | 206,504 |
No | output | 1 | 103,252 | 10 | 206,505 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?
Input
The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.
Output
Print a single integer — the minimum sum in rubles that Ann will need to spend.
Examples
Input
6 2 1 2
Output
6
Input
5 2 2 3
Output
8
Note
In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.
Submitted Solution:
```
if __name__ == "__main__":
n, m, a, b = map(int, input().split())
tr = 0
if (a*m) >= b:
if m > n:
print(b)
else:
tr = (n//m)*b
n %= m
if n != 0:
if (tr+(a*n)) <= (tr+(b*n)):
tr += (a*n)
else:
tr += (b*n)
print(tr)
else:
print(a*n)
``` | instruction | 0 | 103,253 | 10 | 206,506 |
No | output | 1 | 103,253 | 10 | 206,507 |
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