AcWing 3. 完全背包问题

算法1

枚举

python 代码

import sys

def solve(n, t, w, v):

ans = [[0 for i in range(t + 1)] for i in range(n + 1)]

for i in range(1, n + 1):

for j in range(1, t + 1):

tem = int(j/w[i]) + 1

for k in range(tem):

ans[i][j] = max(max(ans[i-1][j], ans[i-1][j-k*w[i]] + k*v[i]), ans[i][j])

return ans

if __name__ == '__main__':

n, t = map(int, input().strip().split())

w = [0 for i in range(n + 1)]

v = [0 for i in range(n + 1)]

for i in range(1, n + 1):

w[i], v[i] = map(int, input().strip().split())

ans = solve(n, t, w, v)

print(ans[n][t])

C++ 代码

#include

#include

#include

#include

using namespace std;

int main()

{

int n, t, w[1010], v[1010], ans[1010][1010];

cin >> n >> t;

for (int i = 1; i <= n; ++i){

cin >> w[i] >> v[i];

}

memset(ans, 0, sizeof(ans));

for(int i = 1; i <= n; ++i){

for(int j = 1; j <= t; ++j){

int tem = j/w[i];

for(int k = 0; k <= tem; ++k){

ans[i][j] = max(max(ans[i - 1][j], ans[i - 1][j - k*w[i]] + k*v[i]), ans[i][j]);

}

// cout << ans[i][j] << " ";

}

// cout << endl;

}

cout << ans[n][t];

return 0;

}

算法2

一种很巧妙的优化，完全背包，当前物品尽可能多放，持续寻找最优解

python 代码

import sys

def solve(n, t, w, v):

ans = [0 for i in range(t + 1)]

for i in range(1, n + 1):

for j in range(w[i], t + 1):

ans[j] = max(ans[j], ans[j - w[i]] + v[i])

return ans[t]

if __name__ == '__main__':

n, t = map(int, input().strip().split())

w = [0 for i in range(n + 1)]

v = [0 for i in range(n + 1)]

for i in range(1, n + 1):

w[i], v[i] = map(int, input().strip().split())

print(solve(n, t, w, v))