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<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>
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))