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01 背包

01 背包

例题1

自建OJ：01 背包

代码实现

记忆化搜索 
#include<bits/stdc++.h>
using namespace std;

const int N = 1005;

int n, m;
int v[N], w[N];
int dp[N][N];

int dfs(int i, int j) {
    if (i == 0) return 0;
    if (dp[i][j] != -1) return dp[i][j];
    int ans = 0;
    if (j >= v[i]) ans = dfs(i - 1, j - v[i]) + w[i];
    ans = max(ans, dfs(i - 1, j));
    return dp[i][j] = ans;
}

int main() {
    memset(dp, -1, sizeof dp);
    cin >> n >> m;
    for (int i = 1; i <= n; i++) cin >> v[i] >> w[i];
    cout << dfs(n, m);
    return 0;
}

import java.util.*;

public class Main {

    static final int N = 1005;

    static int n, m;
    static int[] v = new int[N];
    static int[] w = new int[N];
    static int[][] dp = new int[N][N];

    static int dfs(int i, int j) {
        if (i == 0) return 0;
        if (dp[i][j] != -1) return dp[i][j];
        int ans = 0;
        if (j >= v[i]) ans = dfs(i - 1, j - v[i]) + w[i];
        ans = Math.max(ans, dfs(i - 1, j));
        return dp[i][j] = ans;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        for (int i = 0; i < N; i++) Arrays.fill(dp[i], -1);
        n = sc.nextInt();
        m = sc.nextInt();
        for (int i = 1; i <= n; i++) {
            v[i] = sc.nextInt();
            w[i] = sc.nextInt();
        }
        System.out.println(dfs(n, m));
    }

}

import sys
sys.setrecursionlimit(1000000)

input = sys.stdin.readline

N = 1005

n, m = map(int, input().split())
v = [0] * N
w = [0] * N
dp = [[-1] * N for _ in range(N)]

for i in range(1, n + 1):
    v[i], w[i] = map(int, input().split())

def dfs(i, j):
    if i == 0:
        return 0
    if dp[i][j] != -1:
        return dp[i][j]
    ans = 0
    if j >= v[i]:
        ans = dfs(i - 1, j - v[i]) + w[i]
    ans = max(ans, dfs(i - 1, j))
    dp[i][j] = ans
    return ans

print(dfs(n, m))
动态规划实现 
#include<bits/stdc++.h>
using namespace std;

const int N = 1005;

int n, m;
int v[N], w[N];
int dp[N][N];

int main() {
    cin >> n >> m;
    for (int i = 1; i <= n; i++) cin >> v[i] >> w[i];
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= m; j++) {
            dp[i][j] = dp[i - 1][j];
            if (j >= v[i]) dp[i][j] = max(dp[i][j], dp[i - 1][j - v[i]] + w[i]);
        }
    }
    cout << dp[n][m];
    return 0;
}

import java.util.*;

public class Main {

    static final int N = 1005;

    static int n, m;
    static int[] v = new int[N];
    static int[] w = new int[N];
    static int[][] dp = new int[N][N];

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        for (int i = 1; i <= n; i++) {
            v[i] = sc.nextInt();
            w[i] = sc.nextInt();
        }
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j <= m; j++) {
                dp[i][j] = dp[i - 1][j];
                if (j >= v[i]) {
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - v[i]] + w[i]);
                }
            }
        }
        System.out.println(dp[n][m]);
    }

}

import sys

input = sys.stdin.readline

N = 1005

n, m = map(int, input().split())
v = [0] * N
w = [0] * N
dp = [[0] * N for _ in range(N)]

for i in range(1, n + 1):
    v[i], w[i] = map(int, input().split())

for i in range(1, n + 1):
    for j in range(0, m + 1):
        dp[i][j] = dp[i - 1][j]
        if j >= v[i]:
            dp[i][j] = max(dp[i][j], dp[i - 1][j - v[i]] + w[i])

print(dp[n][m])