背包DP模板

01背包

01背包-1

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N][N], v[N], w[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++) {if (j < v[i]) f[i][j] = f[i - 1][j];else f[i][j] = max(f[i - 1][j], f[i - 1][j - v[i]] + w[i]);}}cout << f[n][m] << endl;return 0;
}

01背包-2

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N], g[N], v[N], w[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) {if (j < v[i]) g[j] = f[j];elseg[j] = max(f[j], f[j - v[i]] + w[i]);}memcpy(f, g, sizeof g);}cout << f[m] << endl;return 0;
}

01背包-3

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#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N], v[N], w[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 = m; j >= v[i]; --j) {f[j] = max(f[j], f[j - v[i]] + w[i]);}}cout << f[m] << endl;return 0;
}

完全背包

完全背包-1

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N][N], v[N], w[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) {if (j < v[i])f[i][j] = f[i - 1][j];elsef[i][j] = max(f[i - 1][j], f[i][j - v[i]] + w[i]);}}cout << f[n][m] << endl;return 0;
}

完全背包-2

在这里插入图片描述

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N], v[N], w[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 = v[i]; j <= m; ++j) {f[j] = max(f[j], f[j - v[i]] + w[i]);}}cout << f[m] << endl;return 0;
}

完全背包-2（恰好装满m）

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N], v[N], w[N];int main() {cin >> n >> m;for (int i = 1; i <= n; ++i) cin >> v[i] >> w[i];memset(f, 128, sizeof f); // 初始化为负无限大f[0] = 0;for (int i = 1; i <= n; ++i) {for (int j = v[i]; j <= m; ++j) {f[j] = max(f[j], f[j - v[i]] + w[i]);}}cout << f[m] << endl;return 0;
}

多重背包

多重背包-1 （n <= 100）

#include <bits/stdc++.h>
using namespace std;const int N = 1e5 + 10;
int n, m, f[N], v[N], w[N], l[N];int main() {cin >> n >> m;for (int i = 1; i <= n; ++i) cin >> v[i] >> w[i] >> l[i];for (int i = 1; i <= n; ++i) {for (int k = 1; k <= l[i]; ++k) {for (int j = m; j >= v[i]; --j) {f[j] = max(f[j], f[j - v[i]] + w[i]);}}}cout << f[m] << endl;return 0;
}