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动态规划 List
1. LCS 最长公共子序列
/* LCS * Au: GG */ #include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> #include <ctime> #include <iostream> #include <algorithm> using namespace std; const int N = 1005; int n, m, d[N][N], A[N], B[N]; int main() { scanf("%d%d", &n, &m); for (int i = 1; i <= n; i++) scanf("%d", &A[i]); for (int i = 1; i <= m; i++) scanf("%d", &B[i]); for (int i = 1; i <= n; i++) { for (int j = 1; j <= m; j++) { d[i][j] = max(d[i - 1][j], d[i][j - 1]); if (A[i] == B[j]) d[i][j] = max(d[i][j], d[i - 1][j - 1] + 1); } } printf("%d\n", d[n][m]); return 0; }
2. LIS 最长上升自序列
/** * LIS * Au: GG **/ #include <cstdio> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <algorithm> using namespace std; const int N = 1000000 + 3; int n, a[N], d[N]; int ans; int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &a[i]); } for (int i = 1; i <= n; i++) { d[i] = 1; for (int j = 1; j < i; j++) { if (a[i] > a[j] && d[j] + 1 > d[i]) d[i] = d[j] + 1; } ans = max(ans, d[i]); } printf("%d\n", ans); return 0; }
3. 01 背包
// 01 Knapsack // Au: GG #include <iostream> #include <cstdlib> #include <cstdio> #include <cmath> #include <cstring> using namespace std; int n, v, w[33], f[33][20003]; int main() { scanf("%d%d", &v, &n); for (int i = 1; i <= n; i++) scanf("%d", &w[i]); for (int i = 1; i <= n; i++) { for (int j = 1; j <= v; j++) { if (j - w[i] < 0) f[i][j] = f[i - 1][j]; else f[i][j] = max(f[i - 1][j - w[i]] + w[i], f[i - 1][j]); } } printf("%d", v - f[n][v]); return 0; }
4. 完全背包
/** * Luogu P1616 疯狂的采药 * Au: GG **/ #include <cstdio> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <algorithm> using namespace std; int n, m, d[100000+4], w[100000+3], v[100000+3]; int main() { scanf("%d%d", &m, &n); for (int i = 1; i <= n; i++) scanf("%d%d", &v[i], &w[i]); for (int i = 1; i <= n; i++) { for (int j = v[i]; j <= m; j++) { d[j] = max(d[j], d[j - v[i]] + w[i]); } } printf("%d\n", d[m]); return 0; }
5. 多维背包
/** * Luogu P1855 榨取kkksc03 * Au: GG **/ #include <cstdio> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <algorithm> using namespace std; const int N = 100 + 3, M = 200 + 3; int n, m, t, time[N], w[N], d[N][M][M]; int main() { scanf("%d%d%d", &n, &m, &t); for (int i = 1; i <= n; i++) scanf("%d%d", &time[i], &w[i]); for (int i = 1; i <= n; i++) { for (int j = 0; j <= m; j++) { for (int k = 0; k <= t; k++) { d[i][j][k] = d[i - 1][j][k]; if (j - time[i] >= 0 && k - w[i] >= 0 && d[i - 1][j - time[i]][k - w[i]] + 1 > d[i][j][k]) d[i][j][k] = d[i - 1][j - time[i]][k - w[i]] + 1; } } } printf("%d\n", d[n][m][t]); return 0; }
6. 树形 DP (Unaccepted)
7. 区间 DP
/* Luogu P1880 石子合并 * Au: GG */ #include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> #include <ctime> #include <iostream> #include <algorithm> using namespace std; const int N = 100 + 5; const int inf = 2147483647; int n, d[2 * N][2 * N], e[2 * N][2 * N], a[N], sum[2 * N]; int ans1 = inf, ans2 = - inf; int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &a[i]); for (int i = 1; i <= 2 * n; i++) sum[i] = sum[i - 1] + a[i > n ? i % n : i]; for (int i = 1; i <= 2 * n; i++) d[i][i] = 0; for (int len = 2; len <= n; len++) { for (int i = 1; i + len - 1 <= 2 * n; i++) { int j = i + len - 1; d[i][j] = inf; for (int k = i; k < j; k++) { d[i][j] = min(d[i][j], d[i][k] + d[k + 1][j] + sum[j] - sum[i - 1]); } } } for (int i = 1; i <= n; i++) ans1 = min(ans1, d[i][i + n - 1]); for (int i = 1; i <= 2 * n; i++) e[i][i] = 0; for (int len = 2; len <= n; len++) { for (int i = 1; i + len - 1 < 2 * n; i++) { int j = i + len - 1; e[i][j] = - inf; for (int k = i; k < j; k++) { e[i][j] = max(e[i][j], e[i][k] + e[k + 1][j] + sum[j] - sum[i - 1]); } } } for (int i = 1; i <= n; i++) ans2 = max(ans2, e[i][i + n - 1]); printf("%d\n%d\n", ans1, ans2); return 0; }
8. 状态压缩 DP (Unaccepted)
9. 例题 (Unaccepted)
#A 传纸条(Accepted)
#B 乘积最大 (Unaccepted)
#C 石子合并 (Accepted)
#D 加分二叉树 (Unaccepted)
#E 没有上司的舞会(Unaccepted)
#F 选课 (Accepted)
#G 警卫安排 (Unaccepted)
#H 通向自由的钥匙 (Unaccepted)
动态规划 List
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