本文主要是介绍HDU 3718 Similarity（KM最大匹配），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
HDU 3718 Similarity
题目链接
题意：给定一个标准答案字符串，然后下面每一行给一个串，要求把字符一种对应一种，要求匹配尽量多
思路：显然的KM最大匹配问题，位置对应的字符连边权值+1
代码：
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;const int MAXNODE = 27;typedef int Type;
const Type INF = 0x3f3f3f3f;struct KM {int n, m;Type g[MAXNODE][MAXNODE];Type Lx[MAXNODE], Ly[MAXNODE], slack[MAXNODE];int left[MAXNODE], right[MAXNODE];bool S[MAXNODE], T[MAXNODE];void init(int n, int m) {this->n = n;this->m = m;memset(g, 0, sizeof(g));}void add_Edge(int u, int v, Type val) {g[u][v] += val;}bool dfs(int i) {S[i] = true;for (int j = 0; j < m; j++) {if (T[j]) continue;Type tmp = Lx[i] + Ly[j] - g[i][j];if (!tmp) {T[j] = true;if (left[j] == -1 || dfs(left[j])) {left[j] = i;right[i] = j;return true;}} else slack[j] = min(slack[j], tmp);}return false;}void update() {Type a = INF;for (int i = 0; i < m; i++)if (!T[i]) a = min(a, slack[i]);for (int i = 0; i < n; i++)if (S[i]) Lx[i] -= a;for (int i = 0; i < m; i++)if (T[i]) Ly[i] += a;}Type km() {memset(left, -1, sizeof(left));memset(right, -1, sizeof(right));memset(Ly, 0, sizeof(Ly));for (int i = 0; i < n; i++) {Lx[i] = -INF;for (int j = 0; j < m; j++)Lx[i] = max(Lx[i], g[i][j]);}for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) slack[j] = INF;while (1) {memset(S, false, sizeof(S));memset(T, false, sizeof(T));if (dfs(i)) break;else update();}}Type ans = 0;for (int i = 0; i < n; i++) {ans += g[i][right[i]];}return ans;}
} gao;const int N = 10005;int t, n, k, m;
char s[N][2];int main() {scanf("%d", &t);while (t--) {scanf("%d%d%d", &n, &k, &m);for (int i = 0; i < n; i++)scanf("%s", s[i]);while (m--) {gao.init(26, 26);char c[2];for (int i = 0; i < n; i++) {scanf("%s", c);gao.add_Edge(s[i][0] - 'A', c[0] - 'A', 1);}printf("%.4lf\n", gao.km() * 1.0 / n);}}return 0;
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