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HDU 1853 Cyclic Tour
题目链接
题意：一个有向图，边有权值，求把这个图分成几个环，每个点只能属于一个环，使得所有环的权值总和最小，求这个总和
思路：KM完美匹配，由于是环，所以每个点出度入度都是1，一个点拆成两个点，出点和入点，每个点只能用一次，这样就满足了二分图匹配，然后用KM完美匹配去就最小权值的匹配即可
代码：
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;const int MAXNODE = 105;typedef int Type;
const Type INF = 0x3f3f3f3f;struct KM {int n;Type g[MAXNODE][MAXNODE];Type Lx[MAXNODE], Ly[MAXNODE], slack[MAXNODE];int left[MAXNODE];bool S[MAXNODE], T[MAXNODE];void init(int n) {this->n = n;for (int i = 0; i < n; i++)for (int j = 0; j < n; j++)g[i][j] = -INF;}void add_Edge(int u, int v, Type val) {g[u][v] = max(g[u][v], val);}bool dfs(int i) {S[i] = true;for (int j = 0; j < n; 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;return true;}} else slack[j] = min(slack[j], tmp);}return false;}void update() {Type a = INF;for (int i = 0; i < n; i++)if (!T[i]) a = min(a, slack[i]);for (int i = 0; i < n; i++) {if (S[i]) Lx[i] -= a;if (T[i]) Ly[i] += a;}}int km() {for (int i = 0; i < n; i++) {left[i] = -1;Lx[i] = -INF; Ly[i] = 0;for (int j = 0; j < n; j++)Lx[i] = max(Lx[i], g[i][j]);}for (int i = 0; i < n; i++) {for (int j = 0; j < n; j++) slack[j] = INF;while (1) {for (int j = 0; j < n; j++) S[j] = T[j] = false;if (dfs(i)) break;else update();}}int ans = 0;for (int i = 0; i < n; i++) {if (g[left[i]][i] == -INF) return -1;ans += g[left[i]][i];}return -ans;}
} gao;int n, m;int main() {while (~scanf("%d%d", &n, &m)) {gao.init(n);int u, v, w;while (m--) {scanf("%d%d%d", &u, &v, &w);u--; v--;gao.add_Edge(u, v, -w);}printf("%d\n", gao.km());}return 0;
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