HDU 2426 interesting housing problem (km perfect match)

HDU 2426 interesting housing problem

Question Link

N students and M rooms. Given the preferences of some students who want to house, find an optimal solution to allocate a room for each student and maximize their liking, note that there is a pitfall in this question, that is, the students will not live in a room with negative liking.

Idea: it is obvious that the maximum matching problem of KM is that the degree of liking is negative and the edge is not connected directly.

Code:

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;const int MAXNODE = 505;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], right[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;right[i] = j;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(int tot) {for (int i = 0; i < n; i++) {left[i] = -1; right[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 < tot; i++) {if (right[i] == -1) return -1;if (g[i][right[i]] == -1) return -1;ans += g[i][right[i]];}return ans;}} gao;int n, m, k;int main() {int cas = 0;while (~scanf("%d%d%d", &n, &m, &k)) {gao.init(max(n, m));int u, v, w;while (k--) {scanf("%d%d%d", &u, &v, &w);if (w >= 0) gao.add_Edge(u, v, w);}printf("Case %d: %d\n", ++cas, gao.km(n));}return 0;}

HDU 2426 interesting housing problem (km perfect match)