HDU 2426 Interesting Housing Problem
题目链接
题意：n个学生，m个房间，给定1些学生想住房的喜欢度，找1个最优方案使得每一个学生分配1个房间，并且使得喜欢度最大，注意这题有个坑，就是学生不会住喜欢度为负的房间
思路：很明显的KM最大匹配问题，喜欢度为负直接不连边便可
代码：
#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] == ⑴ || 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] = ⑴; right[i] = ⑴;
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] == ⑴) return ⑴;
if (g[i][right[i]] == ⑴) return ⑴;
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
", ++cas, gao.km(n));
}
return 0;
}