用C++编写一个km算法,寻找最优匹配,输入顶点数和边权值,输出匹配结果和最大边权和
时间: 2025-01-04 16:40:55 浏览: 6
好的,下面是一个使用C++编写的KM算法示例,用于寻找最优匹配,并输出匹配结果和最大边权和。
```cpp
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAXN = 100;
const int INF = 0x3f3f3f3f;
int n;
int w[MAXN][MAXN];
int lx[MAXN], ly[MAXN];
int match[MAXN];
bool visx[MAXN], visy[MAXN];
bool dfs(int x) {
visx[x] = true;
for (int y = 0; y < n; ++y) {
if (!visy[y] && lx[x] + ly[y] == w[x][y]) {
visy[y] = true;
if (match[y] == -1 || dfs(match[y])) {
match[y] = x;
return true;
}
}
}
return false;
}
int km() {
memset(match, -1, sizeof(match));
memset(ly, 0, sizeof(ly));
for (int i = 0; i < n; ++i) {
lx[i] = -INF;
for (int j = 0; j < n; ++j) {
lx[i] = max(lx[i], w[i][j]);
}
}
for (int x = 0; x < n; ++x) {
while (true) {
memset(visx, false, sizeof(visx));
memset(visy, false, sizeof(visy));
if (dfs(x)) break;
int delta = INF;
for (int i = 0; i < n; ++i) {
if (visx[i]) {
for (int j = 0; j < n; ++j) {
if (!visy[j]) {
delta = min(delta, lx[i] + ly[j] - w[i][j]);
}
}
}
}
for (int i = 0; i < n; ++i) {
if (visx[i]) lx[i] -= delta;
if (visy[i]) ly[i] += delta;
}
}
}
int res = 0;
for (int i = 0; i < n; ++i) {
res += w[match[i]][i];
}
return res;
}
int main() {
cout << "请输入顶点数: ";
cin >> n;
cout << "请输入边权值: " << endl;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
cin >> w[i][j];
}
}
int maxWeight = km();
cout << "匹配结果: " << endl;
for (int i = 0; i < n; ++i) {
cout << "顶点 " << match[i] << " 和顶点 " << i << " 匹配" << endl;
}
cout << "最大边权和: " << maxWeight << endl;
return 0;
}
```
这个程序首先输入顶点数和边权值,然后使用KM算法计算最大边权和,并输出匹配结果。
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