Kruskal 算法原理及证明见提高课。
Kruskal算法求最小生成树 $O(m\log m)$

这里重载运算符的方式也可以通过写cmp()来作为sort的第三个参数
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| bool cmp(Edge a, Edge b)
{
return a.w < b.w;
}
|
完整代码
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| #include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N = 100010, M = 200010, INF = 0x3f3f3f3f;
int p[N];
int n, m;
struct Edge
{
int a, b, w;
bool operator< (const Edge &W)const
{
return w < W.w;
}
}edges[M];
int find(int x)
{
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
int kruskal()
{
sort(edges, edges + m);
for (int i = 1; i <= n; i ++ ) p[i] = i;
int res = 0, cnt = 0;
for (int i = 0; i < m; i ++ )
{
int a = edges[i].a, b = edges[i].b, w = edges[i].w;
a = find(a), b = find(b);
if (a != b)
{
p[a] = b;
res += w;
cnt ++;
}
}
if (cnt < n - 1) return INF;
return res;
}
int main()
{
cin >> n >> m;
for (int i = 0; i < m; i ++ )
{
int a, b, w;
scanf("%d%d%d", &a, &b, &w);
edges[i] = {a, b, w};
}
int t = kruskal();
if (t == INF) puts("impossible");
else cout << t << endl;
return 0;
}
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