最小生成树专题

#include <iostream>
#include <algorithm>
using namespace std;
const int NODE_NUM = 102;
int father[NODE_NUM];
int n, ne;
struct edge
{
int u,v,w;
};
edge e[NODE_NUM*NODE_NUM];

bool cmp(const edge& a, const edge& b)
{
return a.w<b.w;
}

void make_set()
{
for (int i = 1; i <= n; ++i)
father[i] = i;
}

int find_set(int i)
{
if (father[i] != i){
father[i] = find_set(father[i]);
}
return father[i];
}

bool union_set(int a, int b) //a --> b
{
a = find_set(a);
b = find_set(b);
if (a != b){  //没有共同祖先，说明没有形成回路
father[a] = b; //将节点纳入最小生成树集合
return true;
}
else{
return false;
}
}

int kruskal()
{
int i, mst_edge = 0, sum = 0;
make_set();
sort(e, e+ne, cmp);  //将边按升序排序
for (i = 0; i < ne; ++i)//如果加入的边不会使树形成回路
{
if (union_set(e[i].u, e[i].v))
{
sum += e[i].w;//如果纳入的边数等于顶点数-1，则说明最小生成树形成
if (++mst_edge == n - 1)
{
return sum;
}
}
}
return mst_edge;
}

int main()
{
int i, j, cost;
while (scanf("%d", &n) != EOF)
{
ne = 0;
for (i = 1; i <= n; ++i)
{
for (j = 1; j <= n; ++j)
{
scanf("%d", &cost);
if (i != j)
{
e[ne].u = i;
e[ne].v = j;
e[ne++].w = cost;
}
}
}
printf("%d\n", kruskal());
}
return 0;
}