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https://blog.csdn.net/kenden23/article/details/26821635
寻找图中最小连通的路径，图例如以下：
算法步骤：
1. Sort all the edges in non-decreasing order of their weight. 2. Pick the smallest edge. Check if it forms a cycle with the spanning tree
formed so far. If cycle is not formed, include this edge. Else, discard it. 3. Repeat step#2 until there are (V-1) edges in the spanning tree.
关键是第二步难，这里使用Union Find来解决，能够差点儿小于O(lgn)的时间效率来推断是否须要推断的顶点和已经选择的顶点成环。
正由于这步，使得原本简单的贪心法。变得不那么简单了。
这样本算法的时间效率达到：max(O(ElogE) , O(ElogV))
原文參考：http://www.geeksforgeeks.org/greedy-algorithms-set-2-kruskals-minimum-spanning-tree-mst/
#pragma once
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
class KruskalsMST
{
struct Edge
{
int src, des, weight;
};
static int cmp(const void *a, const void *b)
{
Edge *a1 = (Edge *) a, *b1 = (Edge *) b;
return a1->weight - b1->weight;
}
struct Graph
{
int V, E;
Edge *edges;
Graph(int v, int e) : V(v), E(e)
{
edges = new Edge[e];
}
virtual ~Graph()
{
if (edges) delete [] edges;
}
};
struct SubSet
{
int parent, rank;
};
int find(SubSet *subs, int i)
{
if (subs[i].parent != i)
subs[i].parent = find(subs, subs[i].parent);
return subs[i].parent;
}
void UnionTwo(SubSet *subs, int x, int y)
{
int xroot = find(subs, x);
int yroot = find(subs, y);
if (subs[xroot].rank < subs[yroot].rank)
subs[xroot].parent = yroot;
else if (subs[xroot].rank > subs[yroot].rank)
subs[yroot].parent = xroot;
else
{
subs[xroot].rank++;
subs[yroot].parent = xroot;
}
}
Graph *graph;
Edge *res;
SubSet *subs;
void initSubSet()
{
subs = new SubSet[graph->V];
for (int i = 0; i < graph->V; i++)
{
subs[i].parent = i;
subs[i].rank = 0;
}
}
void mst()
{
res = new Edge[graph->V-1];
qsort(graph->edges, graph->E, sizeof(graph->edges[0]), cmp);
initSubSet();
for (int e = 0, i = 0; e < graph->V - 1 && i < graph->E; i++)
{
Edge nextEdge = graph->edges[i];
int x = find(subs, nextEdge.src);
int y = find(subs, nextEdge.des);
if (x != y)
{
res[e++] = nextEdge;
UnionTwo(subs, x, y);
}
}
}
void printResult()
{
printf("Following are the edges in the constructed MST\n");
for (int i = 0; i < graph->V-1; ++i)
printf("%d -- %d == %d\n", res[i].src, res[i].des, res[i].weight);
}
public:
KruskalsMST()
{
/* Let us create following weighted graph
10
0--------1
| \ |
6| 5\ |15
| \ |
2--------3
4 */
int V = 4; // Number of vertices in graph
int E = 5; // Number of edges in graph
graph = new Graph(V, E);
// add edge 0-1
graph->edges[0].src = 0;
graph->edges[0].des = 1;
graph->edges[0].weight = 10;
// add edges 0-2
graph->edges[1].src = 0;
graph->edges[1].des = 2;
graph->edges[1].weight = 6;
// add edges 0-3
graph->edges[2].src = 0;
graph->edges[2].des = 3;
graph->edges[2].weight = 5;
// add edges 1-3
graph->edges[3].src = 1;
graph->edges[3].des = 3;
graph->edges[3].weight = 15;
// add edges 2-3
graph->edges[4].src = 2;
graph->edges[4].des = 3;
graph->edges[4].weight = 4;
mst();
printResult();
}
~KruskalsMST()
{
if (res) delete [] res;
if (subs) delete [] subs;
if (graph) delete graph;
}
};