并查集

并查集的最大作用是检测一个图上面存不存在环。

无向图，六个顶点
显然 1-2-4-3连成一个环

#include<stdio.h>
#include<stdlib.h>#define  VERTICES 6void initialise(int parent[]){int i;for(i=0;i<VERTICES;i++){parent[i]=-1; }}int find_root(int x,int parent[]){int x_root=x;while(parent[x_root]!=-1){x_root=parent[x_root];}return x_root; 
}
/*1- union successfully ,0-failed*/
int union_vertices(int x,int y,int parent[]){int x_root=find_root(x,parent);int y_root=find_root(y,parent);if(x_root==y_root){return 0;} else{parent[x_root]=y_root;return 1;}}int main(){int parent[VERTICES]={0};int edges[6][2]={{0,1},{1,2},{1,3},{2,4},{3,4},{2,5}};initialise(parent);int i;for(i=0;i<6;i++){int x=edges[i][0];int y=edges[i][1];if(union_vertices(x,y,parent)){printf("Cycle detected!\n");exit(0);}}	printf("no cycle found.\n");return 0;
}

进行优化后：

#include<stdio.h>
#include<stdlib.h>#define  VERTICES 6void initialise(int parent[],int rank[]) {int i;for(i=0; i<VERTICES; i++) {parent[i]=-1;rank[i]=0;}}int find_root(int x,int parent[]) {int x_root=x;while(parent[x_root]!=-1) {x_root=parent[x_root];}return x_root;
}/*1- union successfully ,0-failed*/
int union_vertices(int x,int y,int parent[],int rank[]) {int x_root=find_root(x,parent);int y_root=find_root(y,parent);if(x_root==y_root) {return 0;} else {
//		parent[x_root]=y_root;if(rank[x_root]>rank[y_root]) {parent[y_root]=x_root;} else if(rank[y_root]>rank[x_root]) {parent[x_root]=y_root;} else {parent[x_root]=y_root;rank[y_root]++;}return 1;}}int main(void) {int parent[VERTICES]= {0};int rank[VERTICES]= {0};int edges[6][2]= {{0,1},{1,2},{1,3},{2,4},{3,4},{2,5}};initialise(parent,rank);for(int i=0; i<6; i++) {int x=edges[i][0];int y=edges[i][1];if((union_vertices(x,y,parent,rank)==0)) {printf("Cycle detected!\n");exit(0);}}printf("no cycle found.\n");return 0;
}