Union-Find-004-Optimize-by-Rank

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本文深入探讨了并查集在不同优化策略下的实现与性能对比，包括基础版本、路径压缩及按秩合并策略。通过随机生成的数据进行大量操作，演示了各版本并查集的运行效率，展示了按秩合并策略在大规模数据集上的显著优势。

UnionFind1.h

#ifndef INC_05_OPTIMIZE_BY_RANK_UNIONFIND1_H
#define INC_05_OPTIMIZE_BY_RANK_UNIONFIND1_H

#include <iostream>
#include <cassert>

using namespace std;

namespace UF1 {

    class UnionFind {

    private:
        int *id;
        int count;

    public:
        UnionFind(int n) {
            count = n;
            id = new int[n];
            for (int i = 0; i < n; i++)
                id[i] = i;
        }

        ~UnionFind() {
            delete[] id;
        }

        int find(int p) {
            assert(p >= 0 && p < count);
            return id[p];
        }

        bool isConnected(int p, int q) {
            return find(p) == find(q);
        }

        void unionElements(int p, int q) {

            int pID = find(p);
            int qID = find(q);

            if (pID == qID)
                return;

            for (int i = 0; i < count; i++)
                if (id[i] == pID)
                    id[i] = qID;
        }
    };
}
#endif

UnionFind2.h

#ifndef INC_05_OPTIMIZE_BY_RANK_UNIONFIND2_H
#define INC_05_OPTIMIZE_BY_RANK_UNIONFIND2_H

#include <cassert>

using namespace std;


namespace UF2{

    class UnionFind{

    private:
        int* parent;
        int count;

    public:
        UnionFind(int count){
            parent = new int[count];
            this->count = count;
            for( int i = 0 ; i < count ; i ++ )
                parent[i] = i;
        }

        ~UnionFind(){
            delete[] parent;
        }

        int find(int p){
            assert( p >= 0 && p < count );
            while( p != parent[p] )
                p = parent[p];
            return p;
        }

        bool isConnected( int p , int q ){
            return find(p) == find(q);
        }

        void unionElements(int p, int q){

            int pRoot = find(p);
            int qRoot = find(q);

            if( pRoot == qRoot )
                return;

            parent[pRoot] = qRoot;
        }
    };
}

#endif

UnionFind3.h

#ifndef INC_05_OPTIMIZE_BY_RANK_UNIONFIND3_H
#define INC_05_OPTIMIZE_BY_RANK_UNIONFIND3_H

#include <cassert>

using namespace std;


namespace UF3{

    class UnionFind{

    private:
        int* parent;
        int* rank; // rank[i]表示以i为根的集合所表示的树的层数
        int count;

    public:
        UnionFind(int count){
            parent = new int[count];
            rank = new int[count];
            this->count = count;
            for( int i = 0 ; i < count ; i ++ ){
                parent[i] = i;
                rank[i] = 1;
            }
        }

        ~UnionFind(){
            delete[] parent;
            delete[] rank;
        }

        int find(int p){
            assert( p >= 0 && p < count );
            while( p != parent[p] )
                p = parent[p];
            return p;
        }

        bool isConnected( int p , int q ){
            return find(p) == find(q);
        }

        void unionElements(int p, int q){

            int pRoot = find(p);
            int qRoot = find(q);

            if( pRoot == qRoot )
                return;

            if( rank[pRoot] < rank[qRoot] ){
                parent[pRoot] = qRoot;
            }
            else if( rank[qRoot] < rank[pRoot]){
                parent[qRoot] = pRoot;
            }
            else{ // rank[pRoot] == rank[qRoot]
                parent[pRoot] = qRoot;
                rank[qRoot] += 1;
            }
        }
    };
}

#endif

UnionFindTestHelper.h

#ifndef INC_05_OPTIMIZE_BY_RANK_UNIONFINDTESTHELPER_H
#define INC_05_OPTIMIZE_BY_RANK_UNIONFINDTESTHELPER_H

#include <iostream>
#include <ctime>
#include "UnionFind1.h"
#include "UnionFind2.h"
#include "UnionFind3.h"

using namespace std;

namespace UnionFindTestHelper{

    void testUF1( int n ){

        srand( time(NULL) );
        UF1::UnionFind uf = UF1::UnionFind(n);

        time_t startTime = clock();

        for( int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.unionElements(a,b);
        }
        for(int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.isConnected(a,b);
        }
        time_t endTime = clock();

        cout<<"UF1, "<<2*n<<" ops, "<<double(endTime-startTime)/CLOCKS_PER_SEC<<" s"<<endl;
    }

    void testUF2( int n ){

        srand( time(NULL) );
        UF2::UnionFind uf = UF2::UnionFind(n);

        time_t startTime = clock();

        for( int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.unionElements(a,b);
        }
        for(int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.isConnected(a,b);
        }
        time_t endTime = clock();

        cout<<"UF2, "<<2*n<<" ops, "<<double(endTime-startTime)/CLOCKS_PER_SEC<<" s"<<endl;
    }

    void testUF3( int n ){

        srand( time(NULL) );
        UF3::UnionFind uf = UF3::UnionFind(n);

        time_t startTime = clock();

        for( int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.unionElements(a,b);
        }
        for(int i = 0 ; i < n ; i ++ ){
            int a = rand()%n;
            int b = rand()%n;
            uf.isConnected(a,b);
        }
        time_t endTime = clock();

        cout<<"UF3, "<<2*n<<" ops, "<<double(endTime-startTime)/CLOCKS_PER_SEC<<" s"<<endl;
    }
}

#endif

main.cpp

#include <iostream>
#include "UnionFindTestHelper.h"

using namespace std;


int main() {

    int n = 1000000;

    //UnionFindTestHelper::testUF1(n);
    //UnionFindTestHelper::testUF2(n);
    UnionFindTestHelper::testUF3(n);

    return 0;
}