Union-Find-005-UnionFind

最新推荐文章于 2025-08-17 14:48:57 发布

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UnionFind1.h

#ifndef UNIONFIND_UNIONFIND_H
#define UNIONFIND_UNIONFIND_H

#include <cassert>

using namespace std;


// Quick Find
namespace UF1{

    class UnionFind{

    private:
        int* id;
        int count;

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

        ~UnionFind(){
            delete[] id;
        }

        int size(){
            return count;
        }

        bool isConnected( int p , int q ){
            return id[p] == id[q];
        }

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

        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 UNIONFIND_UNIONFIND2_H
#define UNIONFIND_UNIONFIND2_H

#include <cassert>

using namespace std;


// Quick Union
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 size(){
            return count;
        }

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

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

        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 UNIONFIND_UNIONFIND3_H
#define UNIONFIND_UNIONFIND3_H

#include <cassert>

using namespace std;


// Quick Union + sz
namespace UF3{

    class UnionFind{

    private:
        int* parent;
        int* sz; // sz[i]表示以i为根的集合中元素个数
        int count;

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

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

        int size(){
            return count;
        }

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

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

        void unionElements(int p, int q){

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

            if( pRoot == qRoot )
                return;

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

#endif

UnionFind4.h

#ifndef UNIONFIND_UNIONFIND4_H
#define UNIONFIND_UNIONFIND4_H

#include <cassert>

using namespace std;


// Quick Union + rank
namespace UF4{

    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 size(){
            return count;
        }

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

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

        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] ++;
            }
        }
    };
}

#endif

UnionFind5.h

#ifndef UNIONFIND_UNIONFIND5_H
#define UNIONFIND_UNIONFIND5_H

#include <cassert>

using namespace std;


// Quick Union + rank + path compression
namespace UF5{

    class UnionFind{

    private:
        int* parent;
        int* rank;
        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 size(){
            return count;
        }

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

        int find(int p){

            assert( p >= 0 && p < count );

            // path compression 1
            while( p != parent[p] ){
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;

            // path compression 2
//            if( p != parent[p] )
//                parent[p] = find( parent[p] );
//            return parent[p];
        }

        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] ++;
            }

        }

        void show(){
            for( int i = 0 ; i < count ; i ++ )
                cout<<i<<" : "<<parent[i]<<endl;
        }
    };
}

#endif

UnionFindTestHelper.h

#ifndef UNIONFIND_UNIONFINDTESTHELPER_H
#define UNIONFIND_UNIONFINDTESTHELPER_H

#include <iostream>
#include <ctime>
#include "UnionFind1.h"
#include "UnionFind2.h"
#include "UnionFind3.h"
#include "UnionFind4.h"
#include "UnionFind5.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;
    }

    void testUF4( int n ){

        srand( time(NULL) );
        UF4::UnionFind uf = UF4::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<<"UF4, "<<2*n<<" ops, "<<double(endTime-startTime)/CLOCKS_PER_SEC<<" s"<<endl;
    }

    void testUF5( int n ){

        srand( time(NULL) );
        UF5::UnionFind uf = UF5::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<<"UF5, "<<2*n<<" ops, "<<double(endTime-startTime)/CLOCKS_PER_SEC<<" s"<<endl;
    }
}
#endif

main_path_compression.cpp

#include <iostream>
#include "UnionFind5.h"

using namespace std;

int main() {

    UF5::UnionFind uf = UF5::UnionFind(5);
    uf.unionElements(1,0);
    uf.unionElements(2,1);
    uf.unionElements(3,2);
    uf.unionElements(4,3);
    uf.show();

    cout<<"======"<<endl;
    uf.find(4);
    uf.show();

    return 0;
}

main.cpp

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

using namespace std;

int main() {

    int n = 1000000;

    // Quick Find
    //UnionFindTestHelper::testUF1(n);

    // Quick Union
    //UnionFindTestHelper::testUF2(n);

    // Quick Union + sz
    UnionFindTestHelper::testUF3(n);

    // Quick Union + rank
    UnionFindTestHelper::testUF4(n);

    // Quick Union + rank + path compression
    UnionFindTestHelper::testUF5(n);

    return 0;
}