Why are there wide runtime variations when running UnionFind on Windows and Mac OS?

I recently attended courses on data structure, I learned that QuickUnion performance is better than QuickFind when connecting two elements. But when I test the same code in GCC instead of Windows Mac instead of Mac OS X, I got a completely different result, but I didn't know why. Here is the QuickFind code.

#ifndef INC_03_QUICK_UNION_UNIONFIND1_H
#define INC_03_QUICK_UNION_UNIONFIND1_H

#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 //INC_03_QUICK_UNION_UNIONFIND1_H

      

And QuickUnion:

#ifndef INC_03_QUICK_UNION_UNIONFIND2_H
#define INC_03_QUICK_UNION_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 //INC_03_QUICK_UNION_UNIONFIND2_H

      

Then UnionFindTestHelper, a class that can help you test two types of data structures:

#ifndef INC_03_QUICK_UNION_UNIONFINDTESTHELPER_H
#define INC_03_QUICK_UNION_UNIONFINDTESTHELPER_H

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

#endif //INC_03_QUICK_UNION_UNIONFINDTESTHELPER_H  

      

Finally main.cpp:

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

using namespace std;


int main() {

    int n = 100000;

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

    return 0;
}

      

Teacher tested QuickUnion can save half the time than QuickFind, but when I tested on Windows 10 x64, the two execution results are almost the same. I don't know if I can make mistakes or differences in operating systems.

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1 answer


First, you wrote:

I found out that QuickUnion performance is better than QuickFind when connecting two items. But when I test the same code ...

But your test program doesn't just test the performance of the connection, but the union plus find.


Second, here's the order of growth for N elements for QuckUnion and QuickFind:

QuickFind:

  • find

    : O (1)
  • union

    : O (N)

QuickUnion:

  • find

    : O (tree height)
  • union

    : O (tree height)


QuickUnion is not always faster than QuickFind with your test program.

  • QuickFind is effective when you do much more find

    than union

    .
  • QuickUnion can be more efficient if you do more union

    than find

    .

Finally, performance in the QuickUnion data structure is not good in high trees .

In your test program, the height of the tree will depend on the results of the function rand()

. This explains why your results vary from one system to another. You must rewrite your test program without rand()

it to make it reproducible.

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