DATA STRUCTURES PROGRAM • HEAPS, HASHING & DISJOINT SETS

Implement Disjoint-Set Union with Path Compression

Learn how to implement disjoint-set union with path compression using a clear C program.

IntermediateDSUPath compressionUnion by rank

PROBLEM UNDERSTANDING

Input and expected output

Sample input

No input required

Sample output

0 and 2 connected: yes
0 and 4 connected: no

COMPLETE C PROGRAM

Complete C implementation

#include <stdio.h>

int find(int parent[], int value)
{
    if (parent[value] != value) parent[value] = find(parent, parent[value]);
    return parent[value];
}
void unite(int parent[], int rank[], int first, int second)
{
    int left = find(parent, first), right = find(parent, second);
    if (left == right) return;
    if (rank[left] < rank[right]) parent[left] = right;
    else if (rank[left] > rank[right]) parent[right] = left;
    else { parent[right] = left; rank[left]++; }
}

int main(void)
{
    int parent[6], rank[6] = {0};
    for (int index = 0; index < 6; index++) parent[index] = index;
    unite(parent, rank, 0, 1); unite(parent, rank, 1, 2); unite(parent, rank, 3, 4);
    printf("0 and 2 connected: %s\n", find(parent, 0) == find(parent, 2) ? "yes" : "no");
    printf("0 and 4 connected: %s\n", find(parent, 0) == find(parent, 4) ? "yes" : "no");
    return 0;
}

CURRENT STEP

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SELECTED LINE

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EXPECTED OUTPUT FOR THE SAMPLE

0 and 2 connected: yes
0 and 4 connected: no

0%Step 0 of 0

PROGRAM EXPLANATION

Algorithm and explanation

Read the required input values.
Compress find paths and attach the shallower representative tree beneath the deeper one.
Display the computed result.

Compress find paths and attach the shallower representative tree beneath the deeper one.

EFFICIENCY

Time and space complexity

Time complexity

Almost O(1) amortized

Auxiliary space

O(n)

DEBUGGING CHECKLIST

Common mistakes

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Use the correct format specifier for every variable.

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Initialize variables before using their values.

Check this

Check braces, semicolons and input order carefully.

Try it yourself

Practice: Run the program with the sample input, predict its output, and then test one boundary case of your own.