Number of Unequal Triplets in Array - Practice Coding Problems

Number of Unequal Triplets in Array - Problem

You are given a 0-indexed array of positive integers nums. Find the number of triplets (i, j, k) that meet the following conditions:

0 <= i < j < k < nums.length
nums[i], nums[j], and nums[k] are pairwise distinct.
In other words, nums[i] != nums[j], nums[i] != nums[k], and nums[j] != nums[k].

Return the number of triplets that meet the conditions.

Input & Output

Example 1 — Basic Case

$ Input: nums = [4,4,2,4,3]

› Output: 3

💡 Note: Valid triplets are (0,2,4), (1,2,4), (2,3,4) with values (4,2,3). All have distinct values.

Example 2 — No Valid Triplets

$ Input: nums = [1,1,1,1,1]

› Output: 0

💡 Note: All elements are the same, so no triplet can have pairwise distinct values.

Example 3 — All Unique

$ Input: nums = [1,2,3]

› Output: 1

💡 Note: Only one triplet (0,1,2) with values (1,2,3), all distinct.

Constraints

3 ≤ nums.length ≤ 100
1 ≤ nums[i] ≤ 1000

Visualization

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Understanding the Visualization

Input Array

Array with potentially duplicate values

Find Triplets

Locate all (i,j,k) where i<j<k and values are distinct

Count Result

Return total number of valid triplets

Key Takeaway

🎯 Key Insight: Count frequencies first, then use combinatorics instead of checking all O(n³) triplets

Asked in

G Google 15 a Amazon 10

The key insight is to count frequencies first rather than checking every triplet. The optimal approach uses frequency counting with combinatorics: O(n + U³) time, O(U) space where U is unique values.

Common Approaches

Approach	Time	Space	Notes
✓ Frequency Count with Combinatorics	O(n + U³)	O(U)	Count frequency of each value, then use combinatorics to calculate valid triplets
Brute Force - Triple Nested Loop	O(n³)	O(1)	Check every possible triplet (i, j, k) and count those with distinct values

Frequency Count with Combinatorics — Algorithm Steps

Step 1: Count frequency of each unique value in the array
Step 2: Get all unique values and iterate through combinations of 3
Step 3: For each triplet of unique values, multiply their frequencies
Step 4: Sum all products to get total number of valid triplets

Visualization

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Step-by-Step Walkthrough

Count Frequencies

Build frequency map of each unique value

Combine Unique Values

Take combinations of 3 different values

Multiply Frequencies

For each triplet, multiply the frequency counts

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_VAL 1001

int solution(int* nums, int numsSize) {
    int freq[MAX_VAL] = {0};
    
    // Count frequency of each value
    for (int i = 0; i < numsSize; i++) {
        freq[nums[i]]++;
    }
    
    // Get unique values
    int uniqueVals[MAX_VAL];
    int uniqueCount = 0;
    for (int i = 0; i < MAX_VAL; i++) {
        if (freq[i] > 0) {
            uniqueVals[uniqueCount++] = i;
        }
    }
    
    int count = 0;
    // Check all combinations of 3 unique values
    for (int i = 0; i < uniqueCount; i++) {
        for (int j = i + 1; j < uniqueCount; j++) {
            for (int k = j + 1; k < uniqueCount; k++) {
                int val1 = uniqueVals[i];
                int val2 = uniqueVals[j];
                int val3 = uniqueVals[k];
                count += freq[val1] * freq[val2] * freq[val3];
            }
        }
    }
    
    return count;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Parse array
    int nums[1000];
    int size = 0;
    char* ptr = line + 1; // Skip '['
    char* token = strtok(ptr, ",]");
    while (token != NULL) {
        nums[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    printf("%d\n", solution(nums, size));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n + U³)

O(n) to count frequencies, O(U³) to check all unique value triplets where U ≤ n

✓ Linear Growth

Space Complexity

O(U)

Hash map stores frequency count for each unique value

✓ Linear Space

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Medium Frequency

~15 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Frequency Count with Combinatorics — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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