Subarrays with K Different Integers

Subarrays with K Different Integers - Problem

Given an integer array nums and an integer k, return the number of good subarrays of nums.

A good array is an array where the number of different integers in that array is exactly k.

For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3.

A subarray is a contiguous part of an array.

Input & Output

Example 1 — Basic Case

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

› Output: 7

💡 Note: Subarrays with exactly 2 distinct integers: [1,2], [2,1], [1,2], [2,1,2], [1,2,3], [2,3], [1,3]. Total count = 7.

Example 2 — Single Distinct

$ Input: nums = [1,2,1,3,4], k = 3

› Output: 3

💡 Note: Subarrays with exactly 3 distinct integers: [1,2,1,3], [2,1,3], [1,3,4]. Total count = 3.

Example 3 — All Same Elements

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

› Output: 10

💡 Note: All subarrays have exactly 1 distinct integer. With n=4, total subarrays = n*(n+1)/2 = 4*5/2 = 10.

Constraints

1 ≤ nums.length ≤ 2 × 10⁴
1 ≤ nums[i], k ≤ nums.length

Visualization

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Asked in

G Google 15 f Facebook 12 a Amazon 8

The key insight is transforming 'exactly k distinct' into 'at most k distinct' - 'at most k-1 distinct'. Best approach uses sliding window with frequency counting. Time: O(n), Space: O(k)

Common Approaches

✓ Brute Force

⏱️ Time: O(n³) Space: O(n)

Generate every possible subarray, count the number of distinct integers in each subarray, and increment the result if it equals k.

Sliding Window (At Most K Technique)

⏱️ Time: O(n) Space: O(k)

Use the mathematical insight that subarrays with exactly k distinct integers = subarrays with at most k distinct - subarrays with at most k-1 distinct. Implement a helper function using sliding window to count subarrays with at most k distinct integers.

Brute Force — Algorithm Steps

Generate all possible subarrays using nested loops
For each subarray, use a set to count distinct integers
If count equals k, increment result

Visualization

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Step-by-Step Walkthrough

Generate Subarrays

Create all possible contiguous subarrays

Count Distinct

For each subarray, count unique elements

Check Condition

If count equals k, increment result

Code -

solution.c — C

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

int solution(int* nums, int numsSize, int k) {
    int count = 0;
    
    for (int i = 0; i < numsSize; i++) {
        for (int j = i; j < numsSize; j++) {
            int distinct[1001] = {0}; // Assuming values are within reasonable range
            int distinctCount = 0;
            
            for (int idx = i; idx <= j; idx++) {
                if (nums[idx] >= 0 && nums[idx] <= 1000 && distinct[nums[idx]] == 0) {
                    distinct[nums[idx]] = 1;
                    distinctCount++;
                }
            }
            
            if (distinctCount == k) {
                count++;
            }
        }
    }
    
    return count;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int nums[1000];
    int numsSize = 0;
    char* token = strtok(line, "[],\n");
    while (token != NULL) {
        if (strlen(token) > 0) {
            nums[numsSize++] = atoi(token);
        }
        token = strtok(NULL, "[],\n");
    }
    
    int k;
    scanf("%d", &k);
    
    int result = solution(nums, numsSize, k);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Two nested loops to generate O(n²) subarrays, O(n) to count distinct elements in each

✓ Linear Growth

Space Complexity

O(n)

Set to store distinct elements, can hold up to n elements

✓ Linear Space

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Medium Frequency

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force — Algorithm Steps

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Code -

Time & Space Complexity

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