Count the Number of Good Subarrays - Practice Coding Problems

Count the Number of Good Subarrays - Problem

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

A subarray arr is good if there are at least k pairs of indices (i, j) such that i < j and arr[i] == arr[j].

A subarray is a contiguous non-empty sequence of elements within an array.

Input & Output

Example 1 — Basic Case

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

› Output: 4

💡 Note: Good subarrays: [3,1,4,3] has pairs (3,3)=1, not enough. [3,1,4,3,2,2] has pairs (3,3)+(2,2)=2≥2✓. [3,1,4,3,2,2,4] has pairs (3,3)+(2,2)+(4,4)=3≥2✓. Total of 4 good subarrays.

Example 2 — Small Array

$ Input: nums = [1,1,1,1,1], k = 10

› Output: 1

💡 Note: Only the full array [1,1,1,1,1] has enough pairs: C(5,2)=10 pairs of equal elements, which equals k=10.

Example 3 — No Good Subarrays

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

› Output: 0

💡 Note: All elements are distinct, so no pairs of equal elements exist. No subarray can have ≥1 pairs.

Constraints

1 ≤ nums.length ≤ 10⁵
1 ≤ nums[i] ≤ 10⁹
1 ≤ k ≤ 10⁹

Visualization

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Understanding the Visualization

Input

Array [3,1,4,3,2,2,4] with k=2

Process

Find subarrays with ≥2 pairs of equal elements

Output

Count of good subarrays = 4

Key Takeaway

🎯 Key Insight: Use sliding window with frequency counting to efficiently track pairs of equal elements in subarrays

Asked in

G Google 15 f Meta 12 a Amazon 10

The key insight is to use sliding window with frequency counting to efficiently track pairs of equal elements. The optimal approach uses a sliding window that expands to find good subarrays and counts multiple valid subarrays at once. Time: O(n²), Space: O(n)

Common Approaches

Approach	Time	Space	Notes
✓ Sliding Window with Frequency Map	O(n²)	O(n)	Use sliding window technique with frequency counting to efficiently track pairs
Optimized Sliding Window	O(n²)	O(n)	Advanced sliding window with mathematical pair calculation
Brute Force - Check All Subarrays	O(n³)	O(1)	Generate all possible subarrays and count pairs in each

Sliding Window with Frequency Map — Algorithm Steps

Use two pointers to maintain a sliding window
Track frequency of elements and current pair count
Expand window and update pair count when adding elements
When pairs >= k, count all subarrays from left to right

Visualization

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Step-by-Step Walkthrough

Start Window

Begin with left pointer, expand right

Count Pairs

Track frequency and calculate pairs incrementally

Good Subarray

When pairs >= k, count this subarray

Code -

solution.c — C

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

int solution(int* nums, int numsSize, int k) {
    int result = 0;
    
    for (int left = 0; left < numsSize; left++) {
        int freq[100001] = {0};  // Assuming values are within reasonable range
        int pairs = 0;
        
        for (int right = left; right < numsSize; right++) {
            // Add nums[right] to window
            int val = nums[right] + 50000;  // Handle negative values
            pairs += freq[val];  // pairs with existing same elements
            freq[val]++;
            
            // If we have enough pairs, this subarray is good
            if (pairs >= k) {
                result++;
            }
        }
    }
    
    return result;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(n²)

Outer loop runs n times, inner while loop can run up to n times in worst case

⚠ Quadratic Growth

Space Complexity

O(n)

Hash map to store frequency of elements, up to n unique elements

⚡ Linearithmic Space

23.4K Views

Medium Frequency

~25 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sliding Window with Frequency Map — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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