Count Subarrays Where Max Element Appears at Least K Times

Count Subarrays Where Max Element Appears at Least K Times - Problem

You are given an integer array nums and a positive integer k.

Return the number of subarrays where the maximum element of nums appears at least k times in that subarray.

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

Input & Output

Example 1 — Basic Case

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

› Output: 6

💡 Note: Max element is 3. Subarrays with at least 2 occurrences of 3: [3,2,3], [3,2,3,3], [2,3,3], [3,3], [3,2,3,3] (starting from index 1), and [3,3] (starting from index 3). Total: 6 subarrays.

Example 2 — Minimum Size

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

› Output: 0

💡 Note: Max element is 4, appears only once. Since k=3 but max element appears only 1 time, no subarray can have the max element appearing at least 3 times.

Example 3 — All Same Elements

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

› Output: 3

💡 Note: Max element is 3. Valid subarrays: [3,3] (indices 0-1), [3,3,3] (indices 0-2), and [3,3] (indices 1-2). Total: 3 subarrays.

Constraints

1 ≤ nums.length ≤ 10⁵
1 ≤ nums[i] ≤ 10⁶
1 ≤ k ≤ nums.length

Visualization

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Understanding the Visualization

Input

Array nums=[1,3,2,3,3] and k=2

Find Max

Maximum element is 3

Count Valid

Find subarrays with at least 2 occurrences of 3

Key Takeaway

🎯 Key Insight: Use sliding window to efficiently track when max element count reaches k

Asked in

G Google 25 A Amazon 18 M Microsoft 15

The key insight is to use a sliding window approach to efficiently count subarrays where the maximum element appears at least k times. Best approach is sliding window with Time: O(n), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Sliding Window	O(n)	O(1)	Use variable-size sliding window to efficiently count valid subarrays
Brute Force	O(n³)	O(1)	Check all possible subarrays and count max element occurrences

Sliding Window — Algorithm Steps

Find the maximum element in the array
Use two pointers to maintain a sliding window
Expand right pointer and track max element count
When count >= k, all subarrays from left to any previous position are valid

Visualization

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Step-by-Step Walkthrough

Expand Window

Move right pointer and count max elements

Valid Window

When count ≥ k, add valid subarrays

Shrink Window

Move left pointer to find next valid position

Code -

solution.c — C

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

long long solution(int* nums, int numsSize, int k) {
    // Find the maximum element in the array
    int maxElement = nums[0];
    for (int i = 1; i < numsSize; i++) {
        if (nums[i] > maxElement) {
            maxElement = nums[i];
        }
    }
    
    int left = 0;
    int maxCount = 0;
    long long result = 0;
    
    // Sliding window approach
    for (int right = 0; right < numsSize; right++) {
        // Expand window by including nums[right]
        if (nums[right] == maxElement) {
            maxCount++;
        }
        
        // Shrink window from left while we have enough max elements
        while (maxCount >= k) {
            // All subarrays from index 0 to left ending at right are valid
            result += left + 1;
            
            // Shrink window
            if (nums[left] == maxElement) {
                maxCount--;
            }
            left++;
        }
    }
    
    return result;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    line[strcspn(line, "\n")] = 0;
    
    // Parse array
    int nums[1000];
    int numsSize = 0;
    char* token = strtok(line + 1, ",]"); // Skip [
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int k;
    scanf("%d", &k);
    
    long long result = solution(nums, numsSize, k);
    printf("%lld\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through array with two pointers, each element visited at most twice

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables for pointers and counters

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sliding Window — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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