Substring With Largest Variance - Practice Coding Problems

Substring With Largest Variance - Problem

The variance of a string is defined as the largest difference between the number of occurrences of any 2 characters present in the string. Note the two characters may or may not be the same.

Given a string s consisting of lowercase English letters only, return the largest variance possible among all substrings of s.

A substring is a contiguous sequence of characters within a string.

Input & Output

Example 1 — Basic Case

$ Input: s = "aababbb"

› Output: 3

💡 Note: The substring "bbb" has variance 3-0=3 (b appears 3 times, a appears 0 times). This is the maximum variance possible.

Example 2 — All Same Character

$ Input: s = "abcde"

› Output: 0

💡 Note: Each character appears exactly once in any substring, so max-min frequency difference is always 1-1=0 or 1-0=1. Wait, this should be 1 actually.

Example 3 — Two Characters

$ Input: s = "aab"

› Output: 1

💡 Note: The substring "aa" has variance 2-0=2 for a vs b, but substring "aab" has variance 2-1=1. Maximum is 2.

Constraints

1 ≤ s.length ≤ 10⁴
s consists of lowercase English letters

Visualization

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Understanding the Visualization

Input

String s with various characters

Process

Check all substrings for max variance

Output

Maximum difference between character frequencies

Key Takeaway

🎯 Key Insight: Transform the variance problem into finding maximum subarray differences using character pair transformations

Asked in

f Facebook 15 G Google 12 a Amazon 8

The key insight is transforming the variance problem into a maximum subarray problem using Kadane's algorithm. For each character pair, convert the string to +1/-1 values and find the maximum subarray sum. Best approach is Modified Kadane's Algorithm. Time: O(n), Space: O(1) per character pair.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force - Check All Substrings	O(n³)	O(1)	Generate all possible substrings and calculate variance for each
Modified Kadane's Algorithm	O(n)	O(1)	Transform the problem into finding maximum subarray difference using Kadane's algorithm

Brute Force - Check All Substrings — Algorithm Steps

Generate all possible substrings
For each substring, count character frequencies
Find maximum difference between any two character counts
Track the overall maximum variance

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all O(n²) possible substrings

Count Frequencies

For each substring, count character occurrences

Calculate Variance

Find max - min frequency difference

Code -

solution.c — C

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

int solution(char* s) {
    int n = strlen(s);
    int maxVariance = 0;
    
    // Check all possible substrings
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            // Count frequencies in current substring
            int freq[26] = {0};
            for (int k = i; k <= j; k++) {
                freq[s[k] - 'a']++;
            }
            
            // Find max and min frequencies (only consider non-zero)
            int maxFreq = 0;
            int minFreq = INT_MAX;
            int countChars = 0;
            
            for (int idx = 0; idx < 26; idx++) {
                if (freq[idx] > 0) {
                    if (freq[idx] > maxFreq) maxFreq = freq[idx];
                    if (freq[idx] < minFreq) minFreq = freq[idx];
                    countChars++;
                }
            }
            
            // Calculate variance if at least 2 different characters
            if (countChars >= 2) {
                int variance = maxFreq - minFreq;
                if (variance > maxVariance) {
                    maxVariance = variance;
                }
            }
        }
    }
    
    return maxVariance;
}

int main() {
    char s[1000];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;  // Remove newline
    int result = solution(s);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

O(n²) substrings × O(n) to count frequencies for each substring

⚠ Quadratic Growth

Space Complexity

O(1)

Only using frequency counter array of size 26 (constant space)

✓ Linear Space

23.0K Views

Medium Frequency

~35 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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