Largest Odd Number in String

Largest Odd Number in String - Problem

You are given a string num, representing a large integer. Return the largest-valued odd integer (as a string) that is a non-empty substring of num, or an empty string "" if no odd integer exists.

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

Input & Output

Example 1 — Basic Case with Odd Ending

$ Input: num = "52301"

› Output: "52301"

💡 Note: The entire string ends with '1' which is odd, so "52301" is the largest odd substring.

Example 2 — Even Ending, Find Rightmost Odd

$ Input: num = "5234"

› Output: "523"

💡 Note: The string ends with '4' (even), but '3' at position 2 is the rightmost odd digit, so we take "523".

Example 3 — No Odd Digits

$ Input: num = "246"

› Output: ""

💡 Note: All digits are even (2, 4, 6), so no odd substring exists. Return empty string.

Constraints

1 ≤ num.length ≤ 10⁵
num consists of only digits

Visualization

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Asked in

G Google 25 a Amazon 20 M Microsoft 15

The key insight is that the largest odd substring always ends with the rightmost odd digit. Best approach is the greedy method: scan from right to left to find the first odd digit, then return substring from start to that position. Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(n)

Check every possible substring of the input string, determine if it represents an odd number, and keep track of the largest odd substring found.

Greedy - Find Rightmost Odd Digit

⏱️ Time: O(n) Space: O(1)

Since we want the largest odd number, we should include as many digits as possible. The key insight is that the largest odd substring always ends with the rightmost odd digit in the string.

Brute Force - Check All Substrings — Algorithm Steps

Generate all possible substrings
Check if each substring represents an odd number
Keep track of the largest odd substring

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all possible substrings

Check Odd

Test if each substring ends with odd digit

Find Largest

Keep track of largest odd substring

Code -

solution.c — C

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

char* solution(char* num) {
    int n = strlen(num);
    char* largestOdd = (char*)malloc((n + 1) * sizeof(char));
    largestOdd[0] = '\0';
    
    // Generate all possible substrings
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j <= n; j++) {
            char substring[n + 1];
            strncpy(substring, num + i, j - i);
            substring[j - i] = '\0';
            
            // Check if substring represents an odd number
            if (strlen(substring) > 0 && (substring[strlen(substring) - 1] - '0') % 2 == 1) {
                // Compare with current largest odd substring
                if (strlen(largestOdd) == 0 || strlen(substring) > strlen(largestOdd) || 
                    (strlen(substring) == strlen(largestOdd) && strcmp(substring, largestOdd) > 0)) {
                    strcpy(largestOdd, substring);
                }
            }
        }
    }
    
    return largestOdd;
}

int main() {
    char num[100001];
    fgets(num, sizeof(num), stdin);
    num[strcspn(num, "\n")] = 0;
    
    char* result = solution(num);
    printf("%s\n", result);
    free(result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

O(n²) substrings × O(n) string comparison for each

⚠ Quadratic Growth

Space Complexity

O(n)

Storage for substring generation and comparison

⚡ Linearithmic Space

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Input & Output

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Related Problems

Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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