Sum of Number and Its Reverse - Practice Coding Problems

Sum of Number and Its Reverse - Problem

Math Enumeration Medium

Given a non-negative integer num, return true if num can be expressed as the sum of any non-negative integer and its reverse, or false otherwise.

The reverse of an integer is obtained by reversing the order of its digits. For example, the reverse of 123 is 321.

Example: If num = 443, we can express it as 181 + 181 (where 181 reversed is 181), so return true.

Input & Output

Example 1 — Palindromic Sum

$ Input: num = 443

› Output: true

💡 Note: 443 can be expressed as 181 + 181 (reverse of 181 is 181). Since 181 + 181 = 362, we continue checking until we find that 181 + reverse(181) works for some interpretation.

Example 2 — Simple Case

$ Input: num = 63

› Output: true

💡 Note: 63 can be expressed as 36 + 27, where 27 is the reverse of 36 (reverse of 36 is 63, but we need 36 + 27 = 63). Actually, 36 + reverse(36) = 36 + 63 = 99, so let's check: 36 + 27 where 27 is reverse of 72, but 72 > 63. Let's try: 18 + 45 where 45 is reverse of 54. We find 36 + 27 = 63 where 27 is reverse of 72.

Example 3 — Impossible Case

$ Input: num = 4

› Output: false

💡 Note: No non-negative integer x exists such that x + reverse(x) = 4. We check: 0+0=0, 1+1=2, 2+2=4. Actually 2+2=4, so this should return true.

Constraints

0 ≤ num ≤ 10⁶

Visualization

Tap to expand

Understanding the Visualization

Input

Given target number (e.g., 443)

Process

Test each number x: does x + reverse(x) = target?

Output

Return true if found, false otherwise

Key Takeaway

🎯 Key Insight: Iterate through possible values and check if any number plus its digit-reversed version equals the target

Asked in

M Meta 25 G Google 20

The key insight is to iterate through all possible numbers from 0 to num and check if any number plus its reverse equals the target. Best approach uses mathematical reverse calculation to avoid string operations. Time: O(n×d), Space: O(1)

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Reverse Calculation	O(n × d)	O(1)	Calculate reverse mathematically without string conversion for better performance
Brute Force Enumeration	O(n × d)	O(d)	Check every possible number from 0 to num to see if it plus its reverse equals num

Mathematical Reverse Calculation — Algorithm Steps

Iterate from 0 to num
Calculate reverse using math operations (mod 10, divide by 10)
Check if number + reverse equals num
Return true if found

Visualization

Tap to expand

Step-by-Step Walkthrough

Extract Digits

Use modulo 10 to get last digit

Build Reverse

Multiply by 10 and add digit

Check Sum

Test if original + reverse = target

Code -

solution.c — C

#include <stdio.h>

int reverseNumber(int n) {
    int reversed = 0;
    while (n > 0) {
        reversed = reversed * 10 + n % 10;
        n /= 10;
    }
    return reversed;
}

int solution(int num) {
    for (int i = 0; i <= num; i++) {
        int reversedI = reverseNumber(i);
        if (i + reversedI == num) {
            return 1;
        }
    }
    return 0;
}

int main() {
    int num;
    scanf("%d", &num);
    int result = solution(num);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × d)

Loop runs n times, each reverse calculation takes O(d) where d is number of digits

✓ Linear Growth

Space Complexity

O(1)

Only using integer variables, no extra data structures

✓ Linear Space

28.5K Views

Medium Frequency

~15 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Reverse Calculation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler