Kaprekar Number Checker - Problem

A Kaprekar number is a special number where if you square it and split the result into two parts, the sum of those parts equals the original number.

For example, 45 is a Kaprekar number because:

45² = 2025
Split: 20 + 25 = 45

Write a function that checks if a given number is a Kaprekar number. The split should divide the squared number into left and right parts of equal or nearly equal length.

Note: If the left part is empty after splitting, treat it as 0.

Input & Output

Example 1 — Classic Kaprekar Number

$ Input: n = 45

› Output: true

💡 Note: 45² = 2025. Split: '2025' → '20' + '25' = 20 + 25 = 45. Sum equals original, so it's a Kaprekar number.

Example 2 — Not a Kaprekar Number

$ Input: n = 10

› Output: false

💡 Note: 10² = 100. Split: '100' → '1' + '00' = 1 + 0 = 1. Sum (1) ≠ original (10), so not a Kaprekar number.

Example 3 — Single Digit Special Case

$ Input: n = 1

› Output: true

💡 Note: 1² = 1. Split: '1' → '' + '1' = 0 + 1 = 1. By definition, 1 is considered a Kaprekar number.

Constraints

1 ≤ n ≤ 10⁴
n is a positive integer

Visualization

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Asked in

G Google 15 M Microsoft 12 a Amazon 8

The key insight is that a Kaprekar number's square, when split in half, recreates the original number through addition. Best approach uses string manipulation for simplicity. Time: O(d), Space: O(d) where d is digits in n².

Common Approaches

✓ Mathematical Approach

⏱️ Time: O(log n) Space: O(1)

Calculate the number of digits in the square, then use division and modulo operations to split the number mathematically without converting to strings.

String Manipulation Approach

⏱️ Time: O(d) Space: O(d)

Convert the squared number to a string, split it into two halves, convert back to integers, and check if their sum equals the original number. Handle edge cases where left part might be empty.

Mathematical Approach — Algorithm Steps

Square the input number
Count digits in the squared result
Use division to get left part
Use modulo to get right part
Check if sum equals original

Visualization

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Step-by-Step Walkthrough

Calculate Square

Get n² = 45² = 2025

Find Divisor

digits=4, divisor=10^(4/2)=100

Split Mathematically

2025÷100=20, 2025%100=25

Code -

solution.c — C

#include <stdio.h>
#include <math.h>

int solution(int n) {
    if (n == 1) {
        return 1;
    }
    
    long long square = (long long)n * n;
    
    // Count digits in square
    int digits = 0;
    long long temp = square;
    while (temp > 0) {
        digits++;
        temp /= 10;
    }
    
    // Calculate the divisor for splitting
    long long divisor = 1;
    for (int i = 0; i < digits / 2; i++) {
        divisor *= 10;
    }
    
    long long leftPart = square / divisor;
    long long rightPart = square % divisor;
    
    return leftPart + rightPart == n;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(log n)

Counting digits and mathematical operations are logarithmic in the number

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra variables for calculations

✓ Linear Space

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Kaprekar Number Checker - Problem

Input & Output

Constraints

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Related Problems

Common Approaches

Mathematical Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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