C Programming: Perfect square

Last update on August 07 2025 12:49:11 (UTC/GMT +8 hours)

29. Minimal Sum of Squares Variants

Write a C programming to get the smallest number of square numbers that add up to an integer n.

In mathematics, a perfect square is a number that can be expressed as either the product of an integer by itself or as the second exponent of an integer..

Sample Data:
14 = 3² + 2² + 1²
Output – 3
15 = 3² + 2² + 1² + 1²
Output - 4
16 = 4²
Output – 1
17 = 4² + 1²
Output – 2

Sample Solution:

C Code:

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

// Function to find the number of square numbers required to sum up to 'n'
int test(int n) {
  // Allocate memory to store the minimum number of square numbers to sum up to 'n'
  int *nums = (int *)malloc((n + 1) * sizeof(int));

  // Initialize the allocated memory to a large value (here, 10000)
  memset(nums, 10000, (n + 1) * sizeof(int));

  // Base case: number of square numbers to sum to 0 is 0
  nums[0] = 0;

  // Dynamic programming approach to find the minimum number of square numbers needed
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j * j <= i; j++) {
      // Update nums[i] with the minimum of the current value and nums[i - j*j] + 1
      nums[i] = nums[i] < nums[i - j * j] + 1 ? nums[i] : nums[i - j * j] + 1;
    }
  }

  // Return the minimum number of square numbers required to sum up to 'n'
  return nums[n];
}

int main(void) {
  int n = 14;
  printf("%d number of square numbers equal to %d", test(n), n);
  n = 15;
  printf("\n%d number of square numbers equal to %d", test(n), n);
  n = 16;
  printf("\n%d number of square numbers equal to %d", test(n), n);
  n = 17;
  printf("\n%d number of square numbers equal to %d", test(n), n);

  return 0;
}

Sample Output:

3 number of square numbers equal to 14
4 number of square numbers equal to 15
1 number of square numbers equal to 16
2 number of square numbers equal to 17

Flowchart:

$Flowchart: Perfect square$

For more Practice: Solve these Related Problems:

Write a C program to determine the minimum count of perfect squares that sum to a given integer using dynamic programming.
Write a C program to compute the least number of square numbers needed to represent an integer using recursion with memoization.
Write a C program to implement the optimal square-sum representation and output the squares used.
Write a C program to find the minimum square sum decomposition by iterating over all square numbers less than n.

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