# C Programming: Perfect square

## C Programming Mathematics: Exercise-29 with Solution

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 = 3^{2} + 2^{2} + 1^{2}

Output – 3

15 = 3^{2} + 2^{2} + 1^{2} + 1^{2}

Output - 4

16 = 4^{2}

Output – 1

17 = 4^{2} + 1^{2}

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

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