# 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>
#include <mem.h>
int test(int n) {
int * nums = (int * ) malloc((n + 1) * sizeof(int));
memset(nums, 10000, (n + 1) * sizeof(int));
nums[0] = 0;
for (int i = 1; i <= n; i++)
for (int j = 1; j * j <= i; j++)
nums[i] = nums[i] < nums[i - j * j] + 1 ? nums[i] : nums[i - j * j] + 1;
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);
}
```

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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