Problem:
Problem B: Lagrange's Four-Square Theorem

The fact that any positive integer has a representation as the sum of at most four positive
squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The
first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission
however is not to explain the original proof nor to discover a new proof but to show that the
theorem holds for some specific numbers by counting how many such possible representations
there are.

For a given positive integer n, you should report the number of all representations of n as the
sum of at most four positive squares. The order of addition does not matter, e.g. you should
consider 42 + 32 and 32 + 42 are the same representation.

For example, let’s check the case of 25. This integer has just three representations 12 +22 +22 +42 ,
32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and
32 + 42 separately.

Input

The input is composed of at most 255 lines, each containing a single positive integer less than
215 , followed by a line containing a single zero. The last line is not a part of the input data.

Output

The output should be composed of lines, each containing a single integer. No other characters
should appear in the output.

The output integer corresponding to the input integer n is the number of all representations
of n as the sum of at most four positive squares.

Sample Input

1
25
2003
211
20007
0

Output for the Sample Input

1
3
48
7
738

Solution in C (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define num 32768

int square(int sum, int d, int c);

int *dp;
int n;

int main(){
  int N;
  dp = (int *)malloc(num*sizeof(int));
  for(n=0;n<num;n++){
    dp[n] = square(0,1,0);
  }

  while(scanf("%d",&N),N){
    printf("%d\n",dp[N] );
  }

  free(dp);
  exit(0);
}

int square(int sum, int d, int c){
  for(int i=1,sum=0;sum+i*i<num;i++){
    if(sum == n) return 1;
    if(c >= 4) return 0;
    int res = 0;
    for(int i = d; i*i <= n; i++){
      if(sum + i*i > n) break;
      res += square(sum + i*i, i, c+1);
    }
    return res;
  }
}