# 4ms C++ code - Solve it mathematically

• ``````class Solution {
public:
int is_square(int n){
int temp = (int) sqrt(n);
return temp * temp == n;
}
int numSquares(int n) {
while ((n & 3) == 0) //n%4 == 0
n >>= 2;
if ((n & 7) == 7) return 4; //n % 8 == 7
if(is_square(n)) return 1;
int sqrt_n = (int) sqrt(n);
for(int i = 1; i<= sqrt_n; i++){
if (is_square(n-i*i)) return 2;
}
return 3;
}
};
``````

UPDATE: in order to understand, I suggest u read:

here is the Lagrange's Four Square theorem - Limit the result to <= 4:
https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem

And this article, in which you can also find the way to present a number as a sum of four squares:
http://www.alpertron.com.ar/4SQUARES.HTM

• Hi, sorry for bother you. But where can I find the strict math prove for this solution?

• It is the most efficient solution, however it seems to be against what the problem want you to do.
Anyway, it doesn't matter.

• yeap, you are true that this solution seems not "natural" in thinking. It is not natural under a hidden context: Given 30 minutes of an interview. However, if it is under another context: Given your whole life, can you solve the problem?. Then other solution will be so trivial. Anyway, I think if we can prove the theorem ourselves, then we can proudly say that to our interviewers ^_^.

• Agree, which is also pretty cooool.

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