# Why is my solution so slow?

• My solution is showed below. It costs 412 ms. But I think the time complexity is n*sqrt(n), right? I know it would be faster if using `static` keyword but if submit it, it shows a Runtime Error. However, it passes single test by "Run Code" button. How should I use `static` keyword in my code? Thank you in advance.

``````class Solution {
public:
int numSquares(int n) {
vector<int> dp(n + 1, n + 1);
int square = 2;
dp[0] = 0;
dp[1] = 1;
for (int i = 2; i <= n; i++) {
if (i == square * square) {
dp[i] = 1;
square++;
}
else {
for (int j = square - 1; j > 0; j--) {
dp[i] = min(dp[i], 1 + dp[i - j * j]);
}
}
}
return dp[n];
}
};
``````

• @lijunray check my solution below using array instead of vector

``````class Solution {
public:
int numSquares(int n)
{
static int mins[100000]{0};
static int i = 1;
if(mins[n]) return mins[n];
for(; i <= n; ++i)
{
int localMin = i;
for(int j = sqrt(i); j > 0; --j)
{
localMin = min(localMin, mins[i-j*j]+1);
}
mins[i] = localMin;
}
return mins[n];
}
};
``````

• But actually this solution is flawed, could not handle `big` number, perhaps you should try the math solution here as follows.

``````class Solution {
public:
int numSquares(int n)
{
while(!(n&3)) n /= 4;
if(n%8 == 7) return 4;
for(int a = sqrt(n); a > 0; --a)
{
int b = sqrt(n-a*a);
if(a*a+b*b == n) return !b? 1 : 2;
}
return 3;
}
};
``````

• @lijunray check this post if don't know the theory.

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