279. Perfect Squares

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problem

solution

option 1 - dp

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class Solution {
public:
    int numSquares(int n) {
        vector<int> dp(n+1,INT_MAX);
        dp[0] = 0;
        //  0   1   2   3   4   5   6   7   8   9   10  11  12
        //  0   1   2   3   1   2   3   4   2   1   2   3   3
        for(int i=0;i<=n;++i){
            for(int j = 1;i+j*j<=n;++j){
                dp[i+j*j] = min(dp[i]+1, dp[i+j*j]);
            }
        }
        return dp[n];
        
    }
};

option 2 - math

analysis

  • time complexity O(n*sqrt(n)) O(sqrt(n))
  • space complexity O(1)