Perfect Squares in C++


Suppose we have a positive integer n, find the least number of perfect square numbers whose sum is n. So if the number is 13, then the output is 2, as the numbers are 13 = 9 + 4

To solve this, we will follow these steps −

  • create one table for dynamic programming, of length n + 1, and fill it with infinity

  • dp[0] := 0

  • for i := 1, when i*i <= n

    • x = i * i

    • for j := x to n

      • dp[j] := minimum of dp[j] and 1 + dp[j – x]

  • return dp[n]

Example

Let us see the following implementation to get better understanding −

#define INF 1e9
class Solution {
   public:
   int numSquares(int n) {
      vector < int > dp(n+1,INF);
      dp[0] = 0;
      for(int i =1;i*i<=n;i++){
         int x = i*i;
         for(int j = x;j<=n;j++){
            dp[j] = min(dp[j],1+dp[j-x]);
         }
      }
      return dp[n];
   }
};

Input

147

Output

3
raja
Published on 05-Feb-2020 10:30:32
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