279. Perfect Squares

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Problem

Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, …) which sum to n.

Example 1:

Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

Code

class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        for(int i = 1; i <= n; i++){
            for (int j = 0; j <= i; j++){
                if ( (i - j * j) >= 0 && dp[i - j * j] != Integer.MAX_VALUE){
                    dp[i] = Math.min(dp[i], dp[i - j * j] + 1);
                }
            }
        }
        
        return dp[n];
    }
}

class Solution:
    def numSquares(self, n: int) -> int:
        dp = [float('inf')] * (n + 1)

        dp[0] = 0

        for i in range(1, n + 1):
            for j in range(1, i + 1):
                if j * j > i:
                    break
                dp[i] = min(dp[i], dp[i - j * j] + 1)

        return dp[n]