279. Perfect Squares

Example 1:

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

Example 2:

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

class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        for (int i = 2; i < dp.length; i++) {
            dp[i] = Integer.MAX_VALUE;
            for (int j = 1; j * j <= i; j++) {
                dp[i] = Math.min(dp[i], dp[i - j * j] + 1);
            }
        }
        return dp[n];
    }
}

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