Perfect Squares

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

For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.

• Time: O(n) Space: O(n)

public int numSquares(int n) {
    int[] dp = new int[n + 1];
    for (int i = 1; i <= n; i++) {
        dp[i] = Integer.MAX_VALUE;
    }
    for (int i = 1; i <= n; i++) {
        int sqrt = (int) Math.sqrt(i);
        if (i == sqrt * sqrt) {
            dp[i] = 1;
            continue;
        }
        for (int j = 1; j <= sqrt; j++) {
            if (dp[i - j * j] + 1 < dp[i]) {
                dp[i] = dp[i - j * j] + 1;
            }
        }
    }
    return dp[n];
}