279. Perfect Squares (Medium)

https://leetcode.com/problems/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.

Example 1:

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

Example 2:

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

Solutions

class Solution {

    // This problem is pretty much similar with 322. Coin Change. When it comes to
    // exchanges, the squares 1, 4, 9, 16 can be perfectly regarded as the coin denominations.

    public int numSquares(int n) {
        int x = (int) Math.sqrt(n);

        int[] squares = new int[x];
        for (int i = 1; i <= x; i++) {
            squares[i - 1] = i * i;
        }

        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 < x; j++) {
                if (i - squares[j] < 0) {
                    continue;
                }

                dp[i] = Math.min(dp[i], dp[i - squares[j]] + 1);
            }
        }

        return dp[n];
    }
}

Incorrect Solutions

References