# 279. Perfect Squares

https://leetcode.com/problems/perfect-squares/

###### Medium

##### Description
> Given an integer n, return the least number of perfect square numbers that sum to n.
>
> A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.
##### Example1
> Input: n = 12
> Output: 3
> Explanation: 12 = 4 + 4 + 4.
##### Example2
> Input: n = 13
> Output: 2
> Explanation: 13 = 4 + 9.

##### Solution

class Solution {

    fun numSquares(n: Int): Int {

        val dp = Array(n + 1) { Int.MAX_VALUE }

        dp[0] = 0

        for (i in 1 until dp.size) {

            dp[i] = dp[i - 1] + 1

            var j = 1

            while (i - j * j >= 0) {
                dp[i] = minOf(dp[i], dp[i - j * j] + 1)
                j++
            }
        }

        return dp[n]
    }
}

##### Tips
* Dynamic programming

##### Note
dp[0] = 0
dp[1] = dp[0]+1
dp[2] = dp[2-1^2]+1
...
dp[4] = dp[4-1^2]+1 or dp[4-2^2]+1
dp[5] = dp[5-1^2]+1 or dp[5-2^2]+1
...
dp[8] = dp[8-1^2]+1 or dp[8-2^2]+1
dp[9] = dp[9-1^2]+1 or dp[9-2^2]+1
...
dp[11] = dp[11-1^2]+1 or dp[11-2^2]+1 or dp[11-3^2]+1
dp[12] = dp[12-1^2]+1 or dp[12-2^2]+1 or dp[12-3^2]+1