[LeetCode] 279. Perfect Squares

轉自LeetCode

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.

 

Example 1:

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

Example 2:

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

 

Constraints:

• 1 <= n <= 104

Solution

這題最快的解釋用數學公式，但這邊就不討論，因為平常也不會背數學公式

這次採用DP的方式來解，有點像是套用 prefixSum 的概念

dp[n] = min(dp[n], dp[n - j*j]) = min(當下的值，從上一個 perfect squares 再加 1 )

可以想成 n = a + perfect square-> a = n - perfect square

也就是從 a 要變成 n，需要再一個 perfect square

這題的思路也像這題 322. Coin Change

kotlin(參考解法)

	class Solution {
	fun numSquares(n: Int): Int {
	val dp = IntArray(n+1){Int.MAX_VALUE}
	dp[0] = 0
	for(i in 1..n) {
	var j = 1
	while(j*j <= i) {
	dp[i] = Math.min(dp[i], dp[i-j*j]+1)
	++j
	}
	}
	return dp[n]
	}
	}

view raw perfect_squares.kt hosted with ❤ by GitHub