Content

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

1. 动态规划

Java

class Solution {
    public int numSquares(int n) {
        // 1 <= n <= 10⁴
        // dp[i]表示数字i最少由几个平方数累加获取。
        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        dp[1] = 1;
        for (int i = 2; i <= n; i++) {
            int j = (int) Math.sqrt(i);
            while (j > 0) {
                dp[i] = Math.min(dp[i], 1 + dp[i - j * j]);
                j--;
            }
        }
        return dp[n];
    }
}