完全平方数

Perfect Squares

专题: Algorithmic Programming / 算法编程
难度: L3
来源: Citadel

题目详情

问题：完全平方数

考察：动态规划

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/perfect-squares/

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

解析

思路：完全平方数作为可选硬币，求组成 n 的最少数量。dp[i] = min(dp[i - square] + 1)，枚举 i 和所有不超过 i 的平方数。

复杂度：时间 O(n sqrt n)，空间 O(n)。