【LeetCode从零单刷】Perfect Squares
来源:互联网 发布:啊哈算法 pdf 完整版 编辑:程序博客网 时间:2024/06/07 18:14
题目:
Given a positive integer n, find the least number of perfect square numbers (for example,1, 4, 9, 16, ...
) which sum to n.
For example, given n = 12
, return 3
because12 = 4 + 4 + 4
; given n = 13
, return 2
because13 = 4 + 9
.
解答:
想一想,当 n = 13 时答案其实是 n = 9 时答案 + 1 的和;n = 12 时答案其实是 n = 8 时答案+ 1 的和,n = 8 时答案其实是 n = 4 时答案 + 1 的和。
这样,就是明显的动态规划了。当 n = i * i 时,返回值为 1;其余情况下,n 依次减去一个小于自身的平方数后求返回值,取所有返回值中最小值再 + 1。
class Solution {public: int numSquares(int n) { int max = 1; while ((max + 1) * (max + 1) <= n) max++; int* dp = new int[n + 1]; for(int i = 1; i <= max; i++) dp[i * i] = 1; int tmp; for(int i = 1; i < max; i++) { for(int j = i * i + 1; j < (i+1)*(i+1); j++) { int min = n; for(int k = i; k >= 1; k--) { min = min > (1 + dp[j - k*k]) ? (1 + dp[j - k*k]) : min; } dp[j] = min; } } for(int j = max * max + 1; j <= n; j++) { int min = n; for(int k = max; k >= 1; k--) { min = min > (1 + dp[j - k*k]) ? (1 + dp[j - k*k]) : min; } dp[j] = min; } return dp[n]; }};
但其实,这道题拥有解析解:
根据 Lagrange's four-square theorem,自然数被最少的平方数组合的可能解只会是 1,2,3,4 其中之一。
解 = 1 比较易懂,开方即可;解 = 2, 3, 4 就要依靠 Legendre's three-square theorem 来判断了。
class Solution { private: int is_square(int n) { int sqrt_n = (int)(sqrt(n)); return (sqrt_n*sqrt_n == n); }public: // Based on Lagrange's Four Square theorem, there // are only 4 possible results: 1, 2, 3, 4. int numSquares(int n) { // If n is a perfect square, return 1. if(is_square(n)) { return 1; } // The result is 4 if n can be written in the // form of 4^k*(8*m + 7). Please refer to // Legendre's three-square theorem. while (n%4 == 0) // n%4 == 0 n >>= 2; if (n%8 == 7) // n%8 == 7 return 4; // Check whether 2 is the result. int sqrt_n = (int)(sqrt(n)); for(int i = 1; i <= sqrt_n; i++) { if (is_square(n - i*i)) { return 2; } } return 3; } };
0 0
- 【LeetCode从零单刷】Perfect Squares
- leetcode 279: Perfect Squares
- [Leetcode]Perfect Squares
- Leetcode 279 Perfect Squares
- Leetcode #279 Perfect Squares
- [leetcode 279]Perfect Squares
- Leetcode:279Perfect Squares
- Leetcode Perfect Squares
- LeetCode Perfect Squares
- leetcode Perfect Squares
- leetcode: Perfect Squares
- [LeetCode 279] Perfect Squares
- LeetCode -- Perfect Squares
- *LeetCode-Perfect Squares
- LeetCode----Perfect Squares
- [LeetCode]Perfect Squares
- Perfect Squares - LeetCode 279
- [Leetcode] Perfect Squares
- poj 3669 Meteor Shower
- hdoj 一只小蜜蜂
- filter的作用
- GraphX编译
- Android使用AlarmManager全局定时器实现定时更换壁纸
- 【LeetCode从零单刷】Perfect Squares
- 关于内存管理的总结 -02-
- Eclipse中如何设置JSP的模板为pageEncoding="UTF-8"?
- 开启 MySQL 的远程登陆
- 关于开发项目的注意事项-以javaEE为例
- LeetCode-Two Sum
- 四大跨进程通信组件之AIDL(跨进程service通信)
- hdoj 阿牛的EOF牛肉串
- ILSpy For MacOsX