【Leetcode441--数学】Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.

Given n, find the total number of full staircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1:

n = 5

The coins can form the following rows:
¤
¤ ¤
¤ ¤

Because the 3rd row is incomplete, we return 2.

Example 2:

n = 8

The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

题目大意:

用金币累一个楼梯,形式如下:

1

23

456

78910

就是说第n行有n个硬币,以此类推。问你最多能累多少层,多余出来且不足的不算,例如5的话返回2,8的话返回3。

分析:

这题很明显是一道数学题,我们首先观察规律

1

2 3

4 5 6

7 8 9 10

我们首先观察每一层的首项:

1 2 4 7

显然地,这是一个数列,并且首项间的关系为

所以,上下数列形式为:

上下累加得:

所以 :

所以我们就知道了每一层的首项的大小。

所以每一行的尾项为 An + n-1,得:

这时候,我们就可以根据n求出n行的首项(An0)和尾项(Ann)。

我们知道给出一个x,它一定是落在An0和Ann之间的。假设刚好落在(Ann)的时候。得出方程

根据求根公式:

即可求出n

(注意,此时的n是刚好落在Ann的时候,我们需要对结果向下取整)

JAVA CODE:

public class Solution {

    public int arrangeCoins(int n) {
        if (n == 0) {
            return 0;
        }
        long delta = (8L * n) + 1;
        int x = (int) (-1.0 + Math.sqrt(delta)) >> 1;
        return (int) x;
    }

    public static void main(String[] args) {
        Solution s = new Solution();
        System.out.println(s.arrangeCoins(8));
    }

}
时间: 2024-10-10 22:27:09

【Leetcode441--数学】Arranging Coins的相关文章

LeetCode 441. Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

[LeetCode] Arranging Coins 排列硬币

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

441. 硬币楼梯 Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

LeetCode Arranging Coins

原题链接在这里:https://leetcode.com/problems/arranging-coins/ 题目: You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be forme

[Leetcode + Lintcode] 441. Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

441. Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

[LeetCode] 441. Arranging Coins 排列硬币

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of

138.Arranging Coins

题目: You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. 您想要以楼梯形状形成总共n个硬币,其中每个第k行必须具有恰好k个硬币. Given n, find the total number of full staircase rows that can be formed. 给定n,找到可以形成的完整楼梯行

(Easy) Arranging Coins - LeetCode

Description: You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within