#396 B. Mahmoud and a Triangle

最新推荐文章于 2021-09-24 22:12:15 发布

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本文介绍了一个编程挑战，即从给定长度的线段中选择三个能够构成非退化三角形的线段。文章通过示例解释了问题背景，并提供了一种解决方案：先对线段进行排序，再检查每组连续的三个线段是否满足构成三角形的条件。

Mahmoud has n line segments, the i-th of them has length ai. Ehab challenged him to use exactly 3 line segments to form a non-degenerate triangle. Mahmoud doesn't accept challenges unless he is sure he can win, so he asked you to tell him if he should accept the challenge. Given the lengths of the line segments, check if he can choose exactly 3 of them to form a non-degenerate triangle.

Mahmoud should use exactly 3 line segments, he can't concatenate two line segments or change any length. A non-degenerate triangle is a triangle with positive area.

Input

The first line contains single integer n (3 ≤ n ≤ 105) — the number of line segments Mahmoud has.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the lengths of line segments Mahmoud has.

Output

In the only line print "YES" if he can choose exactly three line segments and form a non-degenerate triangle with them, and "NO" otherwise.

        Examples
      
          input
        
5
1 5 3 2 4

          output
        
YES

          input
        
3
4 1 2

          output
        
NO

Note

For the first example, he can use line segments with lengths 2, 4 and 5 to form a non-degenerate triangle.

http://codeforces.com/contest/766/problem/B

思路：先将所有边进行升序排序，然后依次找相邻的三条边。

因为:假设a<=b<=c

则b-a<c,c-a<b,c-b<a.则当b-a,c-a,c-b最小时，最容易组成三角形。

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		int[] d = new int[N];
		for(int i=0;i<N;i++){
			d[i] = scan.nextInt();
		}
		Arrays.sort(d);
		for(int i=0;i<d.length-2;i++){
			if(d[i]+d[i+1]>d[i+2]){
				System.out.println("YES");
				return;
			}
		}
		System.out.println("NO");
	}
}