Boring Segments
题意翻译
在一个 $[1,m]$ 的数轴上有 n 条线段,第 i 条覆盖了 $[l_i,r_i]$ 的区间,权值为 $w_i$ ,你的任务是从这些线段中选出若干条首尾相接线段覆盖整个数轴,使得这些线段权值极差最小化,输出这个极差
首尾相接的定义是,假设你有机会从同一条线段覆盖的任意两个点中移动,如果你可以从位置 1 出发,经过一些线段到达位置 m ,就称为这些线段首尾相接
题目描述
You are given $ n $ segments on a number line, numbered from $ 1 $ to $ n $ . The $ i $ -th segments covers all integer points from $ l_i $ to $ r_i $ and has a value $ w_i $ .
You are asked to select a subset of these segments (possibly, all of them). Once the subset is selected, it's possible to travel between two integer points if there exists a selected segment that covers both of them. A subset is good if it's possible to reach point $ m $ starting from point $ 1 $ in arbitrary number of moves.
The cost of the subset is the difference between the maximum and the minimum values of segments in it. Find the minimum cost of a good subset.
In every test there exists at least one good subset.
输入输出格式
输入格式
The first line contains two integers $ n $ and $ m $ ( $ 1 \le n \le 3 \cdot 10^5 $ ; $ 2 \le m \le 10^6 $ ) — the number of segments and the number of integer points.
Each of the next $ n $ lines contains three integers $ l_i $ , $ r_i $ and $ w_i $ ( $ 1 \le l_i < r_i \le m $ ; $ 1 \le w_i \le 10^6 $ ) — the description of the $ i $ -th segment.
In every test there exists at least one good subset.
输出格式
Print a single integer — the minimum cost of a good subset.
输入输出样例
输入样例 #1
5 12
1 5 5
3 4 10
4 10 6
11 12 5
10 12 3
输出样例 #1
3
输入样例 #2
1 10
1 10 23
输出样例 #2
0