102563: [AtCoder]ABC256 D - Union of Interval

Problem Statement

For real numbers $L$ and $R$, let us denote by $[L,R)$ the set of real numbers greater than or equal to $L$ and less than $R$. Such a set is called a right half-open interval.

You are given $N$ right half-open intervals $[L_i,R_i)$. Let $S$ be their union. Represent $S$ as a union of the minimum number of right half-open intervals.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq L_i \lt R_i \leq 2\times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$L_1$ $R_1$
$\vdots$
$L_N$ $R_N$

Output

Let $k$ be the minimum number of right half-open intervals needed to represent $S$ as their union. Print $k$ lines containing such $k$ right half-open intervals $[X_i,Y_i)$ in ascending order of $X_i$, as follows:

$X_1$ $Y_1$
$\vdots$
$X_k$ $Y_k$

Sample Input 1

3
10 20
20 30
40 50

Sample Output 1

10 30
40 50

The union of the three right half-open intervals $[10,20),[20,30),[40,50)$ equals the union of two right half-open intervals $[10,30),[40,50)$.

Sample Input 2

3
10 40
30 60
20 50

Sample Output 2

10 60

The union of the three right half-open intervals $[10,40),[30,60),[20,50)$ equals the union of one right half-open interval $[10,60)$.

问题描述

对于实数$L$和$R$，我们用$[L,R)$表示大于或等于$L$且小于$R$的实数集合。这样的集合被称为右半开区间。

给你$N$个右半开区间$[L_i,R_i)$。它们的并集表示为$S$。用最少数量的右半开区间表示$S$的并集。

限制条件

• $1 \leq N \leq 2\times 10^5$
• $1 \leq L_i \lt R_i \leq 2\times 10^5$
• 输入中的所有值都是整数。

输入

输入从标准输入按以下格式给出：

$N$
$L_1$ $R_1$
$\vdots$
$L_N$ $R_N$

输出

令$k$为表示$S$并集所需的最少右半开区间的数量。按以下格式打印$k$行，表示这$k$个右半开区间$[X_i,Y_i)$，按$X_i$的升序排列：

$X_1$ $Y_1$
$\vdots$
$X_k$ $Y_k$

样例输入1

3
10 20
20 30
40 50

样例输出1

10 30
40 50

三个右半开区间$[10,20),[20,30),[40,50)$的并集等于两个右半开区间$[10,30),[40,50)$的并集。

样例输入2

3
10 40
30 60
20 50

样例输出2

10 60

三个右半开区间$[10,40),[30,60),[20,50)$的并集等于一个右半开区间$[10,60)$的并集。