201291: [AtCoder]ARC129 B - Range Point Distance
Memory Limit:1024 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $400$ points
Problem Statement
For integers $l$, $r$, and $x$ ($l \leq r$), let us define $dist(l,r,x)$ as follows.
- If $x<l$: $dist(l,r,x)=l-x$
- If $l \leq x \leq r$: $dist(l,r,x)=0$
- If $r<x$: $dist(l,r,x)=x-r$
You are given $N$ pairs of integers, the $i$-th of which is $(L_i,R_i)$. For each $k=1,2,\cdots,N$, solve the following problem.
- Let us choose an integer $x$ freely and compute $\max(dist(L_1,R_1,x),dist(L_2,R_2,x),\cdots,dist(L_k,R_k,x))$. Find the minimum possible value of this.
Constraints
- $1 \leq N \leq 2 \times 10^5$
- $1 \leq L_i \leq R_i \leq 10^9$
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
$N$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_N$ $R_N$
Output
Print the answers for $k=1,2,\cdots,N$ in this order.
Sample Input 1
3 1 3 2 4 5 6
Sample Output 1
0 0 1
- For $k=1$, an optimal choice is $x=1$.
- For $k=2$, an optimal choice is $x=3$.
- For $k=3$, an optimal choice is $x=4$.
Sample Input 2
10 64 96 30 78 52 61 18 28 9 34 42 86 11 49 1 79 13 59 70 95
Sample Output 2
0 0 2 18 18 18 18 18 18 21