102742: [AtCoder]ABC274 C - Ameba

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $300$ points

Problem Statement

You observed amoebae and kept some records.

Initially, there was one amoeba, numbered $1$.

You made $N$ records. According to the $i$-th record, the amoeba numbered $A_i$ disappeared by dividing itself into two new amoebae, which were then numbered $2i$ and $2i+1$.
Here, amoeba $A_i$ is said to be the parent of amoebae $2i$ and $2i+1$.

For each $k=1,\ldots,2N+1$, how many generations away is amoeba $k$ from amoeba $1$?

Constraints

  • $1 \leq N \leq 2\times 10^5$
  • The records are consistent. That is:
    • $1\leq A_i \leq 2i-1$.
    • $A_i$ are distinct integers.

Input

The input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print $2N+1$ lines. The $k$-th line should contain the generation distance between amoeba $1$ and amoeba $k$.


Sample Input 1

2
1 2

Sample Output 1

0
1
1
2
2

From amoeba $1$, amoebae $2$ and $3$ were born. From amoeba $2$, amoebae $4$ and $5$ were born.

  • Amoeba $1$ is zero generations away from amoeba $1$.
  • Amoeba $2$ is one generation away from amoeba $1$.
  • Amoeba $3$ is one generation away from amoeba $1$.
  • Amoeba $4$ is one generation away from amoeba $2$, and two generations away from amoeba $1$.
  • Amoeba $5$ is one generation away from amoeba $2$, and two generations away from amoeba $1$.

Sample Input 2

4
1 3 5 2

Sample Output 2

0
1
1
2
2
3
3
2
2

Input

题意翻译

你有一棵树,起始时仅有一个根节点 $1$。 接下来有 $n$ 次操作。对于第 $i$ 次操作,编号为 $A_i$ 的节点将会增加两个儿子,编号分别为 $2i$ 和 $2i + 1$。 对于 $i=1,2,...,2N+1$,求节点 $i$ 到根节点的距离。

Output

得分:300分

问题描述

你观察了变形虫并记录了一些信息。

最初,有一个变形虫,编号为1。

你记录了N次。根据第i次记录,编号为A_i的变形虫通过分裂成两个新的变形虫消失了,编号分别为2i和2i+1。

在这里,变形虫A_i被称为变形虫2i和2i+1的父代。

对于每个k=1,...,2N+1,变形虫k离变形虫1有多少代远?

约束条件

  • 1≤N≤2×10^5
  • 记录是连贯的。即:
    • 1≤A_i≤2i-1。
    • A_i是不同的整数。

输入

输入从标准输入以以下格式给出:

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

输出

打印2N+1行。第k行应包含变形虫1和变形虫k之间的代数距离。


样例输入1

2
1 2

样例输出1

0
1
1
2
2

从变形虫1,变形虫2和3诞生。从变形虫2,变形虫4和5诞生。

  • 变形虫1离变形虫1有0代远。
  • 变形虫2离变形虫1有1代远。
  • 变形虫3离变形虫1有1代远。
  • 变形虫4离变形虫2有1代远,离变形虫1有2代远。
  • 变形虫5离变形虫2有1代远,离变形虫1有2代远。

样例输入2

4
1 3 5 2

样例输出2

0
1
1
2
2
3
3
2
2

加入题单

上一题 下一题 算法标签: