Ameba

标签：Amoeba generation Ameba away dep amoeba 2i

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

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

按照题意建树，计算深度。

#include<cstdio>
const int N=4e5+5;
int a[N],n,lc[N],rc[N],dep[N];
void dfs(int x)
{
	if(lc[x])
	{
		dep[lc[x]]=dep[x]+1;
		dfs(lc[x]);
	}
	if(rc[x])
	{
		dep[rc[x]]=dep[x]+1;
		dfs(rc[x]);
	}
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",a+i);
	for(int i=1;i<=n;i++)
		lc[a[i]]=2*i,rc[a[i]]=2*i+1;
	dfs(1);
	for(int i=1;i<=2*n+1;i++)
		printf("%d\n",dep[i]);
	return 0;
}

标签：Amoeba,generation,Ameba,away,dep,amoeba,2i
From： https://www.cnblogs.com/mekoszc/p/16906439.html