Codefores 507C Guess Your Way Out!（递归）

C. Guess Your Way Out!

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node.

Let's index all the leaf nodes from the left to the right from 1 to 2^h. The exit is located at some node n where 1 ≤ n ≤ 2^h, the player doesn't know where the exit is so he has to guess his way out!

Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:

• Character 'L' means "go to the left child of the current node";
• Character 'R' means "go to the right child of the current node";
• If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node;
• If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command;
• If he reached a leaf node that is not the exit, he returns to the parent of the current node;
• If he reaches an exit, the game is finished.

Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?

Input

Input consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2^h).

Output

Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.

Sample test(s)

Input

1 2

Output

2

Input

2 3

Output

5

Input

3 6

Output

10

Input

10 1024

Output

2046

Note

A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2^h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one.

Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit.

题意是按照“LRLRLRLR....”这个指令在数上走 。。

然后给了几个返回的条件， 让你算一下经过了多少个结点。

其实就是一个根据指令递归判点在左右子树还是右子树的情况。

做法就是分成4种情况

出口在左子树，指令是L

出口在左子树，指令是R

出口在右子树，指令是L

出口在右子树，指令是R

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
LL n , h , ok ;
LL cal( LL dep , LL pos , int tag ) {
    if( ok ) return 0 ;
    if( dep == 0 ) { ok = 1 ; return 0; }
    LL tmp ;
    if( !tag ) {
        if( pos >(1LL<<(dep-1))) tmp = (1LL<<dep)+cal(dep-1,pos-(1LL<<(dep-1)),0) ;
        else tmp = 1LL + cal(dep-1,pos,1);
    }
    else {
        if( pos > (1LL<<(dep-1)) ) tmp = 1LL+ cal( dep-1,pos-(1LL<<(dep-1)),0) ;
        else tmp = (1LL<<dep) + cal(dep-1,pos,1);
    }
    return tmp ;
}
int main()
{
    while( cin >> h >> n ) {
        ok = 0 ;
        cout << cal(h,n,0) << endl ;
    }
}