codeforces 520 B. Two Buttons (bfs)

B. Two Buttons

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Vasya has found a strange device. On the front panel of a device there are: a red button, a blue button and a display showing some positive integer. After clicking the red button, device multiplies the displayed number by two. After clicking the blue button, device subtracts one from the number on the display. If at some point the number stops being positive, the device breaks down. The display can show arbitrarily large numbers. Initially, the display shows number n.

Bob wants to get number m on the display. What minimum number of clicks he has to make in order to achieve this result?

Input

The first and the only line of the input contains two distinct integers n and m (1 ≤ n, m ≤ 104), separated by a space .

Output

Print a single number — the minimum number of times one needs to push the button required to get the number mout of number n.

Sample test(s)

input

4 6

output

2

input

10 1

output

9

Note

In the first example you need to push the blue button once, and then push the red button once.

In the second example, doubling the number is unnecessary, so we need to push the blue button nine times.

做过一道类似的题

因为是问最短，很容易想到是bfs

对于点x，可以到达点x-1,和点2*x

需要注意的是上界限。

并不是max(m,n)

因为可能先达到比m大，之后再减回来的情况是更优的。

max(2*m,2*n)肯定是足够的

/*************************************************************************
    > File Name: code/cf/#295/B.cpp
    > Author: 111qqz
    > Email: rkz2013@126.com 
    > Created Time: 2015年08月17日 星期一 04时16分51秒
 ************************************************************************/

#include<iostream>
#include<iomanip>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<vector>
#include<stack>
#define y0 abc111qqz
#define y1 hust111qqz
#define yn hez111qqz
#define j1 cute111qqz
#define tm crazy111qqz
#define lr dying111qqz
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)  
typedef long long LL;
typedef unsigned long long ULL;
const int inf = 0x7fffffff;
const int N=1E6+7;
int n,m;
int d[N];
int mx;

void bfs()
{
    memset(d,-1,sizeof(d));
    d[n] = 0 ;
    queue<int>q;
    q.push(n);
    while (!q.empty())
    {
    int px = q.front();q.pop();
    if (px==m)
    {
        cout<<d[m]<<endl;
        return;
    }

    int nxt[2];
    nxt[0] = px - 1;
    nxt[1] = 2*px;
    for ( int i = 0 ; i < 2 ; i++)
    {
        if (nxt[i]>=1&&nxt[i]<=mx&&d[nxt[i]]==-1)
        {
        d[nxt[i]] = d[px] + 1;
        q.push(nxt[i]);
        }
    }
    }
}
int main()
{
    scanf("%d %d",&n,&m);
    mx = max(2*n,2*m);
    bfs();

  
return 0;
}