Farmer John has been informed of the location of a fugitive cow and wants to catch her immediately. He starts at a point N (0 ≤ N ≤ 100,000) on a number line and the cow is at a point K (0 ≤ K ≤ 100,000) on the same number line. Farmer John has two modes of transportation: walking and teleporting.
- Walking: FJ can move from any point X to the points X - 1 or X + 1 in a single minute
- Teleporting: FJ can move from any point X to the point 2 × X in a single minute.
If the cow, unaware of its pursuit, does not move at all, how long does it take for Farmer John to retrieve it?
Input
Line 1: Two space-separated integers: N and K
Output
Line 1: The least amount of time, in minutes, it takes for Farmer John to catch the fugitive cow.
Sample Input
5 17
Sample Output
4
Hint
The fastest way for Farmer John to reach the fugitive cow is to move along the following path: 5-10-9-18-17, which takes 4 minutes.
#include<iostream>
#include<queue>
#include<cstring>
#include<cstdio>
using namespace std;
const int maxn=100001;
int vis[maxn],time[maxn];///vis[i]標記i點是否被訪問過,time[i]
int n,k;
queue<int>que;
int bfs(int n,int k)
{
int head,next;
que.push(n);///n入隊
vis[n]=1;///n點已經被走過了
time[n]=0;///到達n點的時候走了0步
while(!que.empty())///當隊列非空的時候
{
head=que.front();///取出隊首元素
que.pop();
for(int i=0;i<3;i++)///三種操作
{
if(i==0) next=head+1;
else if(i==1) next=head-1;
else next=head*2;
if(next<0||next>=maxn) continue;
if(vis[next]==0)
{
que.push(next);///next入隊
vis[next]=1;///標記next爲已經訪問過了
time[next]=time[head]+1;///時間爲上一次操作加一
}
if(next==k) return time[next];///到達目的地
}
}
}
int main()
{
while(~scanf("%d%d",&n,&k))
{
memset(vis,0,sizeof(vis));
memset(time,0,sizeof(time));
if(n>=k) printf("%d\n",n-k);
else printf("%d\n",bfs(n,k));
}
}