BZOJ 1646: [Usaco2007 Open]Catch That Cow 抓住那只牛
2014-08-02 23:29
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Description
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 numberline. 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?
农夫约翰被通知,他的一只奶牛逃逸了!所以他决定,马上幽发,尽快把那只奶牛抓回来.
他们都站在数轴上.约翰在N(O≤N≤100000)处,奶牛在K(O≤K≤100000)处.约翰有
两种办法移动,步行和瞬移:步行每秒种可以让约翰从z处走到x+l或x-l处;而瞬移则可让他在1秒内从x处消失,在2x处出现.然而那只逃逸的奶牛,悲剧地没有发现自己的处境多么糟糕,正站在那儿一动不动.
那么,约翰需要多少时间抓住那只牛呢?
Input
* Line 1: Two space-separated integers: N and K仅有两个整数N和K.
Output
* Line 1: The least amount of time, in minutes, it takes for Farmer John to catch the fugitive cow.最短的时间.
Sample Input
5 17Farmer John starts at point 5 and the fugitive cow is at point 17.
Sample Output
4OUTPUT DETAILS:
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.
题解
bfs即可。因为可以到x*2也可以往回走,但注意往回走只能一个一个走,所以bfs边界x<=n+k,因为,若x=2*n且x>n+k(n<k)则要往回走>n次才能到k,还不如一开始就往回走到k整除2的地方再一个两倍直接到k或k-1。#include<cstdio> #include<cstring> #include<cstdlib> #include<iostream> #include<cmath> #include<algorithm> #define inf 1<<30 using namespace std; int n,m,t,w,x,b,a[200005],q[200005],mark[200005]; int main() { scanf("%d%d",&n,&m); if(n==m) {printf("0\n"); return 0;} for(int i=0;i<=n+m;i++) a[i]=inf; t=0; w=1; q[0]=n; a =0; mark =1; while(t!=w) {x=q[t]; t=(t+1)%200005; if(x-1>=0&&a[x-1]>a[x]+1) {a[x-1]=a[x]+1; if(!mark[x-1]) {q[w]=x-1; mark[x-1]=1; w=(w+1)%200005;} } if(x+1<=n+m&&a[x+1]>a[x]+1) {a[x+1]=a[x]+1; if(!mark[x+1]) {q[w]=x+1; mark[x+1]=1; w=(w+1)%200005;} } if(x<<1<=n+m&&a[x<<1]>a[x]+1) {a[x<<1]=a[x]+1; if(!mark[x<<1]) {q[w]=x<<1; mark[x<<1]=1; w=(w+1)%200005;} } mark[x]=0; if(a[m]<inf) {printf("%d\n",a[m]); break;} } return 0; }
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