Catch That Cow(广搜)

本文介绍了一种使用BFS算法解决特定路径寻找问题的方法。农民约翰通过步行与传送方式追赶静止不动的逃逸奶牛,文章详细阐述了算法实现思路与代码示例。

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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 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.
    题意是:
    给定一个起点,有三种方法能到达终点,分别是:
    1.每次减 1
    2.每次加 1
  1. 每次以乘 2 前进
    求最少的步数(用BFS)
    分为两种情况:
    一个是 n>=k 就只能以第一种的方法向后退,最少步数就是两数的 差
    另一种是 n<=k 的情况
    满足范围即入队列,对当前的坐标进行标记,步数加1;到达目标点返回结果
    代码如下:
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#define memset(a,n) memset(a,n,sizeof(a))
#define INF 0x3f3f3f3f
using namespace std;
typedef long long LL;
const int MAXX = 1e5+10;

struct NODE
{
    int x;
    int step;
}now,pre,t;
int vis[MAXX];
queue<NODE> q;

int BFS(int x,int y)
{
    while(!q.empty())
        q.pop();
    pre.x = x;
    pre.step = 0;
    q.push(pre);
    vis[x] = 1;
    while(!q.empty()){
        now = q.front();
        q.pop();
        for(int i=0; i<=2; i++){
            if(i == 0)
                t.x = now.x - 1;
            else if(i == 1)
                t.x = now.x + 1;
            else if(i == 2)
                t.x = now.x * 2;
            if(t.x >= 0 && t.x <= 100000 && vis[t.x] == 0){
                if(t.x == y)
                    return now.step + 1;
                else {
                    vis[t.x] = 1;
                    t.step = now.step + 1;
                    q.push(t);
                }
            }
        }
    }

}
int main()
{
    int n,k,ans;
    memset(vis,0);
    cin >> n >> k;
    if(k <= n)
        cout << n-k << endl;
    else {
        ans = BFS(n,k);
        cout << ans << endl;
    }
}

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