Codeforces 877D Olya and Energy Drinks（BFS+剪枝）

Olya loves energy drinks. She loves them so much that her room is full of empty cans from energy drinks.

Formally, her room can be represented as a field of n × m cells, each cell of which is empty or littered with cans.

Olya drank a lot of energy drink, so now she can run k meters per second. Each second she chooses one of the four directions (up, down, left or right) and runs from 1 to k meters in this direction. Of course, she can only run through empty cells.

Now Olya needs to get from cell (x1, y1) to cell (x2, y2). How many seconds will it take her if she moves optimally?

It's guaranteed that cells (x1, y1) and (x2, y2) are empty. These cells can coincide.

Input
The first line contains three integers n, m and k (1 ≤ n, m, k ≤ 1000) — the sizes of the room and Olya's speed.

Then n lines follow containing m characters each, the i-th of them contains on j-th position "#", if the cell (i, j) is littered with cans, and "." otherwise.

The last line contains four integers x1, y1, x2, y2 (1 ≤ x1, x2 ≤ n, 1 ≤ y1, y2 ≤ m) — the coordinates of the first and the last cells.

Output
Print a single integer — the minimum time it will take Olya to get from (x1, y1) to (x2, y2).

If it's impossible to get from (x1, y1) to (x2, y2), print -1.

Example
Input
3 4 4
....

.

....
1 1 3 1
Output
3
Input
3 4 1
....

.

....
1 1 3 1
Output
8
Input
2 2 1
.#

.

1 1 2 2
Output
-1
Note
In the first sample Olya should run 3 meters to the right in the first second, 2 meters down in the second second and 3 meters to the left in the third second.

In second sample Olya should run to the right for 3 seconds, then down for 2 seconds and then to the left for 3 seconds.

Olya does not recommend drinking energy drinks and generally believes that this is bad.

题意：

N×M的迷宫，可以沿着任一方向走K格，从起点到达终点最少需要多少步？

题解：

很容易想到BFS，但是直接BFS的话就TLE，需要剪枝，可以剪枝的是如果当前方向上的某个点访问过，并且到起点的距离大于当前点的距离，则该方向的就不用再搜索了。

#include<iostream>
#include<queue>
#include<algorithm>
using namespace std;
const int maxn=1005,INF=0x3f3f3f3f;
char maze[maxn][maxn];
int dx[]={1,-1,0,0},dy[]={0,0,1,-1};
int d[maxn][maxn];
bool vis[maxn][maxn];
int n,m,k;
int sx,sy,ex,ey;
struct node
{
    int x,y,step;
};
void bfs()
{
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
            d[i][j]=INF;
    node cur;
    cur.x=sx,cur.y=sy,cur.step=0;
    queue<node> que;
    que.push(cur);
    d[sx][sy]=0;//起点要设为0
    while(que.size())
    {
        cur=que.front();
        que.pop();
        for(int i=0;i<4;i++)
            for(int j=1;j<=k;j++)
            {
                node next;
                next.x=cur.x+dx[i]*j;
                next.y=cur.y+dy[i]*j;
                next.step=cur.step+1;
                if(next.x<1||next.x>n||next.y<1||next.y>m||maze[next.x][next.y]=='#'||(vis[next.x][next.y]&&cur.step>=d[next.x][next.y]))
                    break;//如果当前方向上的某个点访问过，并且到起点的距离大于当前点的距离，则该方向的就不用再搜索了
                if(next.step<d[next.x][next.y]&&!vis[next.x][next.y])
                {
                    vis[next.x][next.y]=true;
                    d[next.x][next.y]=next.step;
                    que.push(next);
                }                    
            }
    }
    if(d[ex][ey]==INF)
        cout<<"-1"<<endl;
    else
        cout<<d[ex][ey]<<endl;
}
int main()
{
    cin>>n>>m>>k;
    for(int i=1;i<=n;i++)
        cin>>(maze[i]+1);
    cin>>sx>>sy>>ex>>ey;
    bfs();
    return 0;
}