1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <algorithm>
 5 #include <cmath>
 6 #include <queue>
 7
 8 using namespace std;
 9
10 const int INF = 0x3f3f3f3f;//无穷大
11 const int maxn = 51;
12
13 int go[4][2] = { 1,0,-1,0,0,1,0,-1 };//方向
14 struct node
15 {
16     int x, y;
17 };
18
19 int board[maxn][maxn];//记录位置(i,j)的值
20 int dis[maxn][maxn];//位置(i,j)所经历的最短路
21 int vis[maxn][maxn], n;//记录是否走过
22
23 bool operator < (const node &t1, const node &t2)
24 {
25     return dis[t1.x][t1.y] > dis[t2.x][t2.y];
26 }//重载了比较运算符，用于
27
28 long long num[maxn][maxn];//注意数据范围
29
30 void bfs()
31 {
32     int i;
33     priority_queue<node> q;//定义一个优先队列
34     node now, next;//动态储存现在所在位置和下一步的位置对应的值
35
36     now.x = n;
37     now.y = n;//重点，从重点开始搜索
38
39     q.push(now);
40     memset(vis, 0, sizeof(vis));//根据求最小的决策，初始化为0
41     vis[n][n] = 1;//搜索开始
42     while (!q.empty())//搜索持续到队列为空
43     {
44         now = q.top();
45         q.pop();
46         for (i = 0; i <= 3; i++)
47         {
48             next.x = now.x + go[i][0];
49             next.y = now.y + go[i][1];
50             if (next.x >= 1 && next.x <= n && next.y >= 1 && next.y <= n && dis[next.x][next.y] > dis[now.x][now.y])
51             //加上计数数组累加的条件
52             {
53                 num[next.x][next.y] += num[now.x][now.y];//记录最短路的数量
54                 if (!vis[next.x][next.y] && dis[next.x][next.y] >= dis[now.x][now.y] + board[next.x][next.y])
55                 {
56                     dis[next.x][next.y] = dis[now.x][now.y] + board[next.x][next.y];
57                     vis[next.x][next.y] = 1;//将next标记为已访问
58                     q.push(next);//更新队列
59                 }
60             }
61         }
62     }
63 }
64
65 int main()
66 {
67     int i, j;
68     while (~scanf_s("%d", &n))
69     {
70         memset(dis, 0x3f3f, sizeof(dis));
71         memset(num, 0, sizeof(num));
72         num[n][n] = 1;
73
74         for (i = 1; i <= n; i++)
75             for (j = 1; j <= n; j++)
76                 scanf_s("%d", &board[i][j]);
77
78         dis[n][n] = board[n][n];
79
80         bfs();
81
82         printf("%I64d\n", num[1][1]);//long long 类型对应的格式字符
83     }
84     return 0;
85 }