HDU 1428 漫步校园 （搜索 + dp）

typedef long long LL;
int n;
const int inf = 100000000;
int dir[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};
int grid[51][51];
int dist[51][51];//(i,j)到(n , n)的最短距离
LL dp[52][52];

struct Node
{
int x;
int y;
int dis;//(x, y)距离(n,n)的最短距离
Node(){}
Node(int i , int j , int k):x(i),y(j),dis(k){}
friend bool operator<(const Node &A , const Node &B)
{
return A.dis > B.dis;
}
};

bool cango(int x , int y)
{
return 1 <= x && x <= n && 1 <= y && y <= n;
}

void bfs()//计算所有点到(n,n)的最短距离
{
priority_queue<Node> que;
que.push(Node(n , n , grid

));
dist

= grid

;
while(!que.empty())
{
Node now = que.top();
que.pop();
for(int i = 0;i < 4;i++)
{
int x = now.x + dir[i][0];
int y = now.y + dir[i][1];
if(!cango(x , y)) continue;
if(dist[x][y] > dist[now.x][now.y] + grid[x][y])
{
dist[x][y] = dist[now.x][now.y] + grid[x][y];
que.push(Node(x , y , dist[x][y]));
}
}
}
}

LL DP(int x , int y)
{
if(x == n && y == n) return dp

= 1;
if(dp[x][y] != -1) return dp[x][y];
LL sum = 0;
for(int i = 0;i < 4;i++)
{
int nx = x + dir[i][0];
int ny = y + dir[i][1];
if(!cango(nx , ny)) continue;
if(dist[x][y] > dist[nx][ny])//选择B区域
sum += DP(nx , ny);//不能写成dp[x][y] += DP(nx , ny);!!!!
}
return dp[x][y] = sum;
}

int main()
{
while(scanf("%d",&n) != EOF)
{
int i , j;
memset(dp , -1 , sizeof(dp));
for(i = 1;i <= n;i++)
for(j = 1;j <= n;j++)
{
scanf("%d",&grid[i][j]);
dist[i][j] = inf;
}
bfs();
cout << DP(1,1) << endl;
}
return 0;
}