POJ1376(A*)

题目链接：http://poj.org/problem?id=1376

优先队列默认为大根堆，如果是结构体的比较或者是小根堆的话要自定义cmp函数，但是这里cmp函数和sort里的函数是不一样的，要这样定义：

struct cmp
{
bool operator () (int a, int b)
{
return a > b;  //在sort中返回的是 a < b，正好相反
}
};
priority_queue<int, vector<int>, cmp> Q; //小根堆

这里的int替换成结构体也是可以的。

与一般BFS有所不同的是，A*算法要有估价函数f、g、h，把通过现状态 now 所找到的后继状态按照 f 值的大小放入小根堆（open列表）里面去，然后标记now已经遍历过（放入到close列表中）。只是从队列中取出元素的顺序不同而已。

#include <iostream>
#include <cstdio>
#include <queue>
#include <vector>
#include <cstring>
#include <algorithm>
#define INF (1<<31)-1
using namespace std;

const int dx[4] = {-1,0,1,0}; //北、东、南、西；上、右、下、左
const int dy[4] = {0,1,0,-1};
const int trn[3] = {-1,1,2};

struct node
{
int x, y;
int f, g, h;
int dire;
};
node st, ed;
int n, m;
bool mp[55][55];
int vis[55][55][4];

struct cmp
{
int operator () (const node& a, const node& b)
{
if (a.f == b.f)
return a.g > b.g;
else
return a.f > b.f;
}
};

priority_queue<node,vector<node>,cmp> Q;

int Geth(const node& now)  //估价函数
{
int xx =  abs(now.x-ed.x);
int yy =  abs(now.y-ed.y);
int ans = 0;

if (xx == 0 && yy == 0)
return 0;

ans = xx / 3 + yy / 3;
if (xx % 3 != 0)
ans++;
if (yy % 3 != 0)
ans++;
if (xx != 0 && yy != 0)
ans++;

if (now.x >= ed.x && now.y <= ed.y)
{
if (now.dire >= 2)
ans++;
}
if (now.x >= ed.x && now.y >= ed.y)
{
if (now.dire == 1 || now.dire == 2)
ans++;
}
if (now.x <= ed.x && now.y <= ed.y)
{
if (now.dire == 0 || now.dire == 3)
ans++;
}
if (now.x <= ed.x && now.y >= ed.y)
{
if (now.dire <= 1)
ans++;
}

return ans;
}

int  Astar()
{
while (!Q.empty()) Q.pop();
memset(vis,0,sizeof(vis));

st.f = st.h = Geth(st);
st.g = 0;
vis[st.x][st.y][st.dire] = true;
Q.push(st);
while (!Q.empty())
{
node now = Q.top();
Q.pop();

if (now.x == ed.x && now.y == ed.y)
return now.g;

node New;
for (int step=1; step<=3;step++)
{
New.x = now.x+dx[now.dire]*step;
New.y = now.y+dy[now.dire]*step;
New.dire = now.dire;
if (New.x <= 0 || New.x >= n || New.y <= 0 || New.y >= m || mp[New.x][New.y])
break;
if (!vis[New.x][New.y][New.dire])
{
New.h = Geth(New);
New.g = now.g + 1;
New.f = New.g + New.h;
Q.push(New);
vis[New.x][New.y][New.dire] = true;
}
}

for (int i=0; i<2; i++)
{
New = now;
New.dire = (now.dire+trn[i]+4) % 4;
if (!vis[New.x][New.y][New.dire])
{
New.h = Geth(New);
New.g = now.g + 1;
New.f = New.g + New.h;
Q.push(New);
vis[New.x][New.y][New.dire] = true;
}
}
}

return -1;
}

int main()
{
while (scanf("%d%d",&n,&m))
{
if (n == 0 && m == 0)
break;
memset(mp,0,sizeof(mp));

char str[10];
for (int i=0; i<n; i++)
for (int j=0; j<m; j++)
{
int x;

scanf("%d",&x);
if (x == 1)
mp[i][j] = mp[i][j+1] = mp[i+1][j] = mp[i+1][j+1] = 1;
}

scanf("%d%d",&st.x,&st.y);
scanf("%d%d",&ed.x,&ed.y);
scanf("%s",str);
switch (str[0])
{
case 'n':st.dire = 0; break;
case 'e':st.dire = 1; break;
case 's':st.dire = 2; break;
case 'w':st.dire = 3; break;
}

cout<<Astar()<<endl;
}

return 0;
}