{POJ}{3897}{Maze Stretching}{二分答案+BFS}
题意：给定迷宫，可以更改高度比，问如何使最短路等于输入数据。
思路：由于是单调的，可以用二分答案，然后BFS验证。这里用优先队列，每次压入也要进行检查（dis大小）防止数据过多，A*也可以。好久不写图论，WA成狗
#include <iostream>
#include <string>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <memory>
#include <cmath>
#include <bitset>
#include <queue>
#include <vector>
#include <stack>
using namespace std;
#define CLR(x,y) memset(x,y,sizeof(x))
#define MIN(m,v) (m)<(v)?(m):(v)
#define MAX(m,v) (m)>(v)?(m):(v)
#define ABS(x) ((x)>0?(x):-(x))
#define rep(i,x,y) for(i=x;i<y;++i)
#define SET_NODE(no,a,b,c) {no.x=a;no.y=b;no.val=c;}
const int MAXN = 200;
const double INF = 1<<30;
const double EPS = 0.000001;
int dir[4][2]={1,0,-1,0,0,1,0,-1};
int n,m;
int tag[MAXN];
char g[MAXN][MAXN];
double dist;
bool visit[MAXN][MAXN];
double dis[MAXN][MAXN];
typedef struct
{
int x,y;
double val;
}Node;
Node s,e,node;
bool operator < (const Node& a,const Node& b)
{
return a.val > b.val;
}
bool check(const int& x, const int& y)
{
if(x<0||x>=n) return false;
if(y<0||y>=m) return false;
if(g[x][y] == '#') return false;
if(visit[x][y]) return false;
return true;
}
double BFS(double len)
{
int i,j,k;
Node tmp;
priority_queue<Node> q;
q.push(s);
CLR(visit,0);
rep(i,0,n)
rep(j,0,m)
dis[i][j] = INF;
while(!q.empty())
{
node = q.top();
q.pop();
visit[node.x][node.y] = true;
if(node.x == e.x && node.y == e.y)
return node.val;
if(check(node.x+1,node.y)){
SET_NODE(tmp,node.x+1,node.y,node.val+len);
if(tmp.val<dis[tmp.x][tmp.y])
{
dis[tmp.x][tmp.y] = tmp.val;
q.push(tmp);
}
}
if(check(node.x-1,node.y)){
SET_NODE(tmp,node.x-1,node.y,node.val+len);
if(tmp.val<dis[tmp.x][tmp.y])
{
dis[tmp.x][tmp.y] = tmp.val;
q.push(tmp);
}
}
if(check(node.x,node.y+1)){
SET_NODE(tmp,node.x,node.y+1,node.val+1);
if(tmp.val<dis[tmp.x][tmp.y])
{
dis[tmp.x][tmp.y] = tmp.val;
q.push(tmp);
}
}
if(check(node.x,node.y-1)){
SET_NODE(tmp,node.x,node.y-1,node.val+1);
if(tmp.val<dis[tmp.x][tmp.y])
{
dis[tmp.x][tmp.y] = tmp.val;
q.push(tmp);
}
}
}
return 0;
}
void Solve()
{
int i,j,k,t,tt;
scanf("%d",&tt);
rep(t,1,tt+1){
scanf("%lf%d",&dist,&n);
rep(i,0,n)
{
getchar();
gets(&g[i][0]);
}
m = strlen(g[0]);
rep(i,0,n)
rep(j,0,m)
if(g[i][j]=='S')
{
s.x = i;
s.y = j;
}else if (g[i][j]=='E')
{
e.x = i;
e.y = j;
}
s.val = 0;
double low = 0;
double high = 10;
double mid = (low+high)/2;
double res = 0;
while(ABS(low-high)>EPS)
{
mid = (low+high)/2;
res = BFS(mid);
//printf("[%f %f %f]\n",mid,res,dist);
if(res < dist+EPS)
low = mid ;
else
high = mid;
}
printf("Case #%d: %.3f%%\n",t,mid*100);
}
}
int main()
{
Solve();
return 0;
}