题目链接:
http://acm.hdu.edu.cn/showproblem.php?pid=4568
Hunter
Memory Limit: 32768/32768 K (Java/Others)
输出
For each test case, you should output only a number means the minimum cost.
样例输入
2
3 3
3 2 3
5 4 3
1 4 2
1
1 1
3 3
3 2 3
5 4 3
1 4 2
2
1 1
2 2
样例输出
8
11
题意
给你一个n*m的迷宫,每个方格上标的是花费,现在有些坐标上有宝藏,你可以从边界的方格进入,最后需要从边界处离开,问你获得所有宝藏的最小花费,每个点可以重复走。
题解
构造一个超级节点,点权为0,与所有的边界相连。然后对所有的宝藏的点跑最短路。
重新构造只有宝藏和超级节点的图,任意两个点之间的路径为上面处理出来的最短路。
对于新图跑下TSP就ok啦。
代码
#include<map>
#include<set>
#include<cmath>
#include<queue>
#include<stack>
#include<ctime>
#include<vector>
#include<cstdio>
#include<string>
#include<bitset>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
using namespace std;
#define X first
#define Y second
#define mkp make_pair
#define lson (o<<1)
#define rson ((o<<1)|1)
#define mid (l+(r-l)/2)
#define sz() size()
#define pb(v) push_back(v)
#define all(o) (o).begin(),(o).end()
#define clr(a,v) memset(a,v,sizeof(a))
#define bug(a) cout<<#a<<" = "<<a<<endl
#define rep(i,a,b) for(int i=a;i<(b);i++)
#define scf scanf
#define prf printf
typedef long long LL;
typedef vector<int> VI;
typedef pair<int,int> PII;
typedef vector<pair<int,int> > VPII;
const int INF=1000000000;
const LL INFL=0x3f3f3f3f3f3f3f3fLL;
const double eps=1e-9;
const double PI = acos(-1.0);
//start----------------------------------------------------------------------
const int maxn=222;
int mat[maxn][maxn];
int G[22][22];
PII arr[22];
int n,m;
int dp[1<<15][15];
struct HeapNode{
int x,y,d;
HeapNode(int x,int y,int d):x(x),y(y),d(d){}
bool operator < (const HeapNode& tmp) const {
return d>tmp.d;
}
};
int d[22][maxn][maxn];
bool done[maxn][maxn];
const int dx[]={-1,1,0,0};
const int dy[]={0,0,-1,1};
void dij(int id,int sx,int sy){
priority_queue<HeapNode> Q;
rep(i,0,n) rep(j,0,m) d[id][i][j]=INF;
d[id][sx][sy]=0;
clr(done,0);
Q.push(HeapNode(sx,sy,0));
while(!Q.empty()){
HeapNode u=Q.top(); Q.pop();
int x=u.x,y=u.y;
if(done[x][y]) continue;
if(x==0||y==0||x==n-1||y==m-1){
d[0][sx][sy]=min(d[0][sx][sy],d[id][x][y]+mat[x][y]-mat[sx][sy]);
}
done[x][y]=true;
for(int i=0;i<4;i++){
int nx=x+dx[i],ny=y+dy[i];
if(nx<0||nx>=n||ny<0||ny>=m) continue;
if(mat[nx][ny]==-1) continue;
if(d[id][nx][ny]>d[id][x][y]+mat[x][y]){
d[id][nx][ny]=d[id][x][y]+mat[x][y];
Q.push(HeapNode(nx,ny,d[id][nx][ny]));
}
}
}
}
void init(){
rep(i,0,n) rep(j,0,m) d[0][i][j]=INF;
}
int main() {
int tc,kase=0;
scf("%d",&tc);
while(tc--) {
scf("%d%d",&n,&m);
init();
rep(i,0,n) rep(j,0,m){
scf("%d",&mat[i][j]);
}
int q;
scf("%d",&q);
for(int i=1;i<=q;i++) scf("%d%d",&arr[i].X,&arr[i].Y);
///dijkstra
for(int i=1;i<=q;i++){
dij(i,arr[i].X,arr[i].Y);
}
///TSP
///build
rep(i,0,22) rep(j,0,22) G[i][j]=INF;
rep(i,0,22) G[i][i]=0;
for(int i=0;i<=q;i++){
for(int j=0;j<=q;j++){
if(j==i) continue;
if(j==0){
G[i][j]=G[j][i]+mat[arr[i].X][arr[i].Y];
continue;
}
G[i][j]=d[i][arr[j].X][arr[j].Y];
}
}
///init
rep(i,0,(1<<15)) rep(j,0,15) dp[i][j]=INF;
dp[1][0]=0;
///通路
q++;
for(int i=2;i<(1<<q);i++){
for(int j=0;j<q;j++){
if(i&(1<<j)){
for(int k=0;k<q;k++){
if(k==j||!(i&(1<<k))) continue;
dp[i][j]=min(dp[i][j],dp[i^(1<<j)][k]+G[k][j]);
}
}
}
}
///回路
int ans=INF;
for(int i=1;i<q;i++){
ans=min(ans,dp[(1<<q)-1][i]+G[i][0]);
}
if(ans>=INF) prf("0
");
else prf("%d
",ans);
}
return 0;
}
//end-----------------------------------------------------------------------