舞动的dancing links poj 3740

对于npc问题，我们似乎只能用搜索（或状压dp）。

但是，有时候，搜索的期望得分是满分，比如说，当dancing links跳舞的时候。

dancing link 作为双向链表，拥有优秀的性质，快速的删除和恢复，任何熟练掌握链表的人都可以轻易上手，更重要的是，它为搜索省去大量回朔时间，并且方便启发式进行（只需加估价数组(代码中s)），优美的操作就像绚丽的舞步。

由于是矩阵，所以采用十字链表（up,down,left,right） c记录列号，t记录行号，s记录该列还有多少节点（尽量选择节点少进行拓展）

poj 3740（未加启发式） 219ms

var n,m,ss:longint; flag:boolean; u,d,r,l,c,t:array[0..50000]of longint;procedure link(x,y:longint);begin inc(ss);c[ss]:=y;t[ss]:=x; l[ss]:=l[x];r[l[x]]:=ss;l[x]:=ss; u[ss]:=u[y];d[u[y]]:=ss;u[y]:=ssend;procedure del(x:longint);var i,j:longint;begin r[l[x]]:=r[x];l[r[x]]:=l[x]; i:=x; while d[i]<>x do begin i:=d[i]; j:=i; while r[j]<>i do begin j:=r[j]; if j<>t[i] then begin u[d[j]]:=u[j];d[u[j]]:=d[j] end end endend;procedure rel(x:longint);var i,j:longint;begin r[l[x]]:=x;l[r[x]]:=x; i:=x; while u[i]<>x do begin i:=u[i]; j:=i; while l[j]<>i do begin j:=l[j]; if j<>t[i] then begin u[d[j]]:=j;d[u[j]]:=j end end endend;procedure dfs(k:longint);var i,j,x:longint;begin if r[0]=0 then begin flag:=true;exit end; x:=r[0];del(x);i:=x; while d[i]<>x do begin i:=d[i];j:=i; while r[j]<>i do begin j:=r[j]; if j<>t[i] then del(c[j]) end; dfs(k+1); if flag then exit; j:=i; while l[j]<>i do begin j:=l[j]; if j<>t[i] then rel(c[j]) end end; rel(x)end;procedure origin;var i:longint;begin fillchar(l,sizeof(l),0);fillchar(r,sizeof(r),0); fillchar(u,sizeof(u),0);fillchar(d,sizeof(d),0); fillchar(c,sizeof(c),0);fillchar(t,sizeof(t),0); r[0]:=1;l[0]:=m; for i:=1 to m do begin l[i]:=i-1;r[i]:=i+1;u[i]:=i;d[i]:=i end; r[m]:=0; for i:=m+1 to n+m do begin l[i]:=i;r[i]:=i end; ss:=n+mend;procedure init;var i,j,x:longint;begin readln(n,m); origin; for i:=1 to n do begin for j:=1 to m do begin read(x); if x=1 then link(i+m,j) end; readln end; for i:=1 to m do d[u[i]]:=i; for i:=m+1 to m+n do r[l[i]]:=i; flag:=false; dfs(0); if flag then writeln('Yes, I found it') else writeln('It is impossible')end;begin while not(seekeof) do initend.

poj 3740（加启发式） 172ms

var n,m,ss:longint; flag:boolean; u,d,r,l,c,t:array[0..50000]of longint; s:array[1..300]of longint;procedure link(x,y:longint);begin inc(ss);c[ss]:=y;t[ss]:=x; l[ss]:=l[x];r[l[x]]:=ss;l[x]:=ss; u[ss]:=u[y];d[u[y]]:=ss;u[y]:=ss; inc(s[y])end;procedure del(x:longint);var i,j:longint;begin r[l[x]]:=r[x];l[r[x]]:=l[x]; i:=x; while d[i]<>x do begin i:=d[i];j:=i; while r[j]<>i do begin j:=r[j]; if j<>t[i] then begin u[d[j]]:=u[j];d[u[j]]:=d[j]; dec(s[c[j]]) end end endend;procedure rel(x:longint);var i,j:longint;begin r[l[x]]:=x;l[r[x]]:=x; i:=x; while u[i]<>x do begin i:=u[i];j:=i; while l[j]<>i do begin j:=l[j]; if j<>t[i] then begin u[d[j]]:=j;d[u[j]]:=j; inc(s[c[j]]) end end endend;procedure dfs(k:longint);var i,j,x,y,min:longint;begin if r[0]=0 then begin flag:=true;exit end; x:=0;min:=maxlongint;y:=0; while r[x]<>0 do begin x:=r[x]; if s[x]<min then begin min:=s[x];y:=x end end; x:=y;del(x);i:=x; while d[i]<>x do begin i:=d[i];j:=i; while r[j]<>i do begin j:=r[j]; if j<>t[i] then del(c[j]) end; dfs(k+1); if flag then exit; j:=i; while l[j]<>i do begin j:=l[j]; if j<>t[i] then rel(c[j]) end end; rel(x)end;procedure origin;var i:longint;begin fillchar(l,sizeof(l),0);fillchar(r,sizeof(r),0); fillchar(u,sizeof(u),0);fillchar(d,sizeof(d),0); fillchar(c,sizeof(c),0);fillchar(t,sizeof(t),0); fillchar(s,sizeof(s),0); r[0]:=1;l[0]:=m; for i:=1 to m do begin l[i]:=i-1;r[i]:=i+1;u[i]:=i;d[i]:=i end; r[m]:=0; for i:=m+1 to n+m do begin l[i]:=i;r[i]:=i end; ss:=n+mend;procedure init;var i,j,x:longint;begin readln(n,m); origin; for i:=1 to n do begin for j:=1 to m do begin read(x); if x=1 then link(i+m,j) end; readln end; for i:=1 to m do d[u[i]]:=i; for i:=m+1 to m+n do r[l[i]]:=i; flag:=false; dfs(0); if flag then writeln('Yes, I found it') else writeln('It is impossible')end;begin while not(seekeof) do init;end.  

c++版

#include <cstdio>#include <algorithm>#include <cstring>#include <iostream>#include <string>#include <vector>#include <cassert>using namespace std;int g[100][500];int l[200000],r[200000],u[200000],d[200000],R[200000],C[200000];int row[200000],clo[200000],v[200000];int n,m,ss;int ori(){    ++ss;    l[ss]=r[ss]=u[ss]=d[ss]=ss,R[ss]=C[ss]=0;    return ss;}void linkud(int x,int y){d[x]=y,u[y]=x;}void linklr(int x,int y){r[x]=y,l[y]=x;}void add(int x,int y){ori();    R[ss]=row[x],C[ss]=clo[y];int last=u[clo[y]];linkud(last,ss),linkud(ss,clo[y]);last=l[row[x]];linklr(last,ss),linklr(ss,row[x]);}void build(){    ss=0;    for (int i=1;i<=n;i++) row[i]=ori();    for (int i=0;i<=m;i++) clo[i]=ori();    for (int i=1;i<n;i++) linkud(row[i],row[i+1]);    linkud(row[n],row[1]);    for (int i=0;i<m;i++) linklr(clo[i],clo[i+1]);    linklr(clo[m],clo[0]);    for (int i=1;i<=n;i++)        for (int j=1;j<=m;j++)             if (g[i][j]) add(i,j);}void del(int x){linklr(l[x],r[x]);for (int i=x;d[i]!=x;) {i=d[i];for (int y=i;r[y]!=i;) {y=r[y];if (R[y] && C[y]) linkud(u[y],d[y]);}}}void rel(int x){linklr(l[x],x),linklr(x,r[x]);for (int i=x;u[i]!=x;) {i=u[i];for (int y=i;l[y]!=i;) {y=l[y];if (R[y] && C[y]) linkud(u[y],y),linkud(y,d[y]);}}}bool DLX(int s,int step){if (r[s]==s) return 1;int x;x=r[s],del(x);for (int i=x;d[i]!=x;) {i=d[i];//cout<<'!'<<i<<endl;for (int y=i;r[y]!=i;) {y=r[y];if (R[y] && C[y]) del(C[y]);}v[R[i]]=1;if (DLX(s,step+1)) return 1;v[R[i]]=0;for (int y=i;l[y]!=i;) {y=l[y];if (R[y] && C[y]) rel(C[y]);}}rel(x);return 0;}int main() {    for (;scanf("%d%d",&n,&m)==2;) {//cout<<n<<' '<<m<<endl;        for (int i=1;i<=n;i++)            for (int j=1;j<=m;j++)                scanf("%d",&g[i][j]);        build();        if (DLX(clo[0],0)) {            printf("Yes, I found it\n");        }        else {            printf("It is impossible\n");        }    }    return 0;}