【USACO】Watering Hole 2008 Oct

【算法】MST-Prim

①初步思路就是最小生成树，那么打井操作怎么办呢？

   打井操作可看做是尤一个超级水源引出水，且代价为Wi的操作，所以加一个“超级点”就可以了，接着MST

  1 var
  2     n,heapsize,now,i,j:integer;
  3     temp,mst:longint;
  4     v:array[1..301,1..301] of longint;
  5     p:array[1..301] of integer;
  6     a,place:array[1..301] of integer;
  7     d:array[1..301] of longint;
  8     done:array[1..301] of boolean;
  9 procedure exchange(x,y:integer);
 10 var
 11     i,j,temp:integer;
 12 begin
 13     place[a[x]]:=y;
 14     place[a[y]]:=x;
 15     temp:=a[x];a[x]:=a[y];a[y]:=temp;
 16 end;
 17 
 18 procedure min_heapify(i:integer);
 19 var
 20     l,r,smaller:integer;
 21 begin
 22     l:=i shl 1;
 23     r:=l+1;
 24     smaller:=i;
 25     if (d[a[l]]<d[a[smaller]])and(l<=heapsize) then smaller:=l;
 26     if (d[a[r]]<d[a[smaller]])and(r<=heapsize) then smaller:=r;
 27     if smaller<>i then
 28     begin
 29         exchange(smaller,i);
 30         min_heapify(smaller);
 31     end;
 32 end;
 33 
 34 procedure change(k:integer;x:longint);
 35 var
 36     i:integer;
 37 begin
 38     i:=k;
 39     while (i>1)and(d[a[i shr 1]]>x) do
 40     begin
 41         exchange(i,i shr 1);
 42         i:=i shr 1;
 43     end;
 44 end;
 45 
 46 function extract_min:integer;
 47 var
 48     i:integer;
 49 begin
 50     extract_min:=a[1];
 51     a[1]:=a[heapsize];
 52     place[a[1]]:=1;
 53     dec(heapsize);
 54     min_heapify(1);
 55 end;
 56 
 57 procedure build_heap;
 58 var
 59     i:integer;
 60 begin
 61     for i:=n div 2 downto 1 do min_heapify(i);
 62 end;
 63 begin
 64    assign(input,'water.in');
 65    reset(input);
 66    assign(output,'water.out');
 67    rewrite(output);
 68     readln(n);
 69    fillchar(done,sizeof(done),false);
 70     for i:=1 to n+1 do p[i]:=i;
 71     for i:=2 to n+1 do
 72     begin
 73         readln(temp);
 74         v[1,i]:=temp;
 75       v[i,1]:=temp;
 76     end;
 77     for i:=2 to n+1 do
 78     begin
 79         for j:=2 to n+1 do
 80         begin
 81             read(temp);
 82             v[i,j]:=temp;
 83          v[j,i]:=temp;
 84         end;
 85         readln;
 86     end;
 87  
 88     for i:=1 to n+1 do place[i]:=i;
 89     for i:=1 to n+1 do a[i]:=i;
 90     for i:=1 to n+1 do d[i]:=maxlongint;
 91    d[1]:=0;
 92     heapsize:=n+1;
 93     while heapsize<>0 do
 94     begin
 95         now:=extract_min;
 96         done[now]:=true;
 97         for i:=1 to n+1 do if not done[i] then
 98         if (d[i]>v[i,now])and(v[i,now]<>0) then
 99         begin
100             d[i]:=v[i,now];
101             change(place[i],v[i,now]);
102 
103         end;
104         MST:=MST+d[now];
105    
106     end;
107     writeln(mst);
108    close(input);
109    close(output);
110 end.

 

posted @ 2013-08-14 00:10  OmegaIota  阅读(292)  评论(0)  编辑  收藏  举报