[PKU1679 The Unique MST]

【题目】:The Unique MST

【来源】:POJ1679

【关键字】:图论 次小生成树

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【分析】:先构造最小生成树,再在MST中删边,找次小生成树.

【小结】:刘老师的论文

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【代码】:

View Code

  1 type
  2   rec = record
  3     x, y, d: longint;
  4   end;
  5 var
  6   t, i, n, m, ans, j: longint;
  7   a: array[0..10010] of boolean;
  8   e: array[0..10010] of rec;
  9   f: array[0..4000] of longint;
 10 function get(k: longint):longint;
 11 begin
 12   if f[k] = k then exit(k);
 13   f[k] := get(f[k]);
 14   get := f[k];
 15 end;
 16 procedure qs(l, r: longint);
 17 var
 18   i, j, mid: longint;
 19   t: rec;
 20 begin
 21   i := l;
 22   j := r;
 23   mid := e[(l+r) shr 1].d;
 24   repeat
 25     while e[i].d < mid do inc(i);
 26     while e[j].d > mid do dec(j);
 27     if i <= j then
 28       begin
 29         t := e[i];
 30         e[i] := e[j];
 31         e[j] := t;
 32         inc(i);
 33         dec(j);
 34       end;
 35   until i > j;
 36   if l < j then qs(l,j);
 37   if i < r then qs(i,r);
 38 end;
 39 function judge:boolean;
 40 var
 41   p, i, j, x, y, now: longint;
 42 begin
 43   for j := 1 to m do
 44     if not a[j] then
 45       begin
 46         p := 0;
 47         now := 0;
 48         for i := 1 to n do f[i] := i;
 49         i := 1;
 50         while (i <= m) and (p < n-1) do
 51           begin
 52             x := get(e[i].x);
 53             y := get(e[i].y);
 54             if (x <> y) and (i <> j) then
 55               begin
 56                 f[x] := y;
 57                 inc(now,e[i].d);
 58                 inc(p);
 59               end;
 60             inc(i);
 61           end;
 62         if p <> n-1 then now := -1;
 63         if now = ans then exit(true);
 64       end;
 65   exit(false);
 66 end;
 67 procedure kur;
 68 var
 69   p, i, x, y: longint;
 70 begin
 71   p := 0;
 72   ans := 0;
 73   for i := 1 to n do f[i] := i;
 74   for i := 1 to m do a[i] := true;
 75   i := 1;
 76   while (i <= m) or (p < n-1) do
 77     begin
 78       x := get(e[i].x);
 79       y := get(e[i].y);
 80       if x <> y then
 81         begin
 82           f[x] := y;
 83           inc(ans,e[i].d);
 84           inc(p);
 85           a[i] := false;
 86         end;
 87       inc(i);
 88     end;
 89   if p <> n-1 then ans := -1;
 90 end;
 91 begin
 92   readln(t);
 93   for j := 1 to t do
 94     begin
 95       readln(n,m);
 96       for i := 1 to m do
 97         readln(e[i].x,e[i].y,e[i].d);
 98       qs(1,m);
 99       kur;
100       if judge then writeln('Not Unique!') else writeln(ans);
101     end;
102 end.