【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.
