Secondary Generation tree (Appendix: poj1679)

 

Sub-tree generation:

 

When the Minimum Spanning Tree is obtained, the array path [I] [J] is used to represent the maximum edge weight from I to J in the MST.

After the result is obtained, enumerate all edges that are not in the MST and add them to the MST to form a new tree with a ring, this ring is caused by the newly added edge (I, j). Therefore, you can delete path [I] [J] to obtain a new tree, and one of all such trees will be a child tree.

For example:

G and H are not edges on the MST. By adding an edge (G, H), A ring (B, H, g) is obtained ), then, because G has been calculated when the minimum spanning tree is calculated, the maximum edge weight between H is path [g] [H] = BH, so you can get a Minimum Spanning Tree by deleting BH, and then update the answer.

# Include <iostream> # Include <Cstring> # Include <Cstdio> Using   Namespace  STD;  Const   Int X = 105 ;  Const   Int INF = 100000000  ;  Int  Map [x] [X], DIS [x];  Int Path [x] [x]; ///  Record the maximum edge weight on the I, J Path  Int Pre [x]; ///  Precursor Vertex  Int N; ///  Number of vertices Bool Use [X], In  [X] [x];  Int  Prim () {memset (use,  False , Sizeof  (Use); memset (PRE,  0 , Sizeof  (Pre); memset (  In , False , Sizeof ( In ));  For ( Int I = 0 ; I <= N; I ++ ) Dis [I] = INF; DIS [  1 ] = 0  ;  Int Ans = 0  ;  Int  Min, K, P;  For (Int I = 0 ; I <n; I ++ ) {Min = INF;  For ( Int J = 1 ; J <= N; j ++ )  If (! Use [J] & min> Dis [J]) min = Dis [k = J];  If (Min = INF) Return  INF; P = Pre [k];  In [P] [k] = In [K] [p] = True  ; Path [p] [k] = Path [k] [p] = min; //  Since the vertex K has not been calculated, it is directly equal to Min          For ( Int J = 1 ; J <= N; j ++ )  If (Use [J]) //  Update vertices already in the MST Path [J] [k] = path [k] [J] = Max (path [J] [K], path [p] [k]); use [k] = True  ; Ans + = Min;  For ( Int J = 1 ; J <= N; j ++ )  If (! Use [J] & dis [J]> Map [k] [J]) dis [J] = Map [k] [J], pre [J] = K ;}  Return  Ans ;}  Int  Main (){  //  Freopen ("sum. In", "r", stdin );  //  Freopen ("sum. Out", "W", stdout );      Int  T, M, x, y, z; CIN > T;  While (T -- ) {Scanf (  " % D  " , & N ,& M );  For ( Int I = 1 ; I <= N; I ++ )  For ( Int J = 1 ; J <= N; j ++ ) Map [I] [J] = Map [J] [I] = INF;  While (M --) {Scanf (  "  % D  " , & X, & Y ,& Z); map [x] [Y] = Map [y] [x] = Z ;}  Int Ans = Prim ();  Int OK = True  ;  For ( Int I = 1 ; I <= N & OK; I ++) //  Enumeration finds edge not on the MST              For ( Int J = 1 ; J <= N & OK; j ++ )  If (Map [I] [J]! = Inf &&! In  [I] [J])  If (ANS = ANS-path [I] [J] + Map [I] [J]) OK = False  ; If  (OK) printf (  "  % D \ n  "  , ANS );  Else  Printf (  "  Not unique! \ N  "  );}  Return   0  ;}