Ural 1069. Prufer Code

1069. Prufer Codetime limit:0.25 Second
Memory Limit:8 MBA tree (i.e. a connected graph without cycles) with vertices is given ( N≥2). Vertices of the tree is numbered by the integers 1,..., N. A prufer code for the tree was built as follows:a leaf (a vertex that's incident to the only edge) with a minimal number is taken. Then this vertex and the incident edge is removed from the graph, and the number of the vertex that is adjacent to the L EAF is written down. In the obtained graph once again a leaf with a minimal number are taken, removed and this procedure is repeated until the O nly Vertex is left. It is clear, the only vertex and the vertex with the number N. The written down set of integers ( N−1 numbers, each of a range from 1 to N) is called a Prufer codeof the graph. Your task is, given a prufer code, to reconstruct a tree, and i.e. to find out the adjacency lists for every vertex in the GRA Ph. Assume that 2≤ N≤7500inputa set of numbers corresponding to a prufer code of some tree. The numbers is separated with a spaces and/or line breaks. Outputadjacency lists for each vertex. format:a vertex number, colon, numbers of adjacent vertices separated with a space. The vertices inside lists and lists itself should is sorted by vertex number in a ascending order (look at sample output) . Sample

input	Output
2 1 6) 2 6	1:4 62:3 5 63:24:15:26:1 2

problem Author:Magaz Asanov
problem Source:Ural State univerisity Personal Contest Online February ' 2001 Students Session Tags:Graph theory()difficulty:522 Test instructions: Give Prufer code, ask to find out the original tree. Analysis: It's easy to know after Prufercode.

1 /**2 Create by Yzx-stupidboy3 */4#include <cstdio>5#include <cstring>6#include <cstdlib>7#include <cmath>8#include <deque>9#include <vector>Ten#include <queue> One#include <iostream> A#include <algorithm> -#include <map> -#include <Set> the#include <ctime> -#include <iomanip> - using namespacestd; -typedefLong LongLL; +typedefDoubleDB; - #defineMIT (2147483647) + #defineINF (1000000001) A #defineMLL (1000000000000000001LL) at #defineSZ (x) ((int) (x). Size ()) - #defineCLR (x, y) memset (x, y, sizeof (x)) - #definePUF Push_front - #definePub push_back - #definePOF Pop_front - #definePOB pop_back in #defineFT first - #defineSD Second to #defineMk Make_pair +  -InlineintGetint () the { *     intRet =0; $     CharCh =' ';Panax Notoginseng     BOOLFlag =0; -      while(! (Ch >='0'&& Ch <='9')) the     { +         if(Ch = ='-') Flag ^=1; ACh =GetChar (); the     } +      while(Ch >='0'&& Ch <='9') -     { $RET = RET *Ten+ Ch-'0'; $Ch =GetChar (); -     } -     returnFlag? -Ret:ret; the } - Wuyi Const intN =7510; the intN, Arr[n]; - intCnt[n]; Wupriority_queue<int>que; -vector<int>Ans[n]; About  $InlinevoidInput () - { -     intx; -      while(Cin >>x) A     { +arr[n++] =x; thecnt[x]++; -     } $n++; the } the  theInlinevoidSolve () the { -      for(inti =0; I < n; i++) in         if(!cnt[i +1]) Que.push (-(i +1)); the      for(intStep =1; Step <= N-1; step++) the     { About         intx =-que.top (), now = Arr[step-1]; the Que.pop (); the         if(! (--cnt[now])) Que.push (-Now ); the ans[now].pub (x); + ans[x].pub (now); -     } the Bayi      for(inti =1; I <= N; i++) the     { theprintf"%d:", i); - sort (Ans[i].begin (), Ans[i].end ()); -         intLength =sz (ans[i]); the          for(intj =0; J < length; J + +) theprintf"%d", Ans[i][j]); theprintf"\ n"); the     } - } the  the intMain () the {94Freopen ("a.in","R", stdin); the Input (); the Solve (); the     return 0;98}

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Ural 1069. Prufer Code