POJ 1463 tree-like DP

Strategic game

Time Limit: 2000MS		Memory Limit: 10000K
Total Submissions: 6629		Accepted: 3058

Description

Bob enjoys playing computer games, especially strategic games, but sometimes he cannot find the solution fast enough and T Hen he is very sad. Now he has the following problem. He must defend a medieval city, the roads of which form a tree. He has to put the minimum number of soldiers in the nodes so, they can observe all the edges. Can you help him?

Your program should find the minimum number of soldiers that Bob have to put for a given tree.

For example for the tree:

The solution is a soldier (at the Node 1).

Input

The input contains several data sets in text format. Each data set represents a tree with the following description:

• The number of nodes
• The description of each node in the following format
  Node_identifier: (number_of_roads) node_identifier1 node_identifier2 ... node_identifiernumber_of_roads
  Or
  Node_identifier: (0)

The node identifiers is integer numbers between 0 and n-1, for n nodes (0 < n <=); Line of input would no more than 10. Every edge appears only once in the input data.

Output

The output should is printed on the standard output. For each given input data set, print one, integer number in a, gives the result (the minimum number of sold Iers). An example are given in the following:

Sample Input

40: (1) 11: (2) 2 32: (0) 3: (0) 53: (3) 1 4 21: (1) 02: (0) 0: (0) 4: (0)

Sample Output

12

Source

Southeastern Europe 2000

POJ1463:

Topic Meaning:

Put soldiers on the nodes of the tree, so that each side of the tree is guarded by soldiers, the minimum number of soldiers required ;

Problem Solving Ideas:

Tree-like dp, state transitions to:

If a soldier is placed at this point, the DP of that point is equal to the sum of the minimum values of the soldiers or the soldiers not being placed on the node ;

If this point does not put soldiers, then the point of dp equals all sons nodes must be put on the soldier's and ;

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5#include <cstdio>6#include <vector>7 using namespacestd;8 Const intmaxn=1507;9 Const intinf=0x3f3f3ff;Ten structnode One { A     intTo,next; - }; -Node tree[15007]; thevector<int>G[MAXN]; - intdp[maxn][2]; - intN; - voidInit () + { -      for(intI=0; i<maxn;i++) g[i].clear (); +memset (Tree,0,sizeof(tree)); A      for(intI=0; i<maxn;i++) at     { -dp[i][0]=dp[i][1]=inf; -     } - } - voidDfsintPoint ) - { in     intres1=0, res2=0; -      for(intI=0; I<g[point].size (); i++) to     { + DFS (G[point][i]); -res1+=dp[g[point][i]][1]; theRes2+=min (dp[g[point][i]][1],dp[g[point][i]][0]); *     } $dp[point][0]=res1;Panax Notoginsengdp[point][1]=min (dp[point][1],res2+1); - } the intMain () + { A    //freopen ("In.txt", "R", stdin); the      while(~SCANF ("%d",&N)) { + init (); -         inta,b,c,root=-1; $          for(intI=1; i<=n;i++) $         { -scanf"%d: (%d)",&a,&b); -             if(root==-1) root=A; the              for(intj=0; j<b;j++) -             {Wuyiscanf"%d",&c); the G[a].push_back (c); -              } Wu         } - Dfs (root); About         intAns=min (dp[root][1],dp[root][0]); $printf"%d\n", ans); -     } -     return 0; -}

POJ 1463 tree-like DP