Poj2531--network saboteur (stochastic algorithm water pitch)

Network saboteur

Description
A University Network is composed of N computers. System administrators gathered information on the traffic between nodes, and carefully divided the network into and the subnet Works in order to minimize traffic between parts.
A disgruntled computer science student Vasya, after being expelled from the university, decided to has his revenge. He hacked into the university network and decided to reassign computers to maximize the traffic between.
Unfortunately, he found, calculating such worst subdivision is one of the those problems he, being a student, failed to so Lve. So he asks-a more successful CS student, to-help him.
The traffic data is given in the form of Matrix C, where Cij is the amount of data sent between and ith jth (nodes = Cji, Cii = 0). The goal is to divide the network nodes into the and the disjointed subsets A and B so as to maximize the SUM∑CIJ (I∈A,J∈B).
Input
The first line of input contains a number of nodes N (2 <= n <= 20). The following n lines, containing n space-separated integers each, represent the traffic matrix C (0 <= Cij <= 10000 ).
Output file must contain a single integer-the maximum traffic between the subnetworks.
Output
Output must contain a single integer-the maximum traffic between the subnetworks.
Sample Input
3
0 50 30
50 0 40
30 40 0
Sample Output
90

Main topic:

A graph is separated into two parts by a straight line, and the weights and the maximum values of the edges that intersect the line are obtained.

Problem Solving Ideas:

The maximal cutting problem of the graph theory's non-direction complete graph.

First set up two sets, one containing all points and the other an empty set.

The weighted value at this time is 0.

Randomly pick a point and move it from the collection to another set.

eg

The weight of the current state and Sum, 3rd points, from the collection 1 to the set 2.

The value and the change of the weight is

Sum+=edge[3][i],i represents the point in the collection 1.

The sum-=edge[3][j],j represents the point in the collection 2, excluding the number 3rd points.

Each time a change occurs, a new sum is generated, and the maximum value of the sum is saved.

(Randomly selected 100W times, the more random times, the more likely to produce a standard answer, but note the time)

Code:

1 /*************************************************************************2 > File Name:poj2531.cpp3 > Author:enumz4 > Mail: [email protected]5 > Created time:2014 October 27 Monday 19:08 08 seconds6  ************************************************************************/7 8#include <iostream>9#include <cstdio>Ten#include <cstdlib> One#include <string> A#include <cstring> -#include <list> -#include <queue> the#include <stack> -#include <map> -#include <Set> -#include <algorithm> +#include <cmath> -#include <bitset> +#include <time.h> A#include <climits> at #defineMAXN 100000 - using namespacestd; - voidInit () - { - Srand (Time (NULL)); - } in intedge[ -][ -]; - intMain () to { + init (); -     intN; the      while(cin>>N) *     { $Memset (Edge,0,sizeof(Edge));Panax Notoginseng          for(intI=1; i<=n;i++) -              for(intj=1; j<=n;j++) theCin>>Edge[i][j]; +         inttimes=1000000; A         BOOLgather[ -]; the         intret=0, max=0; +memset (Gather,0,sizeof(gather)); -          while(times--) $         { $             intTmp=rand ()%n+1; -gather[tmp]=!gather[tmp]; -              for(intI=1; i<=n;i++) the             { -                 if(gather[i]!=gather[tmp])Wuyiret+=edge[i][tmp]; the                 if(gather[i]==gather[tmp]&&i!=tmp) -ret-=edge[i][tmp]; Wu             } -Max=max>ret?Max:ret; About         } $cout<<max<<Endl; -     } -     return 0; -}

　　　　

　　　　

Poj2531--network saboteur (stochastic algorithm water pitch)