Poj 2531 (randomization)

Give a full graph and find the maximum cut.

It is said that this is an NP-hard problem. I started to think about DFS + backtracking, And the brute force search times out. Later, I tried some optimizations based on other users' search results. 400 ms. There may be better pruning methods, but unfortunately I did not find them. Here, I will take a look at the randomization algorithm. After all, I have never seen it before.

Burst search code:
# Include <iostream> <br/> # include <cstring> <br/> using namespace STD; <br/> int G [22] [22]; <br/> int Val [22]; <br/> int max_sum = 0; <br/> int sum = 0; <br/> void DFS (int n, int t) <br/>{< br/> int I, j; <br/> If (t = N) <br/>{< br/> If (sum> max_sum) <br/> max_sum = sum; <br/> return; <br/>}< br/> Val [T] = 0; <br/> int TMP = 0; <br/> for (I = 0; I <t; I ++) <br/>{< br/> If (Val [I] = 1) <br/> TMP + = G [T] [I]; <br/>}< br/> sum + = TMP; <br/> DFS (n, t + 1); <br/> sum-= TMP; <br/> TMP = 0; <br/> Val [T] = 1; <br/> for (I = 0; I <t; I ++) <br/>{< br/> If (Val [I] = 0) <br/> TMP + = G [T] [I]; <br/>}< br/> sum + = TMP; <br/> DFS (n, t + 1); <br/> sum-= TMP; <br/>}< br/> int main () <br/>{< br/> int N; <br/> int I, J; <br/> CIN> N; <br/> for (I = 0; I <n; I ++) <br/> for (j = 0; j <n; j ++) <br/> CIN> G [I] [J]; <br/> DFS (n, 0 ); <br/> cout <max_sum <Endl; <br/>}
 

 

Later I referred to other people's randomization algorithms and thought it was quite classic:

It is to divide a large set S into two sets S1 and S2, then randomly select a point from the set S, change the set where it is located, and then form a new S1 and S2, calculate the sum of the new weights.

In this way, after multiple random selections, we can obtain the approximate optimal solution (usually the optimal solution ).

# Include <iostream> <br/> # include <cstdlib> <br/> # include <cstring> <br/> using namespace STD; <br/> int G [22] [22]; <br/> int Val [22]; <br/> int max_sum = 0; <br/> int sum = 0; <br/> void random (int n) <br/>{< br/> int sum1 = 0; <br/> int sum2 = 0; <br/> int sum = 0; <br/> Int J = 0; <br/> int I = 0; <br/> for (j = 0; j <100000; j ++) <br/>{< br/> int r = rand () % N; <br/> sum1 = 0; <br/> sum2 = 0; <br/> If (Val [R] = 0) <br/> {<br/> Val [R] = 1; <br/> for (I = 0; I <n; I ++) <br/> If (Val [I] = 1) <br/> sum1 + = G [r] [I]; <br/> for (I = 0; I <n; I ++) <br/> If (Val [I] = 0) <br/> sum2 + = G [r] [I]; <br/> // cout <sum1 <"" <sum2 <Endl; </P> <p> sum + = sum2-sum1; <br/> If (sum> max_sum) <br/> max_sum = sum; <br/> // cout <max_sum <Endl; <br/>}< br/> else <br/> {<br/> Val [R] = 0; <br/> for (I = 0; I <N; I ++) <br/> If (Val [I] = 0) <br/> sum1 + = G [r] [I]; <br/> for (I = 0; I <n; I ++) <br/> If (Val [I] = 1) <br/> sum2 + = G [r] [I]; <br/> sum + = sum2-sum1; <br/> If (sum> max_sum) <br/> max_sum = sum; <br/>/* <br/> cout <sum1 <"" <sum2 <Endl; <br/> If (sum1 <sum2) <br/> max_sum + = sum2-sum1; <br/> cout <max_sum <Endl; <br/> */<br/>}< br/> cout <max_sum <Endl; <br/>}< br/> int main () <br/>{< br/> int N; <br/> int I, J; <br/> CIN> N; <br/> for (I = 0; I <n; I ++) <br/> for (j = 0; j <n; j ++) <br/> CIN> G [I] [J]; <br/> memset (Val, 0, sizeof (VAL )); <br/> random (n); <br/>}