Question about the for loop condition to efficientlly iterate all subset

[qiao]

Hi wisdompeak,

In the README.md, you mentioned a template

  for (int state=1; state<(1<<n); state++)  
      for (int subset=state; subset>0; subset=(subset-1)&state)
      {
          dp[state] = DoSomething(dp[subset]);
      }  

The inner for loop condition implies when (subset-1&state) == 0, there's no need to search the next subset with the same state.

However, I'm confuse about the reason, would you please explain it or give me some hint?
Thanks.

[yangizone]

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[wisdompeak]

if you write something like for (int subset=state; subset>=0; subset=(subset-1)&state), the loop would never end.