title: Network Flow: Can I change edge capacity while solving for max flow?
body: <p>I want to know if I can change edge capacities in a network flow problem while solving it. </p>
  
  <p>I have a supply/demand problem with goods A, B, and AB. A unit of demand for A will take one unit of A, B will take B, and AB will take one unit of AB or a unit of A and a unit of B. Given a list of supply and demand for each good, I want to figure out if there enough goods on hand to satisfy the demand.</p>
  
  <p>So I my net work looks like this:</p>
  
  <p>Let sX be supply of X.<br>
  Let dX be demand of X.<br>
  All flows go from left to right.</p>
  
  <p><img src="https://i.stack.imgur.com/jBYwb.png" alt="enter image description here"></p>
  
  <p>You can see that if I push x units of A, I have subtract x from the capacity going to (A+B). Similarly if I 'undo' a push, I have add capacity back to (A+B). So I have do this during the algorithm. Does that mess up the algorithm?</p>