title: Minimum product spanning tree
body: <p>In the <code>minimum product spanning tree</code> problem, the cost of a tree is the product of all the edge weights in the tree, instead of the sum of the weights. 
  You may assume that all edges have positive weight. I would like to get answers for the following problems.</p>
  
  <p><strong>(1)</strong> Give a graph whose minimum product spanning tree is different than the minimum weight spanning tree.</p>
  
  <p><strong>(2)</strong> Give an efficient algorithm to compute the minimum product spanning tree. (Hint: think logarithms).</p>