amortized analysis figure lazy binomial queue figure lazy binomial queue after removing the smallest element ( forr <log ++ while|lr > remove two trees from lr merge the two trees into new treeadd the new tree to lr+ figure procedure to reinstate binomial queue be able to perform the merge in time proportional to the number of trees present ( (or log nwhichever is largerto do thiswe form an array of listsl lrmax + where rmax is the rank of the largest tree each listlr contains all of the trees of rank the procedure in figure is then applied each time through the loopat lines to the total number of trees is reduced by this means that this part of the codewhich takes constant time per executioncan only be performed timeswhere is the number of trees the for loop counters and tests at the end of the while loop take (log ntimeso the running time is ( log )as required figure shows the execution of this algorithm on the previous collection of binomial trees amortized analysis of lazy binomial queues to carry out the amortized analysis of lazy binomial queueswe will use the same potential function that was used for standard binomial queues thusthe potential of lazy binomial queue is the number of trees