if we implement the priority queue using sorted listthen we improve the running time of phase to ( )for each operation removemin on now takes ( time unfortunatelyphase now becomes the bottleneck for the running timesincein the worst caseeach insert operation takes time proportional to the size of this sorting algorithm is therefore better known as insertion-sort (see figure )for the bottleneck in this sorting algorithm involves the repeated "insertionof new element at the appropriate position in sorted list figure execution of insertion-sort on sequence ( , , , , , , in phase we repeatedly remove the first element of and insert it into pby scanning the list implementing puntil we find the correct place for this element in phase we repeatedly perform removemin operations on peach of which returns the first element of the list implementing pand we add the element at the end of analyzing the running time of phase of insertion-sortwe note that it is