Question

Give an algorithm with the following properties.

• Worst case running time of O(n 2 log(n)).

• Average running time of Θ(n).

• Best case running time of Ω(1).

Answer 1

/luntil1 left array has elements (right array vanishes) while 11 < len (left StringAry): //add leftstringAry[ii] to the original list astringList [kk]=leftStringAry[11] //Increment left array counter //Increment the element counter kk-kk+1 /luntill RIGHT array has elements (left array vanishes) while ji < len (xightStringAry //Add rightStringAryLǐュ] to the original list //Increment the right array counter //Increment element counter kk=kk+1 Explanation: Merge sort with array of n elements will have height of log n . If the element of the array itself an array with size p then algorithm takes p comparisons to find the larger of two strings. So, at any tree level, merge sort takes n comparisons with cost of p. So worst case running time is O(logn) We know that merge sort algorithm works by the concept of dividing the list, sorting the list and merging the list. The dividing phase takes Θ(1)constant time. Sorting and merging lists takes 0(n) . Hence average running time is Θ(n) (ignoring the constant time Θ(1) All algorithms are having time complexity of Q(1),. Since S2 specifies the lower bound for the algorithm. Hence this above algorithm has Ω(1) best case running time