- suppose you are given an -element sequencescontaining distinct integers that are listed in increasing order given number kdescribe recursive algorithm to find two integers in that sum to kif such pair exists what is the running time of your algorithmc- develop nonrecursive implementation of the version of power from code fragment that uses repeated squaring projects - implement recursive function with signature find(pathfilenamethat reports all entries of the file system rooted at the given path having the given file name - write program for solving summation puzzles by enumerating and testing all possible configurations using your programsolve the three puzzles given in section - provide nonrecursive implementation of the draw interval function for the english ruler project of section there should be precisely lines of output if represents the length of the center tick if incrementing counter from to the number of dashes for each tick line should be exactly one more than the number of consecutive ' at the end of the binary representation of the counter - write program that can solve instances of the tower of hanoi problem (from exercise - - python' os module provides function with signature walk(paththat is generator yielding the tuple (dirpathdirnamesfilenamesfor each subdirectory of the directory identified by string pathsuch that string dirpath is the full path to the subdirectorydirnames is list of the names of the subdirectories within dirpathand filenames is list of the names of non-directory entries of dirpath for examplewhen visiting the cs subdirectory of the file system shown in figure the walk would yield /user/rt/courses/cs homeworks programs ]grades ]give your own implementation of such walk function notes the use of recursion in programs belongs to the folkore of computer science (for examplesee the article of dijkstra [ ]it is also at the heart of functional programming languages (for examplesee the classic book by abelsonsussmanand sussman [ ]interestinglybinary search was first published in but was not published in fully correct form until for further discussions on lessons learnedplease see papers by bentley [ and lesuisse [