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CIT 590 Recursion Recursion • A function calling itself • Factorial def factorial(n): if n == 0: return 1 return n * factorial(n-1) Recursion • Does solving a smaller problem help me solve a bigger one. • Lists are naturally recursive • A list of n elements contains in it a list of n-1 elements • In many languages, lists are defined recursively in this manner • A list of 1 element is a single element • A list of n elements consists of the start element and a list of n- 1elements • Python makes extraction of portions of the list super easy List recursion examples • Sum of elements of a list • Finding max of a list • Replicate - I want to initialize a list with repeats of a certain number All in recursionOnLists.py Divide and Conquer ( a method of solving a problem) • Divide the problem into smaller problem with (usually) similar structure • Solve the smaller problems • Now aggregate/rollup the smaller solutions to get the solution to the original problem Classic divide and conquer = mergesort • Sort a list • If I divide the list into 2 halves and sort each half does that help? • 2 sorted lists can be merged Mergesort Merge • Making a larger sorted array from 2 smaller sorted ones • Exploit the fact that you know the relative ordering within the arrays def merge(a1, a2): a3 = [] len1 = len(a1) len2 = len(a2) i=j=0 while i < len1 and j < len2: if a1[i] < a2[j]: a3.append(a1[i]) i += 1 else: a3.append(a2[j]) j += 1 # we would either have gone through # all of a1 or all of a2 by this time # just tack on the remaining stuff at the end if i < len1: a3.extend(a1[i:]) if j < len2: a3.extend(a2[j:]) return a3 Palindrome finding • palindrome.py A string is a palindrome if and only if Its first character and its last character are the same Everything between the first and the last character is a palindrome Obviously, a single character string is a palindrome.