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# ch05 - Ch 5 Recursion Motivation Problem Solving Tips...

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Ch 5 – Recursion Motivation Problem Solving Tips Factorial Array Reversal Sum Squares Calculates Fibonacci Numbers Ackerman’s Function Binary Search Linked List Traversal Towers of Hanoi Recursive Flood Fill Defining Languages Languages Palindrome Expressions 8 Queens p X

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Motivation Recursion is a powerful problem solving tool that is based on mathematical induction The idea is to express solution to problem X in term of smaller versions of X All recursive solutions can be implemented iteratively, but they often require less code when implemented recursively Recursion also gives an easy way to “backtrack” if a searching algorithm reaches a dead end
Problem Solving Tip Think like a manager! Take large problem and break into parts to delegate to employees Tell employees to think like managers and subdivide their tasks Always need a termination condition so employees know when to stop dividing and delegating For speed, try to divide the problem in half (or even smaller).

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Factorial Example Hence, solution to N factorial can be written as a smaller factorial problem We need a terminating condition to stop this sequence of recursive replacements. N! = N.(N-1).(N-2)….3.2.1 Really (N-1)! N! = N.(N-1)! 1! = 1 0! = 1 Common stopping conditions
Factorial Implementation int factorial (int num) { // check terminating condition if (num <= 1) return 1; // handle recursive case else return (num * factorial(num – 1)); } The code above has same number of multiplies as an iterative solution. Recursive answer slightly slower due to function call overhead. a smaller problem

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Tracing Factorial Execution Box method tracing is helpful for showing what recursive function do Pretend we have multiple copies of code and draw a box for each Draw arrows to show when a function calls itself (pointing to new box) and when it returns to calling function. Show return values on arrows back main fact(3) fact(2) fact(1) 1 2 6
Tracing Factorial Execution Can also show values of local variables inside each box Normally show parameters at top of box

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Array Reversal Example Assume we are given array of N values to reverse N N-2 Problem gets smaller at each step Stop when asked to swap 0 or 1 elements Algorithm: swap first and last elements in array recursively reverse N-2 elements in between
Array Reversal Implementation void reverse(int []data, int low, int high) { // check termination condition int size = high – low + 1; if (size <= 1) return; // handle recursive case else { int temp = data[low]; data[low] = data[high]; data[high] = temp; reverse (data, low + 1, high – 1); } } int main () { int d[9] = {3, 1, 4, 1, 5, 9, 2, 6, 5} reverse (d, 0, 8); }

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Tracing Array Reversal Tracing execution of reverse(d,0,8) using the box methods.
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