Algo3Notes

# Algo3Notes - We have introduced the recursion paradigm for...

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We have introduced the recursion paradigm for the binary tree data structure. Recursion is a general algorithm design approach, and here are additional examples. 1

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Factorial of n is the product of the first n numbers. Factorial of n can be computed recursively as factorial of n-1 times n. The termination condition is if n==1 then return 1. (Note that the == sign is used to emphasize that we test for equality between the left and the right quantities, and we do not assign 1 to n.) This is a termination condition because when it is true there is no more recursive call made. The chain of recursive calls is interrupted. The recursive call is the call to Factorial(n-1). The algorithm uses itself as a sub- algorithm. 2
Left: conventional (non-recursive) minimum algorithm. Right: recursive algorithm for finding minimum. The recursive algorithm is based on the idea that the minimum in an array is the smaller of: - The first element - The minimum of remaining elements MinR is first called as MinR(A, n, 0), since we want the minimum beginning from the first element, which has index 0. Then the minimum of elements 2 to n-1 is found by calling MinR recursively with arguments (A, n, 1) and saved into variable tmp. Finally, the overall minimum being returned is the smaller of the first element or tmp. MinR(A, n, 2) makes another recursive call, MinR(A, n, 3) and so on. When i0 becomes n-1, no more recursive call is made. “If i0 == n-1 then return A[i0]” is the termination condition. 3

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Here is a recursive sorting algorithm. The idea is to sort the array by splitting the array in half, sorting each half independently, and then merging the two sorted halves in the overall sorted algorithm. The recursion keeps splitting the array until the array has a single element. When l
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Algo3Notes - We have introduced the recursion paradigm for...

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