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Object-Oriented Programming Using C++

Object-Oriented Programming Using C++. CLASS 2. Linear Recursion Summing the Elements of an Array Recursively Algorithm LinearSum(A, n): Input: An integer array A and int n Output: The sum of the first n int in A if n = 1 then return A[0] else

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Object-Oriented Programming Using C++

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  1. Object-Oriented Programming Using C++ CLASS 2

  2. Linear Recursion • Summing the Elements of an Array Recursively • Algorithm LinearSum(A, n): • Input: An integer array A and int n • Output: The sum of the first n int in A • if n = 1 then • return A[0] • else • return LinearSum(A, n-1) + A[n-1]

  3. Linear Recursion • Reverse an Array by Recursion • Algorithm ReverseArray(A, i, n): • Input: An integer array A and int i, n • Output: The reversal of n integers in A starting at index i • if n > 1 then • Swap A[i] and A[i+n-1] • Call ReverseArray(A, i+1, n-2) • return

  4. Linear Recursion • Computing Powers • Algorithm Power(x, n): • Input: The number x and int n >= 0 • Output: The value x power n • if n = 0 then • return 1 • if n is odd then • y  Power(x, (n-1)/2) • return x * y * y • else • y  Power(x, n/2) • return y * y

  5. Tail recursion • Using recursion can often be a useful tool for designing algorithms, but this usefulness does come at a modest cost • Whenever we use recursion function to solve a problem, we have to use some of the memory locations in our computer to keep track of the state of each active recursive call • We can use the stack data structure to convert a recursive algorithm into a non-recursive algorithm, easily the ones which use tail recursion • A tail recursion is when the algorithm uses linear recursion and the algorithm only makes a recursive call as its last operation. For example, ReverseArray() uses tail recursion and LinearSum() does not

  6. Linear Recursion • Reverse an Array by Iterative non-Recursion • Algorithm IterativeReverseArray(A, i, n): • Input: An integer array A and int i, n • Output: The reversal of n integers in A starting at index i • while n > 1 do • Swap A[i] and A[i+n-1] • i  i + 1 • n  n - 2 • return

  7. Higher order recursion • When an instance of recursion algorithm makes more than a single recursive call • Algorithm BinarySum(A, i, n): • Input: An int array A and int i and n • Output: The sum of the n integers in A starting at I • if n = 1 then • return A[i] • return BinarySum(A, i, [n/2]) + • BinarySum(A, i, [n/2], [n/2])

  8. Higher order recursion • When an instance of recursion algorithm makes more than a single recursive call • Algorithm BinaryFib(k) • Input: An int k • Output: The kth Fibonacci number • if k <= 1 then • return k • else • return BinaryFib(k-1) + BinaryFib(k-2)

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