Solving Recurrence Relations Iteration method Steps Expand the recurrence

# Solving recurrence relations iteration method steps

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Solving Recurrence Relations - Iteration method Steps: Expand the recurrence Express the expansion as a summation by plugging the recurrence back into itself until you see a pattern. Evaluate the summation In evaluating the summation one or more of the following summation formulae may be used: Arithmetic series: Geometric Series: Special Cases of Geometric Series: 9 Solving Recurrence Relations - Iteration method Harmonic Series: Others: 10 Analysis Of Recursive Factorial method Example 1: Form and solve the recurrence relation describing the number of multiplications carried out by the factorial method and hence determine its big-O complexity: long factorial (int n) { if (n == 0) return 1; else return n * factorial (n – 1); } 11 0 0 ( ) ( 1) 1 0 0 n T n T n n n n Analysis Of Recursive Towers of Hanoi Algorithm The recurrence relation describing the number of times is executed for the method hanoi is: public static void hanoi(int n, char from, char to, char temp){ if (n == 1) System.out.println(from + " --------> " + to); else{ hanoi(n - 1, from, temp, to); System.out.println(from + " --------> " + to); hanoi(n - 1, temp, to, from); } } the printing statement 12 Analysis Of Recursive Towers of Hanoi Algorithm 13 Analysis Of Recursive Binary Search The recurrence relation describing the number of for the method is: public int binarySearch (int target, int[] array, int low, int high) { if (low > high) return -1; else { int middle = (low + high)/2; if (array[middle] == target) return middle; else if(array[middle] < target) return binarySearch(target, array, middle + 1, high); else return binarySearch(target, array, low, middle - 1); } } element comparisons 14  #### You've reached the end of your free preview.

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• Summer '14
• Mr.SaidAbdallah
• Recursion, Recurrence relation
• • • 