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Design and Analysis of Algorithms Consider the following recurrence relation: T(n) = 2T(n/2) + n Use the substitution method to find an asymptotic upper bound for the function T(n).20237mDesign and Analysis of Algorithms Suppose the number of basic operations in an algorithm is defined as: T(n) = T(n-1) + n, with T(1) = 1. Solve this recurrence using the substitution method and determine the time complexity.20247mDesign & Analysis of AlgorithmsWrite time function and calculate the time complexity, space complexity and number of function calls of the following pseudocode using substitution method: ``c rec(n) { if (n <= 1) return(1); else { rec(n / 2); for (i = 1; i <= n; i++) printf("algorithm"); } } ``20227mWeb TechnologyWrite a program in Java to do the following: (a) To swap the two numbers without using the third variable (b) Factorial of a number using recursion202014m
PreviousKruskal algorithm is a (i) Divide & conquer algorithm (ii) Branch and bound algorithm (iii) Greedy algorithm (iv) Dynamic programmingNextWrite the Knuth-Morris-Pratt algorithm for pattern matching. Apply the KMP algorithm for the pattern p = "ababaca" and string s = "bacbabababacaab". Show every step.