Question

Consider the following pseudocode: Algorithm RecursiveFunction (a, b) // a and b are integers if (as1 ) return b; else return RecursiveFunction (a-2, a/2); endif a. What is the time complexity of the RecursiveFunction pseudocode shown above? b What is the space complexity of the RecursiveFunction pseudocode shown above? n(n+1) C. What is the time complexity of the following algorithm (Note that 21-, i = n(n+1)(2n+1). and Σ.,1 ): Provide both T(n) and order, Ofn)). int A=0; for (int i=0;i<n;i++) for (int j-i;j<n; i++) for (int k=0;k<n;k++) A+=i+j+k; 2 d. Starting from a sorted array of n items, what is the time complexity for the most time efficient algorithm for finding the lowest valued item and moving it to the first location of the array ? (The resulting order of the other elements is unimportant.) e. Starting from an unsorted array of n items, what is the time complexity for the most time efficient algorithm for finding the two lowest valued items and moving them to the first two locations of the array ?

Answer 1

a Recurrence Relation (b) = P(n-2) + (1) T(n)= n =10(n) Here aan b space com complexity = Number of Times Recursive calls made 0(n) Here an when iso J- o to n- foe each j inned Loop runs n times Total non times When i=1 1=1 to n-2 Total= (no) хn times Total Run (n) = tn T() - n nant nx (n-1) + nx (n-2) + 1+2+3+ +n] nx n(n+i) [ 10 (13) [. 2 d As assay is sorted . moving smallest element to the first location in Constanttime = ſo (1) Time comple ring a form)