CLRS is the textbook used in this question. The textbook is : Introduction to Algorithms is a book on computer programming by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

4. It isn't obvious that the algorithm for one-pass top-down B-tree delete (x,k) (as described in class and CLRS) is truly a one-pass algorithm, since case 2 seems to require looking ahead to get the key q that is the immediate predecessor (or immediate successor ) of k to swap into x before continuing the recursive descent. (a) Say why this can happen at most one time in a delete operation (i.e once in the entire sequence of recursive calls to delete starting from the root before reaching a leaf node.) (b) Instead of swapping k and q immediately, suppose the code is modified so that the recursive descent just continues to descend from x (always to non-critical nodes) as if still searching for k. If k is keyi in the internal node x, describe how to choose the recursive call. (c) Explain why this recursive search will eventually lead to a node y containing q. (c) How can q be identified when the leaf node y is reached? (d) Outline the recursive one-pass top-down algorithm for delete. 4. It isn't obvious that the algorithm for one-pass top-down B-tree delete (x,k) (as described in class and CLRS) is truly a one-pass algorithm, since case 2 seems to require looking ahead to get the key q that is the immediate predecessor (or immediate successor ) of k to swap into x before continuing the recursive descent. (a) Say why this can happen at most one time in a delete operation (i.e once in the entire sequence of recursive calls to delete starting from the root before reaching a leaf node.) (b) Instead of swapping k and q immediately, suppose the code is modified so that the recursive descent just continues to descend from x (always to non-critical nodes) as if still searching for k. If k is keyi in the internal node x, describe how to choose the recursive call. (c) Explain why this recursive search will eventually lead to a node y containing q. (c) How can q be identified when the leaf node y is reached? (d) Outline the recursive one-pass top-down algorithm for delete