Now consider the decision trees of algorithms for solving this problem. To make the decision tree more explicit, we can augment the tree with square nodes, which mean that a value of -1 is returned, indicating that x does not appear in the array L. The decision tree for binary search with n = 13, augmented in this fashion, is shown below.

Below, you are given two algorithms for searching in a sorted array. Each function is a minor modification of the binary search algorithm discussed in class.

(a) Draw the decision tree for Algorithm 1 with n = 7. If the tree has more than four levels, you only need to draw the first four levels (i.e., levels 0, 1, 2, and 3, where 0 is the root level).

(b) Based on your answer to (a), comment on the correctness of Algorithm 1.

(c) Draw the decision tree for Algorithm 2 with n = 7. If the tree has more than four levels, you only need to draw the first four levels (i.e., levels 0, 1, 2, and 3, where 0 is the root level).

(d) Based on your answer to (c), comment on the correctness of Algorithm 2.

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