State the approximate worst-case running time for each of the following. Appropriate answers are of the form “constant time” or “X in Y”, where X might be “linear,” “quadratic,” or the like, and Y is the name of the variable or quantity in question. For example, a traversal of an array is linear in the length of the array; if the array is named a, it is linear in a.length. (a) (3 points) HashMap.size (b) (3 points) ArrayList.indexOf (c) (4 points) int crossProductIsh(int[] a) { int sum = 0; for (int i = 0; i < a.length; i++) { for (int j = 0; j < a.length; j++) { sum += a[i] + a[j]; } } return sum; }

""Search in Rotated Sorted ArraySuppose an array sorted in ascending order is rotated at some pivot unknownto you beforehand. (i.e., [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2]).You are given a target value to search. If found in the array return its index,otherwise return -1.Your algorithm's runtime complexity must be in the order of O(log n).---------------------------------------------------------------------------------Explanation algorithm:In classic binary search, we compare val with the midpoint to figure out ifval belongs on the low or the high side. The complication here is that thearray is rotated and may have an inflection point. Consider, for example:Array1: [10, 15, 20, 0, 5]Array2: [50, 5, 20, 30, 40]Note that both arrays have a midpoint of 20, but 5 appears on the left side ofone and on the right side of the other. Therefore, comparing val with themidpoint is insufficient.However, if we look a bit deeper, we can see that one half of the array must beordered…

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