Analyze the worst-case time complexity of the algorithm you devised in Exercise 30 of Section 3.1 for locating all modes in a list of nondecreasing integers.

Step 1:

In this problem, we have to explain the worst-case time complexity and we have to find an algorithm for locating all modes in a list of nondecreasing integers.

Step 2:

1) Worst Case:

In the worst case time complexity, we calculate upper bound on running time of an algorithm. We know that the case a maximum number of operations to be executed.For linear search, the worst case happens when the element to be searched is not present in the array. If x is not present, then the search() functions compare it with all the elements of arr[] one by one. Therefore, the worst case time complexity of linear search is defined by (n).