A unimodal array is an array that has a sequence of monotonically increasing integers followed by a sequence of monotonically decreasing integers, assuming all elements in the array are unique. Example: - A= {4, 5, 8, 9, 10, 11, 7, 3, 2, 1}: A is a unimodal array because there is an increasing sequence followed by a decreasing sequence and the maximum element is 11. - B= {11, 9, 8, 7, 5, 4, 3, 2, 1}: B is not a unimodal array because there is no increasing sequence It is simply a decreasing sequence and the maximum element is 11. - C= {1, 2, 3, 4, 5, 7, 8, 9, 11}: C is not a unimodal array because There is an increasing sequence, but there is no decreasing sequence and the maximum element is 11. a) Design an efficient algorithm with the lowest possible complexity to state whether a given array is unimodal or not, and explain why your algorithm is efficient. b) Analyze the complexity of your algorithm.
A unimodal array is an array that has a sequence of monotonically increasing integers
followed by a sequence of monotonically decreasing integers, assuming all elements in
the array are unique.
Example:
- A= {4, 5, 8, 9, 10, 11, 7, 3, 2, 1}:
A is a unimodal array because there is an increasing sequence followed by a
decreasing sequence and the maximum element is 11.
- B= {11, 9, 8, 7, 5, 4, 3, 2, 1}: B is not a unimodal array because there is no increasing
sequence It is simply a decreasing sequence and the maximum element is 11.
- C= {1, 2, 3, 4, 5, 7, 8, 9, 11}: C is not a unimodal array because There is an increasing
sequence, but there is no decreasing sequence and the maximum element is 11.
a) Design an efficient
given array is unimodal or not, and explain why your algorithm is efficient.
b) Analyze the complexity of your algorithm.
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