A sequence of n distinct values A[0..n − 1] is said to be downup if there is an index p with 0 ≤ p < n such that the values of A decrease up to A[p] and then increase for the remainder of the sequence. The index p of value A[p] is the valley of the sequence. For example sequence 50, 10, 5, 2, 1, 20, 30 is downup with valley 4, since A[5] = 60 and the sequence decreases to 1 and then increases. The sequence 5, 1, 4, 3 is not downup. Required:
Design an o(n) worst-case running time algorithm that when given as input an downup sequence, it finds its valley p. Analyze the performance of your proposed algorithm and show that it is o(n) (this is a little-oh).