$[$Divide and Conquer$](16$ points$)$

You are given a list $P[1],$dots,$P[n]$ of distinct integers with $n3.$ You know that $P[n-1]>P[n]iP[i]>P[i+1]O(logn)iP[i]>P[i+1]P[i-1]$ and $P[i]>P[i+1].(Note$ there may $be$ more than one such index, I only want your algorithm $to$ find one index.$)$

$(10$ points Algorithm Description. A high level description $or$ implementation level.$)$

$(6$ points for runtime analysis.$)P[i-1]$ and $P[i]>P[i+1].$

Design $aO(logn)$ algorithm that returns $an$ index i such that $P[i-1]$ and $P[i]>P[i+1].(Note$ there may $be$ more than one such index, I only want your algorithm $to$ find one index.$)$

$(10$ points Algorithm Description. A high level description $or$ implementation level.$)$

$(6$ points for runtime analysis.$)P[1]$ and $P[n-1]>P[n].$

You wish $to$ return $an$ index i such that $P[i-1]$ and $P[i]>P[i+1].$

Design $aO(logn)$ algorithm that returns $an$ index i such that $P[i-1]$ and $P[i]>P[i+1].(Note$ there may $be$ more than one such index, I only want your algorithm $to$ find one index.$)$

$(10$ points Algorithm Description. A high level description $or$ implementation level.$)$

$(6$ points for runtime analysis.$)$