Interview - Find magnitude pole in an array

Question

Magnitude Pole: An element in an array whose left hand side elements are lesser than or equal to it and whose right hand side element are greater than or equal to it.

Answer 1

• Create two bool[N] called NorthPole and SouthPole (just to be humorous.
• step forward through A[]tracking maximum element found so far, and set SouthPole[i] true if A[i] > Max(A[0..i-1])
• step backward through A[] and set NorthPole[i] true if A[i] < Min(A[i+1..N-1)
• step forward through NorthPole and SouthPole to find first element with both set true.

O(N) in each step above, as visiting each node once, so O(N) overall.