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.

Answer 2

Java implementation:

Collection<Integer> magnitudes(int[] A) {
    int length = A.length;
    // what's the maximum number from the beginning of the array till the current position
    int[] maxes = new int[A.length];
    // what's the minimum number from the current position till the end of the array
    int[] mins = new int[A.length];

    // build mins
    int min = mins[length - 1] = A[length - 1];
    for (int i = length - 2; i >= 0; i--) {
        if (A[i] < min) {
            min = A[i];
        }
        mins[i] = min;
    }

    // build maxes
    int max = maxes[0] = A[0];
    for (int i = 1; i < length; i++) {
        if (A[i] > max) {
            max = A[i];
        }
        maxes[i] = max;
    }

    Collection<Integer> result = new ArrayList<>();
    // use them to find the magnitudes if any exists
    for (int i = 0; i < length; i++) {
        if (A[i] >= maxes[i] && A[i] <= mins[i]) {
            // return here if first one only is needed
            result.add(A[i]);
        }
    }
    return result;
}