Peak Finding 2D

def find_1d_peak(the_list, first, last):
    if first == last:
        return first

    if last == first + 1 and the_list[first] >= the_list[last]:
        return first

    if last == first + 1 and the_list[first] < the_list[last]:
        return last

    mid = (first + last )//2

    if the_list[mid] > the_list[mid + 1] and the_list[mid] > the_list[mid - 1]:
        return mid

    if the_list[mid] > the_list[mid + 1] and the_list[mid] < the_list[mid - 1]:
        return find_1d_peak(the_list, first, mid -1)
    else:
        return find_1d_peak(the_list, mid + 1, last)

def find_2d_peak(pm, first, last):
    mid = first - (last + first) / 2
    row = mid
    col = find_1d_peak(pm[row], 0, len(pm[row]))
    if pm[row][col] > pm[row+1][col] and pm[row][col] > pm[row-1][col]:
        return (pm[row][col], row, col)
    elif pm[row][col] > pm[row+1][col] and pm[row][col] < pm[row-1][col]:

        return find_2d_peak(pm, first, row-1)
    else:
        return find_2d_peak(pm, row+1, last)