Solution: Collect Coins in Minimum Steps

def minimum_steps_recursive(lst, left, right, h):
    """
    Helper recursive function to calculate minimum steps to collect coins from the list
    :param lst: List of coins stack
    :param left: Left sided index of the list
    :param right: Right sided index of the list
    :param h: Height of the stack
    :return: Returns minimum steps to collect coins from the list, otherwise 0
    """
    
    # Base Case: When left is greater or equal to right
    if left >= right:
        return 0
    # loop over the list of heights to get minimum height index 
    minimum_height = left
    for i in range(left, right):
        if lst[i] < lst[minimum_height]:
            minimum_height = i
    # Collecting all vertical line coins which are right - left
    # and all the horizontal line coins on both sided segments
    return min(right - left, minimum_steps_recursive(lst, left, minimum_height, lst[minimum_height])
              + minimum_steps_recursive(lst, minimum_height + 1, right, lst[minimum_height])
              + lst[minimum_height] - h)
def minimum_steps(lst):
    """
    Function which calls the helper function to calculate minimum steps to collect coins from the list
    :param lst: List of coins stack
    :return: Returns minimum steps to collect coins from the list, otherwise 0
    """
    return minimum_steps_recursive(lst, 0, len(lst), 0) 
# Driver code to test above function
if __name__ == '__main__':
  lst = [2, 1, 2, 5, 1]
  print('Minimum number of steps:', minimum_steps(lst))