W3_programming_assignment.py

""" 1) Write a function contracting(l) that takes as input a list of integer l and returns 
True if the absolute difference between each adjacent pair of elements strictly decreases.

Here are some examples of how your function should work.

  >>> contracting([9,2,7,3,1])
  True

  >>> contracting([-2,3,7,2,-1]) 
  False

  >>> contracting([10,7,4,1])
  False"""

def contracting(l):
    diff= abs(l[1] - l[0])
    for i in range(2, len(l)):
        if abs(l[i] - l[i-1]) < diff:
            diff = abs(l[i] - l[i-1])
        else:
            return False
    return True 

""" 2)In a list of integers l, the neighbours of l[i] are l[i-1] and l[i+1]. l[i] is a hill 
if it is strictly greater than its neighbours and a valley if it is strictly less than its neighbours.
Write a function counthv(l) that takes as input a list of integers l and returns a list [hc,vc] 
where hc is the number of hills in l and vc is the number of valleys in l.

Here are some examples to show how your function should work. 

>>> counthv([1,2,1,2,3,2,1])
[2, 1]

>>> counthv([1,2,3,1])
[1, 0]

>>> counthv([3,1,2,3])
[0, 1]"""

def counthv(l):
    hc, vc = 0, 0
    for i in range(1, len(l)-1):
        if l[i] > l[i-1] and l[i] > l[i+1]:
            hc += 1
        elif l[i] < l[i-1] and l[i] < l[i+1]:
            vc += 1
    return [hc, vc]     

""" 3) A square n×n matrix of integers can be written in Python as a list with n elements,
where each element is in turn a list of n integers, representing a row of the matrix. For instance, the matrix

  1  2  3
  4  5  6
  7  8  9
would be represented as [[1,2,3], [4,5,6], [7,8,9]].

Write a function leftrotate(m) that takes a list representation m of a square matrix as input, and returns the matrix obtained by rotating the original matrix counterclockwize by 90 degrees. For instance, if we rotate the matrix above, we get

  3  6  9
  2  5  8    
  1  4  7
Your function should not modify the argument m provided to the function rotate().

Here are some examples of how your function should work.
 
  >>> leftrotate([[1,2],[3,4]])
  [[2, 4], [1, 3]]

  >>> leftrotate([[1,2,3],[4,5,6],[7,8,9]])
  [[3, 6, 9], [2, 5, 8], [1, 4, 7]]

  >>> leftrotate([[1,1,1],[2,2,2],[3,3,3]])
  [[1, 2, 3], [1, 2, 3], [1, 2, 3]]"""

def leftrotate(m):
    l = len(m)
    arr = [[0 for i in range(l)] for i in range(l)]
    for i in range(l):
        for j in range(l):   
            arr[i][j] = m[j][(l-1)-i]
    return arr

# def leftrotate(m):
#     l = len(m)
#     arr = []
#     for i in range(l):
#         sub_arr = []
#         for j in range(l):   
#             sub_arr.append(m[j][(l-1)-i])
#         arr.append(sub_arr)
#     return arr