Nptel week 3 assignment datastructure & algorithm

[NIVEDITA-ux]

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.

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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.

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3)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().

def contracting(l): for i in range(len(l)-2): if abs(l[i]-l[i+1])>abs(l[i+1]-l[i+2]): continue else: return False return True

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def counthv(l): hillcount=0 valleycount=0

for  i in range (1,len(l)-1):
    if l[i]>l[i-1] and l[i]>l[i+1]:
        hillcount+=1
    elif l[i]<l[i-1] and l[i]<l[i+1]:
        valleycount+=1
return([hillcount,valleycount]) 

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def leftrotate(m):

N = len(m[0])
for x in range(0, int(N / 2)):  

    for y in range(x, N-x-1):  

        temp = m[x][y]  

        m[x][y] = m[y][N-1-x]  

        m[y][N-1-x] = m[N-1-x][N-1-y]  

        m[N-1-x][N-1-y] = m[N-1-y][x]  

        m[N-1-y][x] = temp  

return(m)

[Raj-Dave368]

Whats an issue?

[AgentArjun]

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

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]

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]]

Here are the questions given to me in my course. Please find the answers for these as I'm unable to find it