Python - Column Minimum in Tuple list

Sometimes, while working with records, we can have a problem in which we need to find min of all the columns of a container of lists which are tuples. This kind of application is common in web development domain. Let’s discuss certain ways in which this task can be performed.

Method #1 : Using min() + list comprehension + zip() 
This task can be performed using combination of above functions. In this, we cumulate the like index elements, i.e columns using zip(), and then iterate through them using list comprehension and perform minimum using min().

# Python3 code to demonstrate working of
# Column Minimum in Tuple list
# using list comprehension + min() + zip()

# initialize list
test_list = [(1, 2, 3), (6, 7, 6), (1, 6, 8)]

# printing original list
print("The original list : " + str(test_list))

# Column Minimum in Tuple list
# using list comprehension + min() + zip()
res = [min(ele) for ele in zip(*test_list)]

# printing result
print("The Cumulative column minimum is : " + str(res))

The original list : [(1, 2, 3), (6, 7, 6), (1, 6, 8)]
The Cumulative column minimum is : [1, 2, 3]

Time Complexity: O(n),The above code iterates through the list once, hence the time complexity is linear, i.e. O(n).
Space Complexity: O(n),The algorithm uses an additional list to store the result, thus consuming linear space which is O(n).
Method #2 : Using zip() + map() + min() 
This method is similar to the above method. In this, the task performed by list comprehension is performed by map(), which extends the minimum of columns to zipped elements.

# Python3 code to demonstrate working of
# Column Minimum in Tuple list
# using zip() + map() + min()

# initialize list
test_list = [(1, 2, 3), (6, 7, 6), (1, 6, 8)]

# printing original list
print("The original list : " + str(test_list))

# Column Minimum in Tuple list
# using zip() + map() + min()
res = list(map(min, zip(*test_list)))

# printing result
print("The Cumulative column minimum is : " + str(res))

The original list : [(1, 2, 3), (6, 7, 6), (1, 6, 8)]
The Cumulative column minimum is : [1, 2, 3]

Time Complexity: O(n*n) where n is the number of elements in the string list. The zip() + map() + min() is used to perform the task and it takes O(n*n) time.
Auxiliary Space: O(n) additional space of size n is created where n is the number of elements in the res list.

Method #3: Using Numpy library

Note: Install numpy module using command "pip install numpy"

We can use numpy library to perform this task. In this, we will first convert list of tuples to numpy matrix, and then perform minimum operation on the axis 1.

# Python3 code to demonstrate working of
# Column Minimum in Tuple list
# using Numpy library

import numpy as np

# initialize list
test_list = [(1, 2, 3), (6, 7, 6), (1, 6, 8)]

# printing original list
print("The original list : " + str(test_list))

# Column Minimum in Tuple list
# using Numpy library
res = np.min(np.array(test_list), axis=0)

# printing result
print("The Cumulative column minimum is : " + str(res))
#This code is contributed by Edula Vinay Kumar Reddy

Output:

The original list : [(1, 2, 3), (6, 7, 6), (1, 6, 8)]
The Cumulative column minimum is : [1 2 3]

Time complexity: O(N * M), where N is the number of rows and M is the number of columns in the matrix. 
Auxiliary space: O(M).

Method #4 : Using for loops and min() method

# Python3 code to demonstrate working of
# Column Minimum in Tuple list

# initialize list
test_list = [(1, 2, 3), (6, 7, 6), (1, 6, 8)]

# printing original list
print("The original list : " + str(test_list))

# Column Minimum in Tuple list
res=[]
for i in range(0,len(test_list)):
    x=[]
    for j in range(0,len(test_list[i])):
        x.append(test_list[j][i])
    res.append(min(x))
    
# printing result
print("The Cumulative column minimum is : " + str(res))

The original list : [(1, 2, 3), (6, 7, 6), (1, 6, 8)]
The Cumulative column minimum is : [1, 2, 3]

Time Complexity : O(N*N)

Auxiliary Space : O(N)

Method 5: Using reduce function:

• First, we import the reduce function from the functools module, which will be used to apply a lambda function to the elements of the test_list.
• Next, we initialize the test_list variable to a list of tuples. This list contains the data that we will be processing to find the column minimums.
• We then print the original list to verify that the input data is correct.
• The reduce function takes two arguments: a lambda function and a list. The lambda function will be applied to the elements of the list in a cumulative way, meaning that it will be applied to the first two elements, then to the result of the first operation and the third element, then to the result of the second operation and the fourth element, and so on.
• The lambda function takes two arguments, acc and curr, which represent the accumulated value and the current value, respectively. The lambda function applies the zip function to the acc and curr tuples to group elements from the same position. It then applies the min function to each group to find the minimum value. The result is a list of minimum values for each column.
• The reduce function returns the final result, which is the list of minimum values for each column.
• Finally, we print the result to verify that the output is correct.

Below is the implementation:

from functools import reduce

# initialize list
test_list = [(1, 2, 3), (6, 7, 6), (1, 6, 8)]

# printing original list
print("The original list : " + str(test_list))

# Column Minimum in Tuple list
res = reduce(lambda acc, curr: [min(x) for x in zip(acc, curr)], test_list)

# printing result
print("The Cumulative column minimum is : " + str(res))

The original list : [(1, 2, 3), (6, 7, 6), (1, 6, 8)]
The Cumulative column minimum is : [1, 2, 3]

Time complexity: O(n*m), where n is the number of tuples in the list and m is the number of elements in each tuple.
Auxiliary space: O(m), where m is the number of elements in each tuple.