Python program to print sorted number formed by merging all elements in array

Given an array arr[], the task is to combine all the elements in the array sequentially and sort the digits of this number in ascending order.

Note: Ignore leading zeros.

Examples:

Input: arr =[7, 845, 69, 60]
Output: 4566789
Explanation: The number formed by combining all the elements is “78456960” after sorting the digits we get 4566789

Input: arr =[8, 5603, 109, 53209]
Output: 1233556899
Explanation: The number formed by combining all the elements is “8560310953209” after sorting the digits we get “1233556899”

Approach 1:

• Convert each element of the list to a string using map() function.
• Join the list using join() function.
• Sort the string using join() and sorted()
• Convert string to an integer using type casting
• Return the result

Below is the implementation of the above approach:

Python3

# Python program to print sorted number by merging
# all the elements in array function to print
# sorted number

def getSortedNumber(number):

    # sorting the string
    number = ''.join(sorted(number))

    # converting string to integer
    number = int(number)

    # returning the result
    print(number)

# function to merge elements in array


def mergeArray(lis):

    # convert the elements of list to string
    lis = list(map(str, lis))

    # converting list to string
    string = ''.join(lis)

    # passing this string to sortednumber function
    getSortedNumber(string)


# Driver code
lis = [7, 845, 69,  60]

# passing list to merge array function to merge
# the elements
mergeArray(lis)

Output

4566789

Time complexity: O(nlogn) because sorting the string in the getSortedNumber function takes O(nlogn) time, where n is the length of the string.
Auxiliary space: O(n), where n is the number of elements in the input list. 

Approach 2: Using list(),str(),extend(),sort(),join() and int() methods

Python3

# Python program to print sorted number by merging
# all the elements in array function to print
# sorted number

lis = [7, 845, 69, 60]
p = []

for i in lis:
    x = list(str(i))
    p.extend(x)
p.sort()
p = "".join(p)
print(int(p))

Output

4566789

Time complexity: O(n log n), where n is the total number of digits in the input list.
Auxiliary space: O(n), where n is the total number of digits in the input list. 

Approach#3:using itertools

Algorithm

1. Convert each number in the input array to a string.
2. Concatenate all the strings to form a single string.
3. Convert the merged string to a list of integers.
4. Sort the list of integers and join them back into a single string.
5. Convert the sorted string to an integer and return it.

Python3

import itertools

# Function to perform the merge sort
def merge_sort(arr):

    # Convert each number in the
    # array to a string
    str_arr = [str(num) for num in arr]

    # Concatenate all the strings to
    # form a single string
    merged_str = ''.join(str_arr)

    # Convert the merged string to a
    # list of integers
    merged_list = [int(char) for char in merged_str]

    # Sort the list of integers and
    # join them back into a single string
    sorted_str = ''.join([str(num) for num in sorted(merged_list)])

    # Convert the sorted string to an
    # integer and return it
    return int(sorted_str)


# Driver Code
arr = [7, 845, 69, 60]

result = merge_sort(arr)

print(result)

Output

4566789

Time Complexity: O(n log n), where n is the length of the input array. This is because we convert the array to a single string in O(n) time, sorting the string takes O(n log n) time, and converting the sorted string back to an integer takes O(n) time.

Space Complexity: O(n), where n is the length of the input array. This is because we need to store the merged list of integers, which has a length of n. The sorted string also has a length of n. The permutations are no longer generated and stored, so the space complexity is improved compared to the previous approach.