# Python Program to Find the Total Sum of a Nested List Using Recursion

A nested list is given. The task is to print the sum of this list using recursion. A nested list is a list whose elements can also be a list.

Examples :

```Input: [1,2,]
Output: 6

Input: [[4,5],[7,8,],100]
Output: 144

Input: [[1,2,3],[4,[5,6]],7]
Output: 28```

Recursion: In recursion, a function calls itself repeatedly. This technique is generally used when a problem can be divided into smaller subproblems of the same form.

Implementation:

Iterate through the list and whenever we find that an element of the list is also a list that means we have to do the same task of finding the sum with this element list (which can be nested) as well.  So we have found a subproblem and, we can call the same function to perform this task and just change the argument to this sublist. And when the element is not a list, then simply add its value to the global total variable.

## Python3

 `# Python Program to find sum` `# of nested list using Recursion`   `def` `sum_nestedlist( l ):` `  `  `    ``# specify that global variable is` `    ``# referred to here in this function` `    ``total ``=` `0` `    `  `    ``for` `j ``in` `range``(``len``(l)):` `      `  `        ``if` `type``(l[j]) ``=``=` `list` `:` `          `  `            ``# call the same function if ` `            ``# the element is a list` `            ``total``+``=` `sum_nestedlist(l[j])` `        ``else``:` `          `  `            ``# if it's a single element` `            ``# and not a list, add it to total ` `            ``total ``+``=` `l[j]   ` `            `  `    ``return` `total` `            `  `print``(sum_nestedlist([[``1``,``2``,``3``],[``4``,[``5``,``6``]],``7``]))`

Output

`28`

Time Complexity: O(N), Where N is the total number of elements in the list.
Auxiliary Space: O(1)

Method 2: Using recursion

This program defines a function sum_nestedlist that takes a nested list as input and returns the sum of all its elements. It does this by using a stack to iterate through each element of the list, adding each non-list element to a running total and extending the stack with any list elements.

## Python3

 `def` `sum_nestedlist(l):` `    ``stack ``=` `l` `    ``total ``=` `0` `    `  `    ``while` `stack:` `        ``elem ``=` `stack.pop()` `        ``if` `type``(elem) ``=``=` `list``:` `            ``stack.extend(elem)` `        ``else``:` `            ``total ``+``=` `elem` `    `  `    ``return` `total`   `# example usage` `my_list ``=` `[[``1``,``2``,``3``],[``4``,[``5``,``6``]],``7``]` `print``(sum_nestedlist(my_list)) ``# Output: 28`

Output

`28`

Time complexity: O(n), where n is the total number of elements in the nested list.
Auxiliary space: O(d), where d is the maximum depth of nesting in the input list.

Method 3: Using Iteration

This function uses a stack to keep track of nested lists. It pops the last element from the stack, and if it’s a list, it pushes its elements to the stack. If it’s a number, it adds it to the total.

Follow the below steps to implement the above idea:

1. Define a function sum_nestedlist_iterative(lst) that takes a nested list lst as input.
2. Initialize a variable total to 0 and a list stack containing the input last.
3. Enter a while loop that continues until the stack list is empty.
4. Pop the last element from the stack list and assign it to current.
5. For each element in current, check if it is a list. If it is a list, append it to the stack list. If it is not a list, add the element to the total variable.
6. Repeat steps 4-5 until all elements in lst have been checked.
7. Return the final value of total.

Below is the implementation of the above approach:

## Python3

 `def` `sum_nestedlist_iterative(lst):` `    ``total ``=` `0` `    ``stack ``=` `[lst]` `    ``while` `stack:` `        ``current ``=` `stack.pop()` `        ``for` `element ``in` `current:` `            ``if` `type``(element) ``=``=` `list``:` `                ``stack.append(element)` `            ``else``:` `                ``total ``+``=` `element` `    ``return` `total`   `print``(sum_nestedlist_iterative([[``1``,``2``,``3``],[``4``,[``5``,``6``]],``7``]))`

Output

`28`

Time complexity: O(n), where n is the total number of elements in the nested list.
Auxiliary space: O(m), where m is the maximum depth of the nested list.

Method 4: Using a Stack

Step-by-step approach:

1. Initialize an empty stack and push the input list onto it.
2. Initialize the sum variable to 0.
3. While the stack is not empty:
a. Pop the top element from the stack.
b. If the element is a list, push all its elements onto the stack.
c. If the element is an integer, add it to the sum variable.
4. Return the sum variable.

## Python3

 `def` `sum_nestedlist(l):` `    ``stack ``=` `[]` `    ``stack.append(l)` `    ``total ``=` `0` `    `  `    ``while` `stack:` `        ``curr ``=` `stack.pop()` `        `  `        ``if` `type``(curr) ``=``=` `list``:` `            ``for` `elem ``in` `curr:` `                ``stack.append(elem)` `        ``else``:` `            ``total ``+``=` `curr` `            `  `    ``return` `total`   `print``(sum_nestedlist([[``1``,``2``,``3``],[``4``,[``5``,``6``]],``7``]))`

Output

`28`

Time Complexity: O(N), where N is the total number of elements in the input list.
Auxiliary Space: O(M), where M is the maximum size of the stack during the execution of the program.

Method 5: Using Queue

step-by-step approach:

1. Define a function named sum_nestedlist_queue that takes in a nested list lst as input.
2. Initialize a variable named total to 0 to keep track of the sum of all the elements in the nested list.
3. Create a queue using the deque function from the collections module. The queue should be initialized with the input nested list lst.
4. Start a loop that continues as long as the queue is not empty. The loop will pop the first element in the queue (using the popleft method), and assign it to a variable named current.
5. For each element in current, check if it is a list by using the type function. If the element is a list, append it to the end of the queue using the append method.
6. If the element is not a list, add it to the total variable.
7. Repeat steps 4-6 until the queue is empty.
8. Return the final value of total.
9. Call the sum_nestedlist_queue function with an example nested list, and print the result.

## Python3

 `from` `collections ``import` `deque`   `def` `sum_nestedlist_queue(lst):` `    ``total ``=` `0` `    ``queue ``=` `deque([lst])` `    ``while` `queue:` `        ``current ``=` `queue.popleft()` `        ``for` `element ``in` `current:` `            ``if` `type``(element) ``=``=` `list``:` `                ``queue.append(element)` `            ``else``:` `                ``total ``+``=` `element` `    ``return` `total`   `print``(sum_nestedlist_queue([[``1``,``2``,``3``],[``4``,[``5``,``6``]],``7``]))`

Output

`28`

Time complexity:  O(n), where n is the total number of elements in the nested list.

Auxiliary space:  O(max_depth), where max_depth is the maximum depth of the nested list.

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