# Sum of distances between the two nearest perfect squares to all the nodes of the given linked list

Given a linked list, the task is to find the sum of distances between the two nearest perfect squares for all the nodes of the given linked list.

**Examples:**

Input:3 -> 15 -> 7 -> NULL

Output:15

For 3: closest left perfect square is 1 and closest right 4 i.e. 4-1 = 3

For 15: 16 – 9 = 7

For 7: 9 – 4 = 5

3 + 7 + 5 = 15

Input:1 -> 5 -> 10 -> 78 -> 23 -> NULL

Output:38

**Approach:** Initialise **sum = 0** and for every node, if the current node’s value is a perfect square itself then the left and right closest perfect square will be the value itself and distance will be 0. Else, find the left and right closest perfect squares say **leftPS** and **rightPS** and update **sum = sum + (rightPS – leftPS)**.

Below is the implementation of the above approach:

`# Python3 implementation of the approach ` `import` `sys ` `import` `math ` ` ` `# Structure for a node ` `class` `Node: ` ` ` `def` `__init__(` `self` `, data): ` ` ` `self` `.data ` `=` `data ` ` ` `self` `.` `next` `=` `None` ` ` `# Function to find the total distance sum ` `def` `distanceSum(head): ` ` ` ` ` `# If head is null ` ` ` `if` `not` `head: ` ` ` `return` ` ` ` ` `# To store the required sum ` ` ` `tsum ` `=` `0` ` ` `temp ` `=` `head ` ` ` ` ` `# Traversing through all the nodes one by one ` ` ` `while` `(temp): ` ` ` `sq_root ` `=` `math.sqrt(temp.data) ` ` ` ` ` `# If current node is not a perfect square ` ` ` `# then find left perfect square and ` ` ` `# right perfect square ` ` ` `if` `sq_root<temp.data: ` ` ` `left_ps ` `=` `math.floor(sq_root)` `*` `*` `2` ` ` `right_ps ` `=` `math.ceil(sq_root)` `*` `*` `2` ` ` `tsum` `+` `=` `(right_ps ` `-` `left_ps) ` ` ` ` ` `# Get to the next node ` ` ` `temp ` `=` `temp.` `next` ` ` `return` `tsum ` ` ` `# Driver code ` `if` `__name__` `=` `=` `'__main__'` `: ` ` ` `head ` `=` `Node(` `3` `) ` ` ` `head.` `next` `=` `Node(` `15` `) ` ` ` `head.` `next` `.` `next` `=` `Node(` `7` `) ` ` ` `head.` `next` `.` `next` `.` `next` `=` `Node(` `40` `) ` ` ` `head.` `next` `.` `next` `.` `next` `.` `next` `=` `Node(` `42` `) ` ` ` ` ` `result ` `=` `distanceSum(head) ` ` ` `print` `(` `"{}"` `.` `format` `(result)) ` |

*chevron_right*

*filter_none*

**Output:**

41

**Time Complexity:** O(n)

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