Pull Zeros to the Front

Given a list of integers nums, rearrange it in place so that every 0 comes first and the non-zero elements follow, keeping their original relative order. The function returns nothing; the list itself must be changed.

Tests call it as (zeros_to_front(a := [1, 0, 2, 0]), a)[1] and inspect the list afterwards.

Examples

Input:  nums = [1, 0, 2, 0]
After:  [0, 0, 1, 2]

Input:  nums = [0, 3, 0, 4, 5]
After:  [0, 0, 3, 4, 5]

Constraints

• 0 <= len(nums) <= 10**5
• Must modify nums in place and return None.
• Target: O(n) time and O(1) extra space (no second list).

Goals

• Modify a list in place using a write pointer
• Scan from the back so the non-zero order is preserved
• Use O(1) extra space