Move Zeroes
The problem requires us to move all zeros in the given array to the end while keeping the relative order of nonzero elements the same. Since we have to do this inplace without making a copy of the array, we will use a twopointer technique.
Approach
 Initialize Two Pointers: Start with two pointers, say
writePointer
andreadPointer
.writePointer
is initialized at 0.  Iterate through the Array: Iterate through the array using
readPointer
. If
nums[readPointer]
is not zero, place it atnums[writePointer]
and incrementwritePointer
.
 If
 Fill the Remaining Part with Zeros: Once all nonzero elements are processed, fill the remaining part of the array with zeros from the
writePointer
to the end of the array.
Code


Explanation
 Pointer
writePointer
keeps track of the position where the next nonzero element should be placed.  Pointer
readPointer
iterates through the array to find nonzero elements.  When a nonzero element is found at
readPointer
, it is placed atwritePointer
.  Zeros naturally get pushed to the end of the array as the nonzero elements are rearranged.
Key Takeaways
 This approach modifies the array inplace, fulfilling the problem’s requirement.
 The time complexity of this solution is (O(n)), where (n) is the length of the array, and the space complexity is (O(1)), since no additional space is used.
class Solution: def moveZeroes(self, nums: List[int]) > None: writePointer = 0
# Read pointer iterates through the array to find nonzero elements
for readPointer in range(len(nums)):
if nums[readPointer] != 0:
# Place the nonzero element at the writePointer and increment it
nums[writePointer] = nums[readPointer]
writePointer += 1
# Fill the rest of the array with zeros
for i in range(writePointer, len(nums)):
nums[i] = 0
## Identifying Problem Isomorphism
"Move Zeroes" can be approximately mapped to "Remove Element".
Reasoning:
Both problems require manipulating a given array inplace.
1. "Move Zeroes" asks you to move all 0's to the end of an array while maintaining the relative order of the nonzero elements.
2. "Remove Element" requires you to remove all instances of a specific value from the array and return the new length.
The strategy for solving these problems is similar: you can use twopointer technique where one pointer maintains the position of the next element in the modified array and the other scans through the array.
Both problems emphasize on array manipulation and inplace operations.
"Move Zeroes" is a fairly straightforward problem that introduces the concept of inplace array manipulations. For easier problems, you could start with these:
1. "344. Reverse String": This problem helps you understand the concept of manipulating an array or string inplace, and the idea of using two pointers.
2. "136. Single Number": This problem introduces the concept of bit manipulation, but it can also be solved using a hash map, which is a common data structure in other problems.
3. "88. Merge Sorted Array": This is another problem that requires inplace array manipulation, but with an added complexity of dealing with two sorted arrays.
These cover inplace array manipulation, which will be crucial in solving the "Move Zeroes" problem.
```python
class Solution:
def moveZeroes(self, nums: list) > None:
slow = 0
for fast in range(len(nums)):
if nums[fast] != 0 and nums[slow] == 0:
nums[slow], nums[fast] = nums[fast], nums[slow]
if nums[slow] != 0:
slow += 1
Problem Classification
This problem can be classified under the following categories:
Array Manipulation: The problem is about rearranging the elements of an array.
InPlace Algorithms: You are required to modify the array inplace without creating a new array or copying the existing one.
Two Pointers Approach: The problem’s most efficient solution uses the twopointers method where one pointer tracks the current element and another one to place the nonzero element.
Order Maintenance: The relative order of the nonzero elements needs to be maintained as per the problem statement. Hence it falls under the order maintenance problems as well.
In terms of difficulty, this problem could be classified as easytointermediate as it requires a fundamental understanding of array manipulation and two pointers strategy but also involves more complex considerations like maintaining relative order and doing the operation inplace.
Language Agnostic Coding Drills
Breaking down this problem and code into its core components can be done as follows:
Understanding Array Traversal: The foundation of this problem is about understanding how to iterate through an array. The traversal in this problem happens linearly, from start to end.
Two Pointers Methodology: In this problem, we use two pointers,
slow
andfast
. Understanding how to use two pointers, one progressing at a slower pace and the other progressing faster is crucial for solving this problem.InPlace Array Manipulation: The problem requires the solution to be done inplace, that is, the manipulation happens within the given array and no new array is created for the solution. This is a crucial step as it needs a clear understanding of how variables/objects are stored and manipulated in memory.
ConditionBased Manipulation: During the traversal, there is a condition to be checked at each step. If the element at the fast pointer is nonzero and the element at the slow pointer is zero, then swap these elements. This combines understanding of condition checks and the Swap operation.
Incrementation of Pointers: After each iteration, it’s necessary to check whether to increment the slow pointer. In this problem, we only increment the slow pointer when the element at the slow pointer is nonzero. This step involves conditional incrementation based on the state of the array at the slow pointer’s position.
To summarize, the problemsolving approach here involves:
a. Initialize two pointers, slow
and fast
.
b. Iterate through the array using the fast
pointer.
c. If the element at the fast pointer is nonzero and the element at the slow pointer is zero, swap these elements.
d. If the element at the slow pointer is nonzero, increment the slow pointer.
e. Repeat steps bd until you have traversed the entire array.
At the end of the process, all zeros will have been moved to the end of the array while the relative order of the nonzero elements is maintained.
Targeted Drills in Python
 Understanding Array Traversal


 Two Pointers Methodology


 InPlace Array Manipulation


 ConditionBased Manipulation


 Incrementation of Pointers


Finally, integrating all the above drills into the final solution:


The final integrated solution uses all the components taught in the drills to solve the problem.