Rotate Array by K places | Union, Intersection of Sorted Arrays | Move Zeros to End | Arrays Part-2 | COFYT

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Rotate Array by K places | Union, Intersection of Sorted Arrays | Move Zeros to End | Arrays Part-2 | COFYT

To revise this lecture effectively, focus on these key areas:

I. Core Concepts & Techniques:

Modular Arithmetic for Array Rotation: Understand how D % n efficiently handles rotations beyond the array's length. This is crucial for the "Left Rotate by D Places" problem.
Two-Pointer Approach: Master the two-pointer technique. This is used in several problems (moving zeros, union/intersection of sorted arrays). Practice visualizing pointer movement and swapping/comparison logic.
In-place Algorithms: Pay attention to algorithms that modify the input array directly without using extra space (O(1) space complexity). Examples include the optimal solutions for array rotation and moving zeros.
Algorithm Optimization: Practice moving beyond brute-force solutions to more efficient methods. Analyze time and space complexity for each approach. The lecture systematically demonstrates this progression for multiple problems.
Handling Sorted Arrays: Recognize how sorted arrays allow for optimizations using techniques like two-pointers and binary search (implicitly touched upon in linear search).

II. Problem-Specific Details:

Left Rotate by One/D: Understand the difference between rotating by one and by D places. Master the optimal O(n) solution for a single rotation and the three-reversal technique for D rotations.
Move Zeros: Thoroughly understand the two-pointer swapping algorithm. Pay attention to the edge cases (no zeros present).
Linear Search: This is a basic algorithm, but practice varying the requirements (first, last, or all occurrences).
Union/Intersection: Focus on the differences in logic between union (unique elements) and intersection (common elements) and the optimizations possible with sorted arrays.

III. Interview Strategies:

Structured Problem Solving: The lecture strongly emphasizes starting with a brute-force approach, then improving it to an optimal solution. Practice this methodical approach.
Articulating Thought Process: Explain your reasoning clearly while solving problems. Practice verbalizing your steps and justifying your choices (as demonstrated in the lecture).
Time & Space Complexity Analysis: Always analyze the efficiency of your solutions. Be able to articulate the time and space complexities (Big O notation) accurately. The lecture provides detailed examples.

IV. Practice & Review:

Code the Problems: Write code for each problem in your preferred language. Pay close attention to edge cases and test your code thoroughly.
Debug and Analyze: If you encounter issues, debug your code systematically. Analyze the time and space complexity of your solution, comparing it to the ones presented in the lecture.
Review the Pseudocode: The pseudocode provides a language-agnostic way to understand the core logic. Review and understand it fully before coding.

By focusing on these notes, you'll effectively revise the lecture and strengthen your understanding of array manipulation techniques. Remember to practice coding the examples and similar problems to solidify your skills.

Detailed Lecture Notes: Rotate Array by K places | Union, Intersection of Sorted Arrays | Move Zeros to End | Arrays Part-2

This lecture covers several array manipulation problems, progressing from brute-force to optimized solutions. The emphasis is on a structured problem-solving approach suitable for coding interviews.

I. Left Rotate an Array by One Place:

Problem: Given an array, shift each element one position to the left, moving the first element to the end. Example: [1, 2, 3, 4, 5] becomes [2, 3, 4, 5, 1].
Optimal Solution:
- Uses a temporary variable to store the first element (temp = array[0]).
- Iterates through the array from the second element, shifting each element one position to the left (array[i-1] = array[i]).
- Finally, places the stored first element at the end (array[n-1] = temp).
- Time Complexity: O(n)
- Space Complexity: O(1) (in-place algorithm; only uses a single temporary variable)

II. Left Rotate an Array by D Places:

Problem: Similar to the above, but shift elements by D positions. Example: [1, 2, 3, 4, 5, 6, 7], D=2 becomes [3, 4, 5, 6, 7, 1, 2].
Key Optimization: Use modular arithmetic (D = D % n) to handle cases where D is larger than the array size (n). Rotations by multiples of n result in the original array.
Brute Force Approach:
- Create a temporary array to store the first D elements.
- Shift the remaining elements to the left.
- Copy the temporary array elements to the end.
- Time Complexity: O(n)
- Space Complexity: O(D)
Cleaner Approach: Similar to brute force but with improved code structure. Time and space complexity remain the same.
Optimal Solution (Three Reversals):
1. Reverse the first D elements.
2. Reverse the remaining (n-D) elements.
3. Reverse the entire array.
- Time Complexity: O(n)
- Space Complexity: O(1) (in-place algorithm)
- This approach is significantly more efficient than creating a temporary array.

III. Move Zeros to End of Array:

Problem: Rearrange the array so that all zeros are moved to the end, maintaining the relative order of other elements. Example: [1, 0, 2, 0, 3] becomes [1, 2, 3, 0, 0].
Brute Force Approach:
1. Iterate through the array, storing non-zero elements in a temporary array/list.
2. Fill the original array with non-zero elements from the temporary structure.
3. Fill the remaining positions with zeros.
- Time Complexity: O(n)
- Space Complexity: O(n) (worst-case scenario, if no zeros are present)
Optimal Solution (Two Pointers):
1. Find the index of the first zero element (j).
2. Use a second pointer (i) to iterate from j + 1 to the end of the array.
3. If array[i] is non-zero, swap array[i] and array[j], then increment j.
- Time Complexity: O(n)
- Space Complexity: O(1) (in-place algorithm)

IV. Linear Search:

Problem: Find the index of the first occurrence of a target number in an array. Return -1 if not found.
Solution: Simple iteration through the array, comparing each element to the target.
Time Complexity: O(n)
Space Complexity: O(1)
Variations discussed: finding the last occurrence, or all occurrences.

V. Union and Intersection of Two Sorted Arrays:

Problem: Find the union and intersection of two sorted arrays. Maintain sorted order for the union. Duplicates are allowed in the intersection.
Union:
- Brute Force: Use a set (or similar data structure) to store unique elements from both arrays. Then, create a new array from the sorted set.
  - Time Complexity: O((n1 + n2) log(n1 + n2)) (where n1 and n2 are array sizes) - due to set insertion.
  - Space Complexity: O(n1 + n2) - the set and the resulting array.
- Optimal Solution (Two Pointers): Compare elements using two pointers. Add the smaller element to the union array (checking for duplicates). If elements are equal, add one and move both pointers. If one array is exhausted, add the remaining elements from the other.
  - Time Complexity: O(n1 + n2)
  - Space Complexity: O(n1 + n2) (for the resulting union array)
Intersection:
- Brute Force: Iterate through each element of the first array. For each element, search the second array for a match (checking for duplicates and previously used elements using a visited array).
  - Time Complexity: O(n1 * n2)
  - Space Complexity: O(min(n1, n2)) (for the visited array – it's best practice to use the smaller array for the visited array)
- Optimal Solution (Two Pointers): Similar to union, but only add elements when both pointers point to equal values. Move both pointers after a match. If the elements are unequal, move the pointer indicating the smaller value.
  - Time Complexity: O(n1 + n2)
  - Space Complexity: O(1) (in-place, if modifying one of the input arrays to store the intersection; otherwise, O(min(n1,n2)) for a new array)

Throughout the lecture:

The speaker consistently emphasizes the importance of articulating the problem-solving approach, explaining the reasoning behind each step, and analyzing the time and space complexity of every solution.
The code examples are provided in pseudocode to be adaptable to various programming languages. Specific language examples (C++, Java, Python) are referenced as available online.

These notes provide a comprehensive overview of the lecture's content. Remember to review the accompanying code examples and practice implementing these solutions yourself.