Summary of "Search/Sort 1 | Sequential and binary Search 1"

Summary of "Search/Sort 1 | Sequential and Binary Search 1"

This video introduces fundamental concepts and implementations of searching and sorting algorithms, focusing primarily on sequential (linear) search and Binary Search, with an overview of sorting techniques and Hashing to be covered in the chapter.

Main Ideas and Concepts

Overview of Chapter Topics:
- Sequential searching (two forms)
- Binary searching (more efficient than sequential)
- Hashing (a search technique)
- Sorting algorithms: selection, bubble, merge, quick, insertion, and shell sort
- Map abstract data type (similar to Python dictionary) and its implementation
Searching in Collections:
- Searching for an item in a list can be done in two ways:
  - Return a boolean (true/false) if the item exists.
  - Return the position (index) of the item if found.
- Python’s built-in in operator returns true/false but the video focuses on implementing searches manually.
Sequential (Linear) Search:
- Definition: Check each element in the list sequentially until the item is found or the list ends.
- Implementation details:
  - Start at index 0.
  - Compare each element with the target item.
  - Return true immediately if found.
  - Return false if the end of the list is reached without a match.
- Programming style note: The video favors early returns from the function upon finding the item rather than using flags, contrasting with strict structural programming.
Performance Analysis of Sequential Search:
- Measure performance by counting the number of comparisons.
- Assumes the list is random and every item has an equal chance of being the target.
- Cases:
  - Best case: Item is at the first position → O(1)
  - Worst case: Item not found after searching all elements → O(n)
  - Average case: Item found halfway through the list → O(n/2), simplified to O(n)
- If the item is missing, search always traverses the entire list.
Sequential Search on a Sorted List (Early Exit Optimization):
- If the list is sorted, the search can stop early if the current element exceeds the target.
- This reduces unnecessary comparisons when the item is not present.
- Slight modification to the Sequential Search code:
  - After checking if the current element matches, check if the current element is greater than the target.
  - If so, return false immediately.
- Performance improves especially when the target is smaller than many elements.
Binary Search:
- Applicable only to sorted lists.
- Strategy:
  - Find the midpoint of the current search range.
  - Compare the midpoint value with the target.
  - If equal, return true.
  - If target is less, search the left half.
  - If target is greater, search the right half.
  - Repeat until the search range is exhausted.
- Implementation details:
  - Use two pointers: first (start index) and last (end index).
  - Calculate midpoint as (first + last) // 2.
  - Adjust first or last based on comparison.
  - Loop continues while first <= last.
  - If not found, return false.
- Binary Search divides the problem size by two each iteration → O(log n) time complexity, much faster than Sequential Search.

Methodologies / Instructions

Sequential Search (Simplified Algorithm)

Input: list, target item
Initialize index = 0
While index < length of list:
- If list[index] == target, return true
- Else increment index
Return false if not found

Sequential Search with Early Exit (Sorted List)

Input: sorted list, target item
Initialize index = 0
While index < length of list:
- If list[index] == target, return true
- Else if list[index] > target, return false (early exit)
- Else increment index
Return false if not found

Binary Search Algorithm

Input: sorted list, target item
Initialize first = 0, last = length of list - 1
While first <= last:
- Calculate mid = (first + last) // 2
- If list[mid] == target, return true
- Else if target < list[mid], set last = mid - 1
- Else set first = mid + 1
Return false if not found