Searching

Searching Suite

Linear and Binary Search strategies for locating target elements within structured datasets.

What is Searching Suite?

Searching algorithms are fundamental techniques for retrieving elements from a collection. Linear Search scans all elements sequentially, making it suitable for unsorted datasets. Binary Search uses a divide-and-conquer strategy on sorted arrays, repeatedly halving the search space to achieve logarithmic query performance.

Key Characteristics:

Linear Search works on any array structure.
Binary Search requires the target array to be pre-sorted.
Binary Search maintains two pointers (low and high) to define the search interval.
Visualizer supports both algorithms dynamically.

Complexity Analysis

Avg Time Complexity: O(log N) for Binary, O(N) for Linear

Space Complexity: O(1) auxiliary space

Best Case: O(1) (target element found at first checked position)

Worst Case: O(N) for Linear Search, O(log N) for Binary Search

How it Works Step-by-Step

Linear Search: Loop through the array from index 0 to N-1. If array[i] matches target, return index; else continue.
Binary Search: Initialize pointers: low = 0, high = N-1.
Calculate Midpoint: Compute mid = low + (high - low) / 2.
Evaluate: If array[mid] matches target, return mid. If target < array[mid], set high = mid - 1. Otherwise, set low = mid + 1.
Loop/End: Repeat steps 3-4 while low <= high. If not found, return -1.

Code Implementation

Worked Trace Example

Searching for target 23 in sorted array [2, 5, 8, 12, 16, 23, 38, 56, 72]:
- Initial state: low=0, high=8.
- Calculate mid = (0+8)/2 = 4 (value 16). Since 23 > 16, set low = mid + 1 = 5.
- Calculate mid = (5+8)/2 = 6 (value 38). Since 23 < 38, set high = mid - 1 = 5.
- Calculate mid = (5+5)/2 = 5 (value 23). Since 23 == 23, target is found at index 5.

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