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Track 05 of 10
AlgorithmsBeginner Level~25 Mins
5. Binary Search & Divide and Conquer
Reduce O(N) linear scans into lightning fast O(log N) search space halving.
The "WHY" Core Principle
Binary Search compares target with the middle element. If smaller, the entire right half is discarded instantly. 1,000,000 items are searched in just 20 checks!
Interactive Visualizer
Binary Search Stepper: O(log N) Search Space Halving
Observe how low, mid, and high pointers halve the search area every step.
Target:
low index:0
mid index:5
high index:10
Steps taken:0
LOW
2i=0
5i=1
8i=2
12i=3
16i=4
MID
23i=5
38i=6
45i=7
56i=8
72i=9
HIGH
91i=10
Interactive Code Snippets (1 Lessons)
Lesson 01
Classic Binary Search Algorithm
O(log N)O(1)
Implement Binary Search on a sorted array returning the target index in O(log N) time.
WHY Under The Hood:
At each step, `mid = (low + high) // 2`. If `arr[mid] == target`, we return. If `arr[mid] < target`, we shift `low = mid + 1` eliminating the left sub-array.
CPython C Struct Detail: Python integer division `//` in CPython evaluates `PyLong_FloorDiv`.
Classic Binary Search Algorithm
Pyodide WASM EngineType, edit code, and click 'Run & Profile' to see live runtime ms and operation count!
Python 3.12 Code (Editable)
Expected:Time: O(log N)Space: O(1)