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AlgoPlus//searching / binary search
Read the theory

Binary Search · Dimensional Collapse

Sorted space collapses by half each step — converging on the target.

Stability
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In-Place
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Space Complexity
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Avg Time
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Target
Legend
Element being checked
Eliminated (outside window)
Target found
AI Tutor Workspace
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In a nutshell
Binary search finds a value in a sorted list astonishingly fast by always checking the middle. If the middle is the target, done; if the target is smaller, throw away the whole right half; if larger, throw away the left. Each check halves what's left, so even a list of a million items is found in about twenty steps. Its one requirement: the list must already be sorted.
Ready
Press play to begin the cinematic walkthrough.
Halve the search space each step — the sorted array collapses into a single point of certainty.
Key terms
Go deeper in the lesson
Read the full theory, intuition & complexity for Binary Search · Dimensional Collapse.
Code Simulator
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def binary_search(arr, target):
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    low, high = 0, len(arr) - 1
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    while low <= high:
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        mid = (low + high) // 2
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        if arr[mid] == target:
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            return mid  # Found
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        elif arr[mid] < target:
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            low = mid + 1
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        else:
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            high = mid - 1
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    return -1  # Not Found
Why Python? · Readable first, fast second

Dynamically typed and interpreted — every comparison and swap is dispatched by the interpreter at run time, so tight loops run roughly 10–100× slower than compiled C/C++. Unbeatable for learning the idea with the least code; not what you reach for when the inner loop is the bottleneck.