Editing Algorithms and Complexity (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Comparing Linear Search vs. Binary Search:'''
<syntaxhighlight lang="python">
def linear_search(arr, target):
    """O(n) complexity: checks every item."""
    steps = 0
    for item in arr:
        steps += 1
        if item == target: return steps
    return steps

def binary_search(arr, target):
    """O(log n) complexity: halves the search space each step."""
    low = 0
    high = len(arr) - 1
    steps = 0
    while low <= high:
        steps += 1
        mid = (low + high) // 2
        if arr[mid] == target: return steps
        elif arr[mid] < target: low = mid + 1
        else: high = mid - 1
    return steps

# Test with 1 million items
data = list(range(1000000))
target = 999999

print(f"Linear Search steps: {linear_search(data, target)}") # ~1,000,000
print(f"Binary Search steps: {binary_search(data, target)}") # ~20
# Binary search finds 1 item in a million in just 20 guesses!
</syntaxhighlight>

; Real-World Algorithms
: '''Google Search''' → PageRank (an algorithm for ranking web pages).
: '''GPS/Google Maps''' → Dijkstra's Algorithm (finding the shortest path).
: '''Cryptography''' → RSA (based on the complexity of factoring large prime numbers).
: '''Compression''' → Huffman Coding (making files smaller without losing info).
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