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Constant Time O(1): Runtime independent of input size (hash table lookups)
Logarithmic Time O(log n): Runtime grows logarithmically
Linear Time O(n): Runtime grows proportionally with input
Quadratic O(n²), Cubic O(n³), Exponential O(2ⁿ): Increasingly worse runtime
Factorial Time O(n!): "Pathological case" with astronomical growth
Polynomial Time (P): Algorithms with O(nᵏ) runtime where k is constant
Non-deterministic Polynomial Time (NP)
NP-Complete: Hardest problems in NP
NP-Hard: At least as hard as NP-complete problems
Formal Definition: Find shortest possible route visiting each city exactly once and returning to origin
Computational Scaling: Solution space grows factorially (n!)
Real-World Challenges:
Online Marketplace Selling:
Job Search Optimization:
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