Explain amortized analysis and give examples.

Amortized analysis averages time over a sequence of operations, showing that expensive operations are rare enough that average cost is low. Methods: Aggregate (total time / operations), Accounting (assign artificial costs, save credits), Potential (define potential function measuring 'saved work'). Examples: Dynamic array resizing - individual push may be O(n), but amortized O(1). Splay tree operations - worst case O(n), amortized O(log n). Union-Find with optimizations - amortized O(alpha(n)).