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Step 07
Complexity Analysis
Time
O(n)
Space
O(n)
Approach Breakdown
BRUTE FORCE
O(n²) time
O(1) space
Two nested loops check every pair of elements. The outer loop picks one element, the inner loop scans the rest. For n elements that is n × (n−1)/2 comparisons = O(n²). No extra memory — just two loop variables.
TWO POINTERS
O(n) time
O(1) space
Each pointer traverses the array at most once. With two pointers moving inward (or both moving right), the total number of steps is bounded by n. Each comparison is O(1), giving O(n) overall. No auxiliary data structures are needed — just two index variables.
Shortcut: Two converging pointers on sorted data → O(n) time, O(1) space.
Coach Notes
Common Mistakes
Review these before coding to avoid predictable interview regressions.
Moving both pointers on every comparison
Wrong move: Advancing both pointers shrinks the search space too aggressively and skips candidates.
Usually fails on: A valid pair can be skipped when only one side should move.
Fix: Move exactly one pointer per decision branch based on invariant.