Binary Search mind map
Halve the search space on sorted data.
Core idea: Find a monotonic yes/no boundary while preserving which side can still contain the answer.
Mnemonic: Invariant → mid → discard · Cost: O(log n) decisions
Locate: Exact match
Signal: A sorted domain can discard half after one comparison.
Move: Choose a closed or half-open interval and keep its membership invariant consistent.
Examples: Binary Search, Search Insert Position, Guess Number
Bound: First true / last false
Signal: Many answers satisfy a monotonic predicate, but one boundary matters.
Move: Keep the possible boundary inside the interval and bias mid when progress requires it.
Examples: First and Last Position, Lower Bound, First Bad Version
Decode: Hidden order
Signal: The array is rotated, mountain-shaped, or partitioned.
Move: Identify the ordered half or local slope, then retain only the side compatible with the target.
Examples: Search Rotated Array, Find Minimum, Find Peak
Answer: Search the answer space
Signal: A candidate value has a cheap monotonic feasibility check.
Move: Binary-search the value; let one linear pass prove whether the candidate is possible.
Examples: Koko Eating Bananas, Ship Capacity, Split Array Largest Sum