Visualized DSA Strategies

Episode 8 Binary Search

1 h 10 min · C++

Title card of Episode 8: Binary Search

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The complete guide to binary search for coding interviews, in C++. First the idea: halve the range with every look, the two templates (an exact value, and where a yes or no question flips), why the middle is lo + (hi − lo) / 2 (in C++, lo + hi overflowing an int is undefined behaviour), what it saves, the standard library's lower_bound, upper_bound, equal_range and partition_point, and five traps. Then nine types, each worked as a small problem in full: examples, the brute force animated beside the running line of code, the complete code, every line explained, and the binary search the same way.

What you'll learn

  • How binary search halves the range, and why it's O(log n)
  • The exact-value template: lo <= hi with mid ± 1
  • The lower-bound template: lo < hi with hi = mid, the search std::lower_bound runs
  • Why (lo + hi) / 2 is undefined behaviour in C++, unsigned size() traps, and the safe middle
  • lower_bound, upper_bound, equal_range, binary_search, partition_point, and set::lower_bound for floor and ceiling
  • First and last position with two lower bounds
  • Rotated sorted arrays: the minimum, and search, by asking which half is sorted
  • A sorted grid as one long line, and a peak without sorting
  • Binary search on the answer, and searching a key's timestamps

Chapters

  1. 0:00Intro
  2. 0:29Halve the range
  3. 1:04A question that flips once
  4. 1:58Template 1: an exact value
  5. 3:10Template 2: where it flips
  6. 4:11The overflow bug: undefined behaviour
  7. 5:33What binary search saves
  8. 6:02lower_bound, upper_bound and equal_range
  9. 7:55Five traps
  10. 9:08Nine binary search types
  11. 9:50Type 1 · Find a number in a sorted array
  12. 15:54Type 2 · Where does it fit?
  13. 21:50Type 3 · First and last position
  14. 28:44Type 4 · Smallest number in a rotated array
  15. 35:17Type 5 · Search in a rotated array
  16. 41:35Type 6 · Search a sorted grid
  17. 47:45Type 7 · Find a peak
  18. 54:08Type 8 · Slowest eating speed
  19. 1:01:05Type 9 · Time based key-value store
  20. 1:08:04Spot the type
  21. 1:08:49Quiz: which type?
  22. 1:09:37Recap