Binary search:

-> When to use

• use l <= r when
  • searching exact target
  • answer can be mid
  • you may return inside loop
• use l < r when
  • shrinking to one answer
  • finding boundary/min/max/first true
  • answer is final pointer position

Strings:

-> If repetitive updates on strings better to use list and store and use "".join to get the final string. -> Reason: everytime using += python creates new string and then stores it and recreating costs -> += repetitive gets to O(n^2) while list is just O(n)

KMP - Exact matching Rabin-karp - multiple patterns/hashing Z algorithm - prefix matching problems

Linked List

• Use dummy when:
  • deleting nodes, merging lists, returning new head
  • it helps avoid head edge cases

Two pointers

• at least K = total substrings - at most (K-1)
• no. of substrings equal to k = atmost(k) - atmost(k - 1)

Heaps

• heapq module in python only implements min heap
• negate the numbers while pushing into heap and negate them back while popping to get the value. This works as max heap.
• Max heap is implemented in heapq from Python 3.14 where you can use any of the heapq functions you used normally with _max suffix.