1. Is the data sorted? (or monotonic?)
   ├── Yes → Binary search is possible
   └── No → Can I sort it? If yes, maybe. If no → skip BS

2. What am I searching for?
   ├── An exact value in a collection? → Patterns 1, 4
   ├── A boundary/transition point? → Patterns 2, 5
   └── A minimum/maximum feasible value? → Pattern 3

3. Is there a monotonic condition?
   ├── "If X works, does X+1 also work?" → Pattern 3 or 5
   └── "Can I eliminate half the search space?" → Binary search applies

Problem: Minimum eating speed to finish piles in h hours

Step 1 — Not sorted? But there IS a monotonic answer space.
  → Speed k: if k works, k+1 also works
  → Answer space: [1, max(piles)]

Step 2 — "Minimum feasible speed"
  → Pattern 3 — Search on Answer

Step 3 — Define condition function
  canFinish(k): sum(ceil(pile/k)) ≤ h

Step 4 — Binary search template
  lo=1, hi=max(piles), result=hi
  while (lo <= hi):
    mid = lo + (hi-lo)/2
    if canFinish(mid): result=mid, hi=mid-1
    else: lo=mid+1
  return result

Problem: Find target in [4,5,6,7,0,1,2]

Step 1 — Array is sorted but rotated?
  → Pattern 4 — Rotated Array

Step 2 — Which half is sorted?
  Compare nums[lo] with nums[mid]

Step 3 — Binary search with modified decision
  if left half sorted:
    if target in [nums[lo], nums[mid]): search left
    else: search right
  if right half sorted:
    if target in (nums[mid], nums[hi]]: search right
    else: search left

Problem: Find first version where isBadVersion(v) returns true

Step 1 — Monotonic boolean condition
  F F F T T T T  → Find boundary
  → Pattern 5 — Monotonic Function

Step 2 — Use lo < hi, hi = mid, lo = mid + 1

Step 3 — Return lo