🪨 The Big Rocks of DSA
Core Concepts + Analogies + Common Problems + Time & Space Complexity
Most DSA problems are just one of these big rocks in disguise.
Identify the rock → solution shape → complexity answer.
🪨 BIG ROCK #1: COUNTING & MEMORY
(Hash Maps, Arrays)
🧠 Core Concept
Remember what you’ve seen so you don’t redo work.
🎓 Analogy
Taking attendance once instead of recounting the room.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Two Sum | O(n) | O(n) |
| Majority Element | O(n) | O(n) |
| Group Anagrams | O(n·k) | O(n) |
| First Unique Character | O(n) | O(1) / O(n) |
🧠 Counting = Hash Map
🪨 BIG ROCK #2: SHRINKING THE SEARCH SPACE
(Two Pointers)
🧠 Core Concept
Solve faster by closing in from both ends.
🧹 Analogy
Cleaning a table from left and right.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Valid Palindrome | O(n) | O(1) |
| Container With Most Water | O(n) | O(1) |
| Remove Duplicates (sorted) | O(n) | O(1) |
🧠 Sorted data = Two Pointers
🪨 BIG ROCK #3: CONTINUOUS RANGE CONTROL
(Sliding Window)
🧠 Core Concept
Track a moving range without restarting.
🚗 Analogy
Driving forward while looking through a window.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Longest Substring Without Repeating Characters | O(n) | O(n) |
| Max Sum Subarray | O(n) | O(1) |
| Minimum Window Substring | O(n) | O(n) |
🧠 Continuous range = Sliding Window
🪨 BIG ROCK #4: LAST ACTION MATTERS MOST
(Stack)
🧠 Core Concept
Most recent action controls the next step.
🍽️ Analogy
Plates stacked in a sink.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Valid Parentheses | O(n) | O(n) |
| Daily Temperatures | O(n) | O(n) |
| Min Stack | O(1) | O(n) |
🧠 Nested / undo = Stack
🪨 BIG ROCK #5: FOLLOW THE NEXT POINTER
(Linked Lists)
🧠 Core Concept
You only know where to go next.
🧭 Analogy
Scavenger hunt clues.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Reverse Linked List | O(n) | O(1) |
| Merge Two Lists | O(n) | O(1) |
| Detect Cycle | O(n) | O(1) |
| Remove Nth Node | O(n) | O(1) |
🧠 No random access = Linked List
🪨 BIG ROCK #6: BRANCHING DECISIONS
(Trees)
🧠 Core Concept
Each choice creates new paths.
🌳 Analogy
Family tree.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Max Depth of Binary Tree | O(n) | O(h) |
| Invert Binary Tree | O(n) | O(h) |
| Validate BST | O(n) | O(h) |
| Lowest Common Ancestor | O(n) | O(h) |
h = tree height
🧠 Hierarchy = Tree
🪨 BIG ROCK #7: SOLVE SMALL TO SOLVE BIG
(Recursion)
🧠 Core Concept
Same problem, smaller input.
🪆 Analogy
Russian nesting dolls.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Fibonacci (naive) | O(2ⁿ) | O(n) |
| Fibonacci (memoized) | O(n) | O(n) |
| Merge Sort | O(n log n) | O(n) |
🧠 Self-similar = Recursion
🪨 BIG ROCK #8: TRY, FAIL, UNDO
(Backtracking)
🧠 Core Concept
Explore all possibilities safely.
👕 Analogy
Trying outfits before leaving.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Subsets | O(2ⁿ) | O(n) |
| Permutations | O(n!) | O(n) |
| Combination Sum | Exponential | O(n) |
| Word Search | O(m·n·4ᵏ) | O(k) |
🧠 All possibilities = Backtracking
🪨 BIG ROCK #9: ALWAYS PICK THE BEST NEXT
(Heaps)
🧠 Core Concept
Priority beats order.
🚑 Analogy
Emergency room triage.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Kth Largest Element | O(n log k) | O(k) |
| Top K Frequent | O(n log k) | O(n) |
| Merge K Sorted Lists | O(n log k) | O(k) |
🧠 Top / best / worst = Heap
🪨 BIG ROCK #10: CONNECTED WORLDS
(Graphs)
🧠 Core Concept
Relationships matter more than order.
🗺️ Analogy
City map.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Number of Islands | O(m·n) | O(m·n) |
| Course Schedule | O(V + E) | O(V + E) |
| Clone Graph | O(V + E) | O(V) |
🧠 Free connections = Graph
🪨 BIG ROCK #11: DON’T REPEAT WORK
(Dynamic Programming)
🧠 Core Concept
Store results to avoid recomputation.
🏋️ Analogy
Progressive overload tracking.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Climbing Stairs | O(n) | O(1) |
| House Robber | O(n) | O(1) |
| Coin Change | O(n·m) | O(n) |
| LIS | O(n²) / O(n log n) | O(n) |
🧠 Optimization = DP
🪨 BIG ROCK #12: BINARY STATES
(Bit Manipulation)
🧠 Core Concept
On / off decisions only.
💡 Analogy
Light switches.
Common Problems + Complexity
| Problem | Time | Space |
|---|---|---|
| Single Number | O(n) | O(1) |
| Counting Bits | O(n) | O(n) |
| Missing Number | O(n) | O(1) |
🧠 Toggle logic = Bits
🧭 Interview Cheat Code
- Identify the Big Rock
- State the pattern
- Explain why it’s optimal
- Drop time & space complexity confidently
That alone puts you ahead of most candidates.
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