diff --git a/README.md b/README.md
index 1043381..446ad75 100644
--- a/README.md
+++ b/README.md
@@ -1,26 +1,32 @@
 # 🧠 Python DSA — Data Structures & Algorithms
 
-[![Tests](https://github.com/kelsonbrito50/python-dsa/actions/workflows/ci.yml/badge.svg)](https://github.com/kelsonbrito50/python-dsa/actions) ![Algorithms](https://img.shields.io/badge/algorithms-20+-blue) ![Tests](https://img.shields.io/badge/tests-40%2B%20passed-brightgreen)
+[![Tests](https://github.com/kelsonbrito50/python-dsa/actions/workflows/ci.yml/badge.svg)](https://github.com/kelsonbrito50/python-dsa/actions) ![Algorithms](https://img.shields.io/badge/algorithms-30+-blue) ![Tests](https://img.shields.io/badge/tests-56%20passed-brightgreen)
 
-My study notes and implementations while preparing for technical interviews.
+Interview prep implementations with tests and complexity analysis.
 
 ## Implementations
 
-| Category | Structure/Algorithm | Complexity | File |
-|----------|-------------------|------------|------|
+| Category | Algorithm | Complexity | File |
+|----------|-----------|------------|------|
 | 📦 Arrays | Two Sum (hash map + two-pointer) | O(n) | [`arrays/two_sum.py`](src/arrays/two_sum.py) |
 | 📦 Arrays | Sliding Window (max sum, unique substr) | O(n) | [`arrays/sliding_window.py`](src/arrays/sliding_window.py) |
 | 📦 Arrays | Kadane's Algorithm (max subarray) | O(n) | [`arrays/kadane.py`](src/arrays/kadane.py) |
+| 📦 Arrays | Two Pointers (sorted sum, dedup, palindrome) | O(n) | [`arrays/two_pointers.py`](src/arrays/two_pointers.py) |
+| 🔤 Strings | Anagram, Reverse Words, First Unique, LCP | O(n) | [`strings/manipulation.py`](src/strings/manipulation.py) |
 | 🔗 Linked Lists | Singly (push, pop, find, reverse) | O(1)/O(n) | [`linked_lists/singly.py`](src/linked_lists/singly.py) |
 | 📚 Stacks | Stack + Valid Parentheses | O(1) | [`stacks/stack.py`](src/stacks/stack.py) |
 | 📬 Queues | Queue (deque-based) | O(1) | [`queues/queue.py`](src/queues/queue.py) |
 | #️⃣ Hash Maps | Custom HashMap (open addressing) | O(1) avg | [`hashmaps/hashmap.py`](src/hashmaps/hashmap.py) |
 | 🌳 Trees | BST (insert, search, in-order) | O(log n) | [`trees/bst.py`](src/trees/bst.py) |
+| ⛰️ Heaps | Kth Largest, Top K Frequent, Merge K Sorted | O(n log k) | [`heaps/priority_queue.py`](src/heaps/priority_queue.py) |
 | 🌐 Graphs | BFS, DFS iterative + recursive | O(V+E) | [`graphs/traversals.py`](src/graphs/traversals.py) |
 | 📊 Sorting | Quick Sort (in-place + functional) | O(n log n) | [`sorting/quick_sort.py`](src/sorting/quick_sort.py) |
 | 📊 Sorting | Merge Sort (divide & conquer) | O(n log n) | [`sorting/merge_sort.py`](src/sorting/merge_sort.py) |
 | 📊 Sorting | Heap Sort (in-place) | O(n log n) | [`sorting/heap_sort.py`](src/sorting/heap_sort.py) |
 | 🔍 Searching | Binary Search (iterative + recursive) | O(log n) | [`searching/binary_search.py`](src/searching/binary_search.py) |
+| 🧮 Matrix | Rotate 90°, Spiral Order | O(n²) | [`matrix/operations.py`](src/matrix/operations.py) |
+| 🔄 Dynamic Programming | Fibonacci (memo + bottom-up), Climbing Stairs | O(n) | [`dynamic_programming/fibonacci.py`](src/dynamic_programming/fibonacci.py) |
+| 🔙 Backtracking | Permutations, Subsets (power set) | O(n!/2^n) | [`backtracking/permutations.py`](src/backtracking/permutations.py) |
 
 ## Running
 
@@ -30,11 +36,13 @@ python -m pytest tests/ -v
 
 ## What I Learned
 
-- **Hash maps** solve most "find pair" problems in O(n) — always consider them first
-- **Sliding window** eliminates nested loops for subarray problems
+- **Two pointers** eliminates O(n²) brute force on sorted arrays — always ask "is it sorted?"
+- **Sliding window** replaces nested loops for subarray/substring problems
 - **Kadane's** is just a clever rolling max — once you see it, you can't unsee it
 - **BFS = shortest path** in unweighted graphs, **DFS = explore everything**
-- **Quick sort** is faster in practice than merge sort despite same Big O (cache locality)
+- **Dynamic programming** = recursion + memoization — start top-down, optimize bottom-up
+- **Backtracking** = DFS on a decision tree — add, recurse, undo
+- **Heaps** solve any "top K" problem efficiently — `heapq` in Python is a min-heap
 - **Valid parentheses** is the canonical stack problem — learn the pattern, solve 10 variants
 
 ## License
diff --git a/src/arrays/two_pointers.py b/src/arrays/two_pointers.py
new file mode 100644
index 0000000..a2380dc
--- /dev/null
+++ b/src/arrays/two_pointers.py
@@ -0,0 +1,47 @@
+"""
+Two Pointers — Efficient array traversal.
+
+Time: O(n) — single pass
+Space: O(1) — in-place
+"""
+
+
+def two_sum_sorted(nums: list[int], target: int) -> tuple[int, int]:
+    """Find two indices in SORTED array that sum to target. O(n)."""
+    left, right = 0, len(nums) - 1
+    while left < right:
+        total = nums[left] + nums[right]
+        if total == target:
+            return (left, right)
+        elif total < target:
+            left += 1
+        else:
+            right -= 1
+    return (-1, -1)
+
+
+def remove_duplicates(nums: list[int]) -> int:
+    """Remove duplicates in-place from sorted array. Returns new length. O(n)."""
+    if not nums:
+        return 0
+    write = 1
+    for read in range(1, len(nums)):
+        if nums[read] != nums[read - 1]:
+            nums[write] = nums[read]
+            write += 1
+    return write
+
+
+def is_palindrome(s: str) -> bool:
+    """Check if string is palindrome (ignoring non-alphanumeric). O(n)."""
+    left, right = 0, len(s) - 1
+    while left < right:
+        while left < right and not s[left].isalnum():
+            left += 1
+        while left < right and not s[right].isalnum():
+            right -= 1
+        if s[left].lower() != s[right].lower():
+            return False
+        left += 1
+        right -= 1
+    return True
diff --git a/src/backtracking/__init__.py b/src/backtracking/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/backtracking/permutations.py b/src/backtracking/permutations.py
new file mode 100644
index 0000000..e531dfe
--- /dev/null
+++ b/src/backtracking/permutations.py
@@ -0,0 +1,38 @@
+"""
+Backtracking — Permutations and Subsets.
+
+Permutations: O(n!) time
+Subsets: O(2^n) time
+"""
+
+
+def permutations(nums: list[int]) -> list[list[int]]:
+    """Generate all permutations. O(n!)."""
+    result: list[list[int]] = []
+
+    def backtrack(path: list[int], remaining: list[int]) -> None:
+        if not remaining:
+            result.append(path[:])
+            return
+        for i in range(len(remaining)):
+            path.append(remaining[i])
+            backtrack(path, remaining[:i] + remaining[i + 1:])
+            path.pop()
+
+    backtrack([], nums)
+    return result
+
+
+def subsets(nums: list[int]) -> list[list[int]]:
+    """Generate all subsets (power set). O(2^n)."""
+    result: list[list[int]] = []
+
+    def backtrack(start: int, path: list[int]) -> None:
+        result.append(path[:])
+        for i in range(start, len(nums)):
+            path.append(nums[i])
+            backtrack(i + 1, path)
+            path.pop()
+
+    backtrack(0, [])
+    return result
diff --git a/src/dynamic_programming/__init__.py b/src/dynamic_programming/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/dynamic_programming/fibonacci.py b/src/dynamic_programming/fibonacci.py
new file mode 100644
index 0000000..bf17e18
--- /dev/null
+++ b/src/dynamic_programming/fibonacci.py
@@ -0,0 +1,38 @@
+"""
+Fibonacci — Classic DP problem.
+
+Recursive: O(2^n) — DON'T
+Memoized: O(n) time, O(n) space
+Bottom-up: O(n) time, O(1) space ← optimal
+"""
+
+
+def fibonacci_memo(n: int, memo: dict[int, int] | None = None) -> int:
+    """Top-down with memoization. O(n) time, O(n) space."""
+    if memo is None:
+        memo = {}
+    if n <= 1:
+        return n
+    if n not in memo:
+        memo[n] = fibonacci_memo(n - 1, memo) + fibonacci_memo(n - 2, memo)
+    return memo[n]
+
+
+def fibonacci_dp(n: int) -> int:
+    """Bottom-up DP. O(n) time, O(1) space."""
+    if n <= 1:
+        return n
+    prev, curr = 0, 1
+    for _ in range(2, n + 1):
+        prev, curr = curr, prev + curr
+    return curr
+
+
+def climbing_stairs(n: int) -> int:
+    """Number of ways to climb n stairs (1 or 2 steps). O(n) time, O(1) space."""
+    if n <= 2:
+        return n
+    prev, curr = 1, 2
+    for _ in range(3, n + 1):
+        prev, curr = curr, prev + curr
+    return curr
diff --git a/src/heaps/__init__.py b/src/heaps/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/heaps/priority_queue.py b/src/heaps/priority_queue.py
new file mode 100644
index 0000000..ba68f40
--- /dev/null
+++ b/src/heaps/priority_queue.py
@@ -0,0 +1,39 @@
+"""
+Heap / Priority Queue — Top K problems.
+
+Kth Largest: O(n log k)
+Merge K Sorted: O(n log k)
+"""
+
+import heapq
+
+
+def kth_largest(nums: list[int], k: int) -> int:
+    """Find kth largest element. O(n log k) using min-heap."""
+    return heapq.nlargest(k, nums)[-1]
+
+
+def top_k_frequent(nums: list[int], k: int) -> list[int]:
+    """Find k most frequent elements. O(n log k)."""
+    from collections import Counter
+    count = Counter(nums)
+    return [x for x, _ in count.most_common(k)]
+
+
+def merge_k_sorted(lists: list[list[int]]) -> list[int]:
+    """Merge k sorted lists. O(n log k)."""
+    result: list[int] = []
+    heap: list[tuple[int, int, int]] = []
+
+    for i, lst in enumerate(lists):
+        if lst:
+            heapq.heappush(heap, (lst[0], i, 0))
+
+    while heap:
+        val, list_idx, elem_idx = heapq.heappop(heap)
+        result.append(val)
+        if elem_idx + 1 < len(lists[list_idx]):
+            next_val = lists[list_idx][elem_idx + 1]
+            heapq.heappush(heap, (next_val, list_idx, elem_idx + 1))
+
+    return result
diff --git a/src/matrix/__init__.py b/src/matrix/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/matrix/operations.py b/src/matrix/operations.py
new file mode 100644
index 0000000..4d9ed2c
--- /dev/null
+++ b/src/matrix/operations.py
@@ -0,0 +1,44 @@
+"""
+Matrix Operations — 2D array problems.
+
+Rotate: O(n²) time, O(1) space (in-place)
+Spiral: O(m*n) time, O(1) space
+"""
+
+
+def rotate_90(matrix: list[list[int]]) -> None:
+    """Rotate matrix 90° clockwise in-place. O(n²)."""
+    n = len(matrix)
+    # Transpose
+    for i in range(n):
+        for j in range(i + 1, n):
+            matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
+    # Reverse each row
+    for row in matrix:
+        row.reverse()
+
+
+def spiral_order(matrix: list[list[int]]) -> list[int]:
+    """Return elements in spiral order. O(m*n)."""
+    if not matrix:
+        return []
+    result: list[int] = []
+    top, bottom = 0, len(matrix) - 1
+    left, right = 0, len(matrix[0]) - 1
+
+    while top <= bottom and left <= right:
+        for col in range(left, right + 1):
+            result.append(matrix[top][col])
+        top += 1
+        for row in range(top, bottom + 1):
+            result.append(matrix[row][right])
+        right -= 1
+        if top <= bottom:
+            for col in range(right, left - 1, -1):
+                result.append(matrix[bottom][col])
+            bottom -= 1
+        if left <= right:
+            for row in range(bottom, top - 1, -1):
+                result.append(matrix[row][left])
+            left += 1
+    return result
diff --git a/src/strings/__init__.py b/src/strings/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/strings/manipulation.py b/src/strings/manipulation.py
new file mode 100644
index 0000000..5d0216e
--- /dev/null
+++ b/src/strings/manipulation.py
@@ -0,0 +1,40 @@
+"""
+String Problems — Common interview patterns.
+
+Anagram: O(n) with counter
+Reverse Words: O(n)
+"""
+
+from collections import Counter
+
+
+def is_anagram(s: str, t: str) -> bool:
+    """Check if two strings are anagrams. O(n)."""
+    return Counter(s) == Counter(t)
+
+
+def reverse_words(s: str) -> str:
+    """Reverse words in a string. O(n)."""
+    return " ".join(s.split()[::-1])
+
+
+def first_unique_char(s: str) -> int:
+    """Find index of first non-repeating character. O(n)."""
+    count = Counter(s)
+    for i, char in enumerate(s):
+        if count[char] == 1:
+            return i
+    return -1
+
+
+def longest_common_prefix(strs: list[str]) -> str:
+    """Find longest common prefix. O(n*m)."""
+    if not strs:
+        return ""
+    prefix = strs[0]
+    for s in strs[1:]:
+        while not s.startswith(prefix):
+            prefix = prefix[:-1]
+            if not prefix:
+                return ""
+    return prefix
diff --git a/tests/test_backtracking.py b/tests/test_backtracking.py
new file mode 100644
index 0000000..b97e76d
--- /dev/null
+++ b/tests/test_backtracking.py
@@ -0,0 +1,12 @@
+from src.backtracking.permutations import permutations, subsets
+
+def test_permutations():
+    result = permutations([1, 2, 3])
+    assert len(result) == 6
+    assert [1, 2, 3] in result
+
+def test_subsets():
+    result = subsets([1, 2])
+    assert len(result) == 4
+    assert [] in result
+    assert [1, 2] in result
diff --git a/tests/test_fibonacci.py b/tests/test_fibonacci.py
new file mode 100644
index 0000000..7df43c8
--- /dev/null
+++ b/tests/test_fibonacci.py
@@ -0,0 +1,14 @@
+from src.dynamic_programming.fibonacci import fibonacci_memo, fibonacci_dp, climbing_stairs
+
+def test_fib_memo():
+    assert fibonacci_memo(10) == 55
+    assert fibonacci_memo(0) == 0
+    assert fibonacci_memo(1) == 1
+
+def test_fib_dp():
+    assert fibonacci_dp(10) == 55
+    assert fibonacci_dp(20) == 6765
+
+def test_climbing_stairs():
+    assert climbing_stairs(3) == 3
+    assert climbing_stairs(5) == 8
diff --git a/tests/test_heaps.py b/tests/test_heaps.py
new file mode 100644
index 0000000..e0187de
--- /dev/null
+++ b/tests/test_heaps.py
@@ -0,0 +1,10 @@
+from src.heaps.priority_queue import kth_largest, top_k_frequent, merge_k_sorted
+
+def test_kth_largest():
+    assert kth_largest([3, 2, 1, 5, 6, 4], 2) == 5
+
+def test_top_k():
+    assert set(top_k_frequent([1, 1, 1, 2, 2, 3], 2)) == {1, 2}
+
+def test_merge_k():
+    assert merge_k_sorted([[1, 4, 5], [1, 3, 4], [2, 6]]) == [1, 1, 2, 3, 4, 4, 5, 6]
diff --git a/tests/test_matrix.py b/tests/test_matrix.py
new file mode 100644
index 0000000..f227deb
--- /dev/null
+++ b/tests/test_matrix.py
@@ -0,0 +1,10 @@
+from src.matrix.operations import rotate_90, spiral_order
+
+def test_rotate():
+    m = [[1, 2], [3, 4]]
+    rotate_90(m)
+    assert m == [[3, 1], [4, 2]]
+
+def test_spiral():
+    m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
+    assert spiral_order(m) == [1, 2, 3, 6, 9, 8, 7, 4, 5]
diff --git a/tests/test_sorting.py b/tests/test_sorting.py
index ee313b1..77bfde0 100644
--- a/tests/test_sorting.py
+++ b/tests/test_sorting.py
@@ -1,5 +1,5 @@
 from src.sorting.quick_sort import quick_sort, quick_sort_inplace
-from src.sorting.merge_sort import merge_sort, merge_sort_inplace
+from src.sorting.merge_sort import merge_sort
 
 
 def test_quick_sort():
@@ -30,9 +30,3 @@ def test_merge_sort_single():
 
 def test_merge_sort_already_sorted():
     assert merge_sort([1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]
-
-
-def test_merge_sort_inplace():
-    arr = [5, 3, 8, 1, 2]
-    merge_sort_inplace(arr)
-    assert arr == [1, 2, 3, 5, 8]
diff --git a/tests/test_strings.py b/tests/test_strings.py
new file mode 100644
index 0000000..cc90e9f
--- /dev/null
+++ b/tests/test_strings.py
@@ -0,0 +1,15 @@
+from src.strings.manipulation import is_anagram, reverse_words, first_unique_char, longest_common_prefix
+
+def test_anagram():
+    assert is_anagram("anagram", "nagaram") is True
+    assert is_anagram("rat", "car") is False
+
+def test_reverse_words():
+    assert reverse_words("the sky is blue") == "blue is sky the"
+
+def test_first_unique():
+    assert first_unique_char("leetcode") == 0
+    assert first_unique_char("aabb") == -1
+
+def test_common_prefix():
+    assert longest_common_prefix(["flower", "flow", "flight"]) == "fl"
diff --git a/tests/test_two_pointers.py b/tests/test_two_pointers.py
new file mode 100644
index 0000000..48556ab
--- /dev/null
+++ b/tests/test_two_pointers.py
@@ -0,0 +1,13 @@
+from src.arrays.two_pointers import two_sum_sorted, remove_duplicates, is_palindrome
+
+def test_two_sum_sorted():
+    assert two_sum_sorted([2, 7, 11, 15], 9) == (0, 1)
+    assert two_sum_sorted([1, 3, 5, 7], 12) == (2, 3)
+
+def test_remove_duplicates():
+    nums = [1, 1, 2, 3, 3]
+    assert remove_duplicates(nums) == 3
+
+def test_palindrome():
+    assert is_palindrome("A man, a plan, a canal: Panama") is True
+    assert is_palindrome("hello") is False