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+#+PROPERTY: STUDY_DECK_02
+#+TITLE: DSA Tricks & Patterns
+
+* Common Patterns
+** Sliding Window
+Use when: contiguous subarray/substring, "longest/shortest/most k"
+Template:
+#+begin_src cpp
+int left = 0;
+for (int right = 0; right < n; right++) {
+    // expand window
+    while (/* window invalid */) {
+        // shrink window
+        left++;
+    }
+    // update answer
+}
+#+end_src
+
+** Two Pointers
+Use when: sorted array, palindrome, pair sum
+Template:
+#+begin_src cpp
+int l = 0, r = n - 1;
+while (l < r) {
+    if (/* condition */) l++;
+    else r--;
+}
+#+end_src
+
+** Binary Search
+Use when: monotonic function, "minimum maximum", "first/last"
+Template:
+#+begin_src cpp
+int lo = 0, hi = n;
+while (lo < hi) {
+    int mid = lo + (hi - lo) / 2;
+    if (/* check(mid) */) hi = mid;
+    else lo = mid + 1;
+}
+#+end_src
+
+** BFS vs DFS
+- BFS: shortest path (unweighted), level-order, queue
+- DFS: path existence, backtracking, cycle detection, stack/recursion
+
+** Union-Find
+Use when: connected components, cycle detection, grouping
+- Path compression + union by rank = O(α(n))
+
+** Monotonic Stack
+Use when: next greater/smaller element, stock span
+Template:
+#+begin_src cpp
+stack<int> st;
+for (int i = 0; i < n; i++) {
+    while (!st.empty() && st.top() < arr[i]) {
+        // process st.top()
+        st.pop();
+    }
+    st.push(i);
+}
+#+end_src
+
+** Topological Sort
+Use when: dependency ordering, DAG, course schedule
+- Kahn's (BFS + in-degree) or DFS post-order reversal
+
+** Dijkstra's
+Use when: shortest path, non-negative weights, weighted graph
+- Priority queue + relaxation
+
+** Bit Manipulation Tricks
+- ~x = -x - 1
+- x & (x - 1) clears lowest set bit
+- x & -x isolates lowest set bit
+- XOR swap: a ^= b; b ^= a; a ^= b;
+
+** KMP / Z-Algorithm
+Use when: pattern matching, repeated substrings
+- KMP: O(n + m), failure function
+- Z: O(n + m), Z-array
+
+** DP State Design
+- Ask: what do I need to track? (index, remaining, previous choice)
+- State = f(index, constraint1, constraint2, ...)
+- Space optimize with rolling array when only previous row needed
+
+** Graph Coloring (2-coloring / Bipartite)
+Use when: odd cycle check, two groups
+- BFS/DFS alternating colors
+
+** Prefix Sum
+Use when: subarray sum, range queries
+- Build once O(n), query O(1)
+
+** Trie
+Use when: prefix search, autocomplete, word dictionary
+- Each node = character, path = word
+
+** Heap / Priority Queue
+Use when: k-th element, merge k sorted, median maintenance
+- C++: `priority_queue` (max-heap by default)
+
+** Fast & Slow Pointers
+Use when: cycle detection, linked list midpoint
+- Floyd's tortoise and hare