108 lines
2.5 KiB
Org Mode
108 lines
2.5 KiB
Org Mode
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#+ANKI_DECK: study_deck_02
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#+TITLE: DSA Tricks & Patterns
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* Common Patterns
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** Sliding Window
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Use when: contiguous subarray/substring, "longest/shortest/most k"
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Template:
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#+begin_src cpp
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int left = 0;
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for (int right = 0; right < n; right++) {
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// expand window
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while (/* window invalid */) {
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// shrink window
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left++;
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}
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// update answer
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}
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#+end_src
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** Two Pointers
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Use when: sorted array, palindrome, pair sum
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Template:
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#+begin_src cpp
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int l = 0, r = n - 1;
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while (l < r) {
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if (/* condition */) l++;
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else r--;
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}
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#+end_src
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** Binary Search
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Use when: monotonic function, "minimum maximum", "first/last"
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Template:
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#+begin_src cpp
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int lo = 0, hi = n;
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while (lo < hi) {
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int mid = lo + (hi - lo) / 2;
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if (/* check(mid) */) hi = mid;
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else lo = mid + 1;
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}
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#+end_src
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** BFS vs DFS
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- BFS: shortest path (unweighted), level-order, queue
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- DFS: path existence, backtracking, cycle detection, stack/recursion
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** Union-Find
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Use when: connected components, cycle detection, grouping
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- Path compression + union by rank = O(α(n))
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** Monotonic Stack
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Use when: next greater/smaller element, stock span
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Template:
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#+begin_src cpp
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stack<int> st;
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for (int i = 0; i < n; i++) {
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while (!st.empty() && st.top() < arr[i]) {
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// process st.top()
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st.pop();
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}
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st.push(i);
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}
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#+end_src
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** Topological Sort
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Use when: dependency ordering, DAG, course schedule
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- Kahn's (BFS + in-degree) or DFS post-order reversal
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** Dijkstra's
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Use when: shortest path, non-negative weights, weighted graph
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- Priority queue + relaxation
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** Bit Manipulation Tricks
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- ~x = -x - 1
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- x & (x - 1) clears lowest set bit
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- x & -x isolates lowest set bit
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- XOR swap: a ^= b; b ^= a; a ^= b;
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** KMP / Z-Algorithm
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Use when: pattern matching, repeated substrings
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- KMP: O(n + m), failure function
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- Z: O(n + m), Z-array
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** DP State Design
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- Ask: what do I need to track? (index, remaining, previous choice)
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- State = f(index, constraint1, constraint2, ...)
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- Space optimize with rolling array when only previous row needed
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** Graph Coloring (2-coloring / Bipartite)
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Use when: odd cycle check, two groups
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- BFS/DFS alternating colors
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** Prefix Sum
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Use when: subarray sum, range queries
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- Build once O(n), query O(1)
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** Trie
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Use when: prefix search, autocomplete, word dictionary
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- Each node = character, path = word
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** Heap / Priority Queue
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Use when: k-th element, merge k sorted, median maintenance
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- C++: `priority_queue` (max-heap by default)
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** Fast & Slow Pointers
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Use when: cycle detection, linked list midpoint
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- Floyd's tortoise and hare
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