#+ANKI_DECK: 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