DSA with Python Training Topic-Wise Online Mock Tests & Free MCQ Practice
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DSA with Python Training — Topic-Wise Mock Tests
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All Modules & Topics in DSA with Python Training
Algorithm Time & Space Complexity in Python — CPython Stdlib Costs & Hidden `O(N)` Traps
Purpose: To understand and apply Algorithm Time & Space Complexity in Python — CPython Stdlib Costs & Hidden `O(N)` Traps in real DSA with Python systems — specifically: Understand worst, average, and amortized complexity in CPython: why `list.append`/`pop()` are `O(1)` amortized while `list.pop(0)`/`insert(0, x)` shift pointers in `O(N)`, and why `arr[mid:]` inside recursion secretly adds `O(N)` copy cost!, so your code stays reliable, fast, and easy to maintain in production.
Master Theorem (`T(n) = aT(n/b) + f(n)`) — Critical Exponent `n^(log_b a)` & Cases 1, 2, 3
Purpose: To understand and apply Master Theorem (`T(n) = aT(n/b) + f(n)`) — Critical Exponent `n^(log_b a)` & Cases 1, 2, 3 in real DSA with Python systems — specifically: Solve recurrences for Binary Search (`a=1, b=2, f=1 -> Θ(log n)`), Merge Sort (`a=2, b=2, f=n -> Θ(n log n)`), Karatsuba (`a=3, b=2, f=n -> Θ(n^1.585)`), and Strassen (`a=7, b=2, f=n^2 -> Θ(n^2.807)`) by comparing `f(n)` with watershed `n^(log_b a)`, so your code stays reliable, fast, and easy to maintain in production.
Binary Search in Python — `bisect_left` vs `bisect_right` & Parametric Search on Answer
Purpose: To understand and apply Binary Search in Python — `bisect_left` vs `bisect_right` & Parametric Search on Answer in real DSA with Python systems — specifically: Master C-implemented `bisect.bisect_left` / `bisect_right` (Python 3.10+ supports `key=`), counting duplicates in `O(log N)`, and monotonic predicate search (`Koko Eating Bananas`, `Minimize Max Distance`), so your code stays reliable, fast, and easy to maintain in production.
Merge Sort in Python — Index-Bounded Divide & Conquer, Stability & CPython Timsort (`O(N)` Best Case)
Purpose: To understand and apply Merge Sort in Python — Index-Bounded Divide & Conquer, Stability & CPython Timsort (`O(N)` Best Case) in real DSA with Python systems — specifically: Implement clean `Θ(N log N)` stable Merge Sort using a single shared auxiliary list, and understand how Tim Peters’ **Timsort** (`sorted()`) combines natural monotonic runs with binary insertion sort + galloping merge, so your code stays reliable, fast, and easy to maintain in production.
Quick Sort & Quickselect — Randomized Pivot, 3-Way Partitioning & Python Recursion Depth Guard
Purpose: To understand and apply Quick Sort & Quickselect — Randomized Pivot, 3-Way Partitioning & Python Recursion Depth Guard in real DSA with Python systems — specifically: Understand Quick Sort’s `O(N log N)` expected divide-and-conquer partition mechanics, why CPython’s default recursion limit (`1000`) immediately crashes naive fixed-pivot Quick Sort on sorted `N = 2000`, and iterative Quickselect, so your code stays reliable, fast, and easy to maintain in production.
Binary Heap Sort & Python `heapq` — `O(N)` Sift-Down `heapify`, `O(1)` Space Sort & Min-Heap Idioms
Purpose: To understand and apply Binary Heap Sort & Python `heapq` — `O(N)` Sift-Down `heapify`, `O(1)` Space Sort & Min-Heap Idioms in real DSA with Python systems — specifically: Sort any array in worst-case `O(N log N)` time and strict `O(1)` auxiliary space via in-place Max-Heapification + root swaps, and master Python’s C-accelerated `heapq` module (`heapify`, `heappush`, `heappop`, `heappushpop`), so your code stays reliable, fast, and easy to maintain in production.
Hashing & CPython `dict` Internals — Compact Open Addressing, Tombstones & `frozenset`/Tuple Keys
Purpose: To understand and apply Hashing & CPython `dict` Internals — Compact Open Addressing, Tombstones & `frozenset`/Tuple Keys in real DSA with Python systems — specifically: How Python’s `dict` preserves insertion order while cutting memory by ~25% via Raymond Hettinger’s compact index array, why open-addressed `del d[k]` writes a dummy **tombstone**, and rolling polynomial Rabin-Karp hashing, so your code stays reliable, fast, and easy to maintain in production.
Red-Black Tree — 5 Color Invariants, Black-Height, Recoloring vs Rotations & `O(1)` Fixup Bound
Purpose: To understand and apply Red-Black Tree — 5 Color Invariants, Black-Height, Recoloring vs Rotations & `O(1)` Fixup Bound in real DSA with Python systems — specifically: Understand why Linux `CFS` scheduler (`rbtree`), C++ `std::map`, and Java `TreeMap` choose **Red-Black Trees**: how color flips + at most **2 rotations on insert** (3 on delete) bound tree height to `<= 2 log2(N + 1)`, so your code stays reliable, fast, and easy to maintain in production.
Dynamic Programming — Overlapping Subproblems, Optimal Substructure & State Compression
Purpose: To understand and apply Dynamic Programming — Overlapping Subproblems, Optimal Substructure & State Compression in real DSA with Python systems — specifically: Understand Richard Bellman’s Dynamic Programming: caching shared subproblem DAG vertices so exponential `O(2^N)` trees collapse into `O(|States| * |Transitions|)`, plus `O(1)` rolling-variable compression, so your code stays reliable, fast, and easy to maintain in production.
Tabulation vs Memoization — `@functools.cache` Top-Down vs Iterative Rolling-Row Bottom-Up
Purpose: To understand and apply Tabulation vs Memoization — `@functools.cache` Top-Down vs Iterative Rolling-Row Bottom-Up in real DSA with Python systems — specifically: Compare Top-Down Memoization (`@cache` lazy DFS over reachable states) against Bottom-Up Tabulation (tight CPU loops, zero recursion stack frames, and instant `O(M)` row-swapping space reduction), so your code stays reliable, fast, and easy to maintain in production.
0/1 Knapsack — Reverse-Capacity `O(W)` 1D Compression, Subset Sum & Pseudo-Polynomial Time
Purpose: To understand and apply 0/1 Knapsack — Reverse-Capacity `O(W)` 1D Compression, Subset Sum & Pseudo-Polynomial Time in real DSA with Python systems — specifically: Maximize value within capacity `W` where each item can be taken `0` or `1` time (no fractions — greedy value/weight ratio FAILS on 0/1 Knapsack!), and master the reverse-loop `O(W)` 1D array trick, so your code stays reliable, fast, and easy to maintain in production.
Longest Common Subsequence (LCS) — 2-String Alignment DP, Backtracking & `O(min(N, M))` Space
Purpose: To understand and apply Longest Common Subsequence (LCS) — 2-String Alignment DP, Backtracking & `O(min(N, M))` Space in real DSA with Python systems — specifically: Align two sequences `s1` and `s2` via `dp[i][j] = 1 + dp[i-1][j-1]` (match) vs `max(dp[i-1][j], dp[i][j-1])` (mismatch), reconstruct the actual LCS string, and derive Shortest Common Supersequence & Longest Palindromic Subsequence, so your code stays reliable, fast, and easy to maintain in production.
Longest Increasing Subsequence (LIS) — `O(N^2)` DP vs `O(N log N)` Patience `tails` + `bisect_left`
Purpose: To understand and apply Longest Increasing Subsequence (LIS) — `O(N^2)` DP vs `O(N log N)` Patience `tails` + `bisect_left` in real DSA with Python systems — specifically: Maintain `tails[k]` = smallest possible tail value of all increasing subsequences of length `k + 1`: because `tails` stays strictly sorted, `bisect_left(tails, x)` updates or extends LIS in `O(log N)` per element!, so your code stays reliable, fast, and easy to maintain in production.
Greedy Algorithms — Greedy Choice Property, Exchange Argument, Interval Scheduling & Fractional Knapsack
Purpose: To understand and apply Greedy Algorithms — Greedy Choice Property, Exchange Argument, Interval Scheduling & Fractional Knapsack in real DSA with Python systems — specifically: Make locally irrevocable optimal choices backed by **Exchange Argument** proofs: Activity Selection (sort by earliest finish!), Minimum Meeting Rooms (min-heap / sweep-line), Jump Game, and Gas Station, so your code stays reliable, fast, and easy to maintain in production.
Huffman Coding — Optimal Prefix-Free Binary Tree, `heapq` Merging & Compression Bit Ratio
Purpose: To understand and apply Huffman Coding — Optimal Prefix-Free Binary Tree, `heapq` Merging & Compression Bit Ratio in real DSA with Python systems — specifically: Assign shorter bit codes to frequent symbols and longer codes to rare symbols by repeatedly merging the two lightest subtrees in a Min-Heap (`O(K log K)` over `K` unique symbols), so your code stays reliable, fast, and easy to maintain in production.
Backtracking — State-Space Tree, `Choose -> Explore -> Unchoose`, Pruning & Duplicate Skipping
Purpose: To understand and apply Backtracking — State-Space Tree, `Choose -> Explore -> Unchoose`, Pruning & Duplicate Skipping in real DSA with Python systems — specifically: Explore combinatorial search spaces systematically by mutating a single shared `path` list in place (`path.append(x)` -> recurse -> `path.pop()`), sorting candidates for early `break` pruning, and skipping duplicate branches, so your code stays reliable, fast, and easy to maintain in production.
N-Queens Problem — Row-by-Row Placement & `O(1)` Diagonal Invariants (`r - c` and `r + c`)
Purpose: To understand and apply N-Queens Problem — Row-by-Row Placement & `O(1)` Diagonal Invariants (`r - c` and `r + c`) in real DSA with Python systems — specifically: Place one Queen per row (`N^N -> N!` immediately) and prune illegal columns/diagonals in `O(1)` using two mathematical invariants: cells on the same `\` main diagonal share `r - c`, and cells on the same `/` anti-diagonal share `r + c`!, so your code stays reliable, fast, and easy to maintain in production.
Dijkstra’s Algorithm — Non-Negative Edge Relaxation, Lazy `heapq` & Stale-Entry Guard
Purpose: To understand and apply Dijkstra’s Algorithm — Non-Negative Edge Relaxation, Lazy `heapq` & Stale-Entry Guard in real DSA with Python systems — specifically: Compute single-source shortest paths across non-negative weighted graphs (`w >= 0`) in `O((V + E) log V)` using Python `heapq`, lazy duplicate entries (replacing complex `decrease-key`), and `if d > dist[u]: continue`, so your code stays reliable, fast, and easy to maintain in production.
Bellman-Ford Algorithm — `V - 1` Edge Relaxations, Negative Cycle Detection & `K`-Stop Flights
Purpose: To understand and apply Bellman-Ford Algorithm — `V - 1` Edge Relaxations, Negative Cycle Detection & `K`-Stop Flights in real DSA with Python systems — specifically: Why any simple shortest path in a `V`-vertex graph has at most `V - 1` edges: relax all edges `V - 1` rounds in `O(V * E)` to support negative weights safely, and detect negative cycles if any edge still relaxes on round `V`!, so your code stays reliable, fast, and easy to maintain in production.
Knuth-Morris-Pratt (KMP) — `LPS` Prefix-Suffix Automaton & Worst-Case `O(N + M)` Pattern Search
Purpose: To understand and apply Knuth-Morris-Pratt (KMP) — `LPS` Prefix-Suffix Automaton & Worst-Case `O(N + M)` Pattern Search in real DSA with Python systems — specifically: Eliminate naive `O(N * M)` string-matching backtracking (e.g., `"AAAAAAAAB"` in `"AAAA...AAAA"`) by precomputing `lps[k]` = length of the longest **proper** prefix of `pat[0..k]` that is also a suffix of `pat[0..k]`, so your code stays reliable, fast, and easy to maintain in production.
collections.deque BFS, Iterative DFS & Recursion-Limit Safety
Purpose: To understand and apply collections.deque BFS, Iterative DFS & Recursion-Limit Safety in real DSA with Python systems — specifically: Avoid Python RecursionError crashes on 10^5-node graphs using explicit stacks/deques, so your code stays reliable, fast, and easy to maintain in production.
Dijkstra with heapq, 0-1 BFS & Shortest Path with State Tuples
Purpose: To understand and apply Dijkstra with heapq, 0-1 BFS & Shortest Path with State Tuples in real DSA with Python systems — specifically: Solve constrained shortest-path OA problems cleanly using tuple priority queues, so your code stays reliable, fast, and easy to maintain in production.
Topological Sort (Kahn’s Algorithm) & Disjoint Set Union (Union-Find)
Purpose: To understand and apply Topological Sort (Kahn’s Algorithm) & Disjoint Set Union (Union-Find) in real DSA with Python systems — specifically: Detect dependency cycles and merge dynamic connected components in O(alpha(N)), so your code stays reliable, fast, and easy to maintain in production.
Multi-Source Grid BFS & Implicit Word/State-Space Graphs
Purpose: To understand and apply Multi-Source Grid BFS & Implicit Word/State-Space Graphs in real DSA with Python systems — specifically: Crack shortest transformation and grid wave-propagation problems rapidly, so your code stays reliable, fast, and easy to maintain in production.
functools.cache Top-Down -> Iterative Bottom-Up -> 1D Rolling Arrays
Purpose: To understand and apply functools.cache Top-Down -> Iterative Bottom-Up -> 1D Rolling Arrays in real DSA with Python systems — specifically: Prototype recurrence relations in 3 minutes and optimize memory to pass strict OA limits, so your code stays reliable, fast, and easy to maintain in production.
0/1 & Unbounded Knapsack, Partition & Target-Sum Patterns
Purpose: To understand and apply 0/1 & Unbounded Knapsack, Partition & Target-Sum Patterns in real DSA with Python systems — specifically: Identify state variables and base cases immediately under timed test pressure, so your code stays reliable, fast, and easy to maintain in production.
LCS, Edit Distance, bisect_left O(N log N) LIS & Interval DP
Purpose: To understand and apply LCS, Edit Distance, bisect_left O(N log N) LIS & Interval DP in real DSA with Python systems — specifically: Combine Python bisect binary search with DP for optimal subsequence runtimes, so your code stays reliable, fast, and easy to maintain in production.
Tree DP, Bitmask DP (N <= 20) & Stock Cooldown State Machines
Purpose: To understand and apply Tree DP, Bitmask DP (N <= 20) & Stock Cooldown State Machines in real DSA with Python systems — specifically: Conquer hard-tier product-company OA problems with clean bitwise transitions, so your code stays reliable, fast, and easy to maintain in production.
Nested-Dict / Node Tries & Word-Search Pruning
Purpose: To understand and apply Nested-Dict / Node Tries & Word-Search Pruning in real DSA with Python systems — specifically: Implement fast prefix autocomplete and prune exponential board backtracking searches, so your code stays reliable, fast, and easy to maintain in production.
Fenwick Tree (Binary Indexed Tree) & Iterative Segment Tree
Purpose: To understand and apply Fenwick Tree (Binary Indexed Tree) & Iterative Segment Tree in real DSA with Python systems — specifically: Support O(log N) dynamic prefix sums and range queries without TLE in Python, so your code stays reliable, fast, and easy to maintain in production.
Polynomial Rolling Hash, KMP & Z-Array Linear String Matching
Purpose: To understand and apply Polynomial Rolling Hash, KMP & Z-Array Linear String Matching in real DSA with Python systems — specifically: Find repeated substrings and palindromes in guaranteed O(N) linear time, so your code stays reliable, fast, and easy to maintain in production.
Interval Sweep-Line, Prefix Difference Arrays & bisect Event Queries
Purpose: To understand and apply Interval Sweep-Line, Prefix Difference Arrays & bisect Event Queries in real DSA with Python systems — specifically: Solve calendar booking, CPU scheduling, and overlapping skylines cleanly, so your code stays reliable, fast, and easy to maintain in production.
Monotonic Stack & collections.deque Sliding Window Maximum
Purpose: To understand and apply Monotonic Stack & collections.deque Sliding Window Maximum in real DSA with Python systems — specifically: Achieve strict O(N) amortized window scans where naive slicing O(N*K) times out, so your code stays reliable, fast, and easy to maintain in production.
Two-Heap Streaming Median, K-Way Merge & Counter/heapq Top-K
Purpose: To understand and apply Two-Heap Streaming Median, K-Way Merge & Counter/heapq Top-K in real DSA with Python systems — specifically: Maintain real-time percentiles and merge sorted log streams effortlessly, so your code stays reliable, fast, and easy to maintain in production.
OrderedDict / Custom Doubly-Linked O(1) LRU/LFU & Time-Based KV Store
Purpose: To understand and apply OrderedDict / Custom Doubly-Linked O(1) LRU/LFU & Time-Based KV Store in real DSA with Python systems — specifically: Build clean, extensible classes for 60-minute machine-coding interviews, so your code stays reliable, fast, and easy to maintain in production.
Python Constant-Factor Speedups & Interview Verbalization Framework
Purpose: To understand and apply Python Constant-Factor Speedups & Interview Verbalization Framework in real DSA with Python systems — specifically: Avoid list.pop(0) O(N) traps, prove Big-O clearly, and test corner cases first, so your code stays reliable, fast, and easy to maintain in production.
Trie Prefix Trees, Rolling Hash / KMP & Counter/Deque Sliding-Window Idioms
Purpose: To understand and apply Trie Prefix Trees, Rolling Hash / KMP & Counter/Deque Sliding-Window Idioms in real DSA with Python systems — specifically: Write concise, bug-free Python string and stream algorithms using collections.deque and defaultdict, so your code stays reliable, fast, and easy to maintain in production.
Union-Find (Rank + Path Compression), Shortest Paths (0-1 BFS, Dijkstra) & DAG DP
Purpose: To understand and apply Union-Find (Rank + Path Compression), Shortest Paths (0-1 BFS, Dijkstra) & DAG DP in real DSA with Python systems — specifically: Solve multi-source grid, network latency, and scheduling dependency problems optimally, so your code stays reliable, fast, and easy to maintain in production.
Binary Search on Answer, Monotonic Stacks & Bitmask Dynamic Programming
Purpose: To understand and apply Binary Search on Answer, Monotonic Stacks & Bitmask Dynamic Programming in real DSA with Python systems — specifically: Crack hard optimization and subset-state problems using functools.cache and clean state transitions, so your code stays reliable, fast, and easy to maintain in production.
Python Performance Rules: Avoiding O(N) list.pop(0), String Concatenation & Recursion Limits
Purpose: To understand and apply Python Performance Rules: Avoiding O(N) list.pop(0), String Concatenation & Recursion Limits in real DSA with Python systems — specifically: Prevent Time Limit Exceeded (TLE) verdicts caused by hidden quadratic operations in Python, so your code stays reliable, fast, and easy to maintain in production.
Property/Stress Testing: Generating Random Counterexamples to Catch Edge-Case Bugs
Purpose: To understand and apply Property/Stress Testing: Generating Random Counterexamples to Catch Edge-Case Bugs in real DSA with Python systems — specifically: Prove your optimal algorithm matches brute-force output across 1,000+ tricky boundary inputs, so your code stays reliable, fast, and easy to maintain in production.
FAANG / Product-Company Live Coding Framework & Spoken Complexity Walkthroughs
Purpose: To understand and apply FAANG / Product-Company Live Coding Framework & Spoken Complexity Walkthroughs in real DSA with Python systems — specifically: Clarify constraints, dry-run examples aloud, and write clean typed Python under 35-minute timers, so your code stays reliable, fast, and easy to maintain in production.