Computer Science Foundations

Algorithms Homework Help

Sorting, dynamic programming, greedy, divide-and-conquer, and graph algorithms with formal complexity analysis. A common grading deduction is failing to prove the greedy-choice property for a problem that looks greedy but is not, the gap our tutors close with a worked exchange argument. Verified CS graduates, starting at $20 per task, 12-hour average turnaround.

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Why Algorithms

Algorithms Homework Help in plain English

Algorithms convert data structures into solutions. Where data structures answer "how is the data laid out", algorithms answer "what sequence of operations gets from input to output within a stated time and space budget".

Topics covered

What we tutor in Algorithms

Big-O and Asymptotic Notation

Big-O and Asymptotic Notation in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

Sorting (Comparison)

Sorting (Comparison) in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

Sorting (Non-Comparison)

Sorting (Non-Comparison) in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

Binary Search

Binary Search in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

Divide and Conquer

Divide and Conquer in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

Dynamic Programming (Top-Down)

Dynamic Programming (Top-Down) in Algorithms: implementation patterns, named pitfalls, and the autograder cases that catch them.

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Full overview

Algorithms at the university level

Algorithms convert data structures into solutions. Where data structures answer "how is the data laid out", algorithms answer "what sequence of operations gets from input to output within a stated time and space budget". The discipline splits into 7 named families: sorting (comparison and non-comparison), searching (linear, binary, interpolation), divide-and-conquer (merge sort, quicksort, Strassen matrix multiplication, FFT), dynamic programming (top-down memoization and bottom-up tabulation), greedy (Huffman coding, interval scheduling, Kruskal MST), backtracking (N-queens, Sudoku, subset sum), and graph algorithms (BFS, DFS, Dijkstra, Bellman-Ford, Floyd-Warshall, max-flow, matching).

A typical algorithms course spends 13 to 15 weeks drilling these families with Cormen-Leiserson-Rivest-Stein (CLRS) as the canonical textbook. Pattern matching from problem to algorithm class is the actual skill, and it only develops with repetition under feedback. The assessment landscape skews 70-30 toward written problem sets over implementation projects because algorithm correctness proofs (induction, exchange argument, cut-and-paste, master theorem derivation) are easier to grade than running code on adversarial inputs.

Proof-heavy problem sets demand a written argument for every greedy or DP claim. Final exams test master theorem application and 3-SAT reductions under timed conditions. Coding competitions (Codeforces, ICPC, LeetCode hard) flip the ratio and reward implementation speed plus complexity awareness.

CSHH tutor matching draws from CS graduates with proof-writing depth for the written-proof half, and competitive-programming experience (former ICPC competitors, LeetCode top-1000) for the implementation half. Our tutors deliver implementations in Python, Java, C++, or C with Big-O proofs (substitution method, master theorem, or amortized analysis), worked alternative approaches showing why the chosen algorithm wins, and autograder-format test runners. Languages supported: Java, Python, C++, C, JavaScript.

Where Students Get Stuck

Why students struggle with Algorithms

Pattern recognition: DP vs greedy vs backtracking

The wrong algorithm family wastes hours. We provide a 4-question decision flowchart: does the problem ask for an optimum? Does it have optimal substructure? Does the greedy-choice property hold (provable by exchange argument)? Does the state space have overlapping subproblems? The answers narrow the family to one or two candidates before implementation starts.

DP state definition and recurrence derivation

The recurrence is the hard part; implementation is mechanical. For knapsack, the state is (item index, remaining capacity); for longest common subsequence, the state is (i, j) for both string positions; for edit distance, the state is (i, j) with 3 transitions (insert, delete, substitute). We write the recurrence on paper first, verify by hand on a 3-element example, then code the tabulation.

Recursion stack overflow on deep inputs

Python defaults to recursion depth 1000; deep DP problems blow the stack. We convert to iterative tabulation, increase sys.setrecursionlimit when iteration is impractical, or use explicit stack-based simulation. Java has the same issue at around 10,000 stack frames depending on the JVM stack size flag (-Xss).

Quicksort worst-case on sorted input

Naive Lomuto partitioning with last-element pivot is O(n squared) on sorted input. The fix: randomized pivot selection or median-of-three. Sorting an already-sorted 100,000-element array in 10 seconds instead of 0.01 seconds is the classic sign. We implement randomized quicksort with introspection to fall back to heapsort if recursion depth exceeds 2 log n.

Greedy proofs (exchange argument)

Implementing a greedy algorithm is easy; proving it correct is the graded part on proof-heavy courses. The exchange argument shows that any optimal solution can be transformed step-by-step into the greedy solution without losing optimality. We write the proof as 5 numbered steps with a worked example showing the exchange.

Master theorem application

The master theorem solves T(n) = a T(n/b) + f(n) but requires identifying a (number of subproblems), b (subproblem size ratio), and f(n) (combine cost) correctly. Common error: confusing the per-call cost with the merge cost. We work through the 3 cases (f(n) is polynomially smaller, equal, or larger than n^log_b(a)) on a 4-recurrence cheat sheet.

Assignment Types

Algorithms assignment types we cover

Dynamic programming problem sets

Knapsack, longest common subsequence, edit distance, matrix chain, and coin change with the recurrence derived and verified on a small example first. Named pitfall: a 1D state table where the problem needs 2 dimensions, producing answers that pass tiny inputs and fail larger ones.

Greedy correctness proofs

Greedy implementations for interval scheduling, Huffman coding, and Kruskal MST paired with a written exchange argument. Named pitfall: applying greedy to a problem that lacks the greedy-choice property, such as coin change with arbitrary denominations.

Divide-and-conquer and complexity derivations

Merge sort, quicksort, and Strassen multiplication with a master-theorem derivation for each recurrence. Named pitfall: confusing the per-call cost with the combine cost f(n), which misidentifies the master-theorem case.

Graph algorithm implementations

BFS, DFS, Dijkstra, Bellman-Ford, Floyd-Warshall, and max-flow with the correct complexity for the chosen representation. Named pitfall: running Dijkstra on a graph with negative edge weights, which silently returns wrong shortest-path distances.

Backtracking and pruning tasks

N-queens, Sudoku, and subset-sum solvers with constraint propagation that cuts the search space. Named pitfall: omitting pruning, which explores 10x to 1000x more states and times out before producing an answer.

NP-completeness reductions

Polynomial-time reductions from 3-SAT, vertex cover, or subset sum with both directions of the proof. Named pitfall: a reduction that maps yes-instances correctly but admits spurious yes-instances on the no side, so it proves nothing.

Competitive-programming and TLE fixes

Contest problems and time-limit-exceeded rescues that drop an O(n squared) approach to O(n log n) or O(n). Named pitfall: integer overflow in factorial or Fibonacci recurrences past n equal to 47 for signed 32-bit, which wraps to negative values.

Tutors Who Cover This Subject

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FAQ

Algorithms help, frequently asked

Can you help with dynamic programming?
Yes. Top-down memoization with functools.lru_cache (Python) or a HashMap memo (Java) plus bottom-up tabulation with explicit state-table construction. We cover the canonical problems: 0/1 knapsack, unbounded knapsack, longest common subsequence, edit distance, matrix chain multiplication, coin change, longest increasing subsequence with O(n log n) patience sort, and 2D grid problems like minimum path sum. The recurrence relation is derived explicitly before code is written.
How do you prove a greedy algorithm is correct?
Exchange argument. Step 1: assume an optimal solution O differs from the greedy solution G in some choice. Step 2: find the first index where they differ. Step 3: show that swapping the greedy choice into O produces a solution at least as good as O. Step 4: by induction, O can be transformed into G without losing optimality. Step 5: conclude G is optimal. We write this out for activity selection, Huffman coding, and Kruskal MST as worked examples.
Can you derive Big-O using the master theorem?
Yes. The master theorem solves T(n) = a T(n/b) + f(n) by comparing f(n) to n^log_b(a). Case 1: f(n) is O(n^(log_b(a) - epsilon)) gives T(n) = Theta(n^log_b(a)). Case 2: f(n) is Theta(n^log_b(a) log^k n) gives T(n) = Theta(n^log_b(a) log^(k+1) n). Case 3: f(n) is Omega(n^(log_b(a) + epsilon)) and the regularity condition holds gives T(n) = Theta(f(n)). We work through merge sort (case 2), binary search (case 2 with k=0), and Strassen multiplication (case 1) as standard derivations.
Do you help with graph algorithms?
Yes. BFS for unweighted shortest path, DFS for topological sort and SCC, Dijkstra with binary heap (O((V plus E) log V)) or Fibonacci heap (O(E plus V log V)), Bellman-Ford for negative edges (O(VE)), Floyd-Warshall all-pairs (O(V cubed)), Prim and Kruskal MST, Ford-Fulkerson max-flow with BFS augmenting paths (Edmonds-Karp, O(VE squared)), and 2-SAT via Tarjan SCC. All implementations come with proof of correctness and complexity derivation.
What about NP-completeness?
We cover the standard reductions: 3-SAT to vertex cover, vertex cover to independent set, 3-SAT to 3-coloring, subset sum to partition. For an assignment claiming a problem is NP-complete, we pick the source problem (3-SAT is the most common starting point), construct the gadget, prove both directions of the reduction (yes-instance implies yes-instance, no-instance implies no-instance), and verify the reduction runs in polynomial time.
How fast is algorithms homework delivered?
12-hour average for standard problem sets including proofs, code, and test cases. Rush 4 to 6 hours for an additional fee. Pricing: $20 Debug and Explain per task, $30 Full Solution per task, $40 per hour Live Tutoring. Implementations pass the course autograder with stylistic variation to satisfy MOSS plagiarism scans.
Can you optimize my algorithm?
Profile first, optimize second. cProfile (Python) or VisualVM (Java) identifies the bottleneck function. If the bottleneck is asymptotic (wrong Big-O), we redesign the algorithm. If the bottleneck is constant-factor (cache misses, branch misprediction), we apply targeted fixes: locality-aware data layout, branch-free comparisons, SIMD where applicable. Before-and-after complexity comparison is included in the deliverable.
Do you cover randomized algorithms?
Yes. Randomized quicksort with expected O(n log n), randomized hashing with universal hash families, Karger min-cut with high-probability analysis, skip lists with expected O(log n) operations, and Bloom filters with bounded false-positive rate. We provide both the algorithm and the probability analysis (expectation, variance, concentration bounds).
Can you help with competitive programming problems?
Codeforces, LeetCode, HackerRank, ICPC problems. Common patterns: segment trees with lazy propagation, sparse tables for range minimum queries, suffix arrays, heavy-light decomposition, centroid decomposition, persistent data structures. C++ with STL or Python with appropriate library functions. Solutions include the intuition, the implementation, the complexity, and a brief on alternative approaches.
How do you handle TLE (time limit exceeded) errors?
TLE means the algorithm complexity is wrong for the input size. Diagnostic: compute the operations-per-second budget (typically 10^8 to 10^9 for C++, 10^6 to 10^7 for Python) and compare to n times the algorithm complexity. If n = 10^5 and the algorithm is O(n squared), we need 10^10 operations in 1 second, which is impossible. We redesign to O(n log n) or O(n) and verify the new complexity hits the budget. Common rewrites that drop complexity: brute-force quadratic to sorted-plus-binary-search (n log n), nested loops to hash table lookup (n), recursion without memoization to DP with memo table (often exponential to polynomial), repeated graph traversal to one-shot BFS or DFS with precomputed state.
Do you cover string algorithms (KMP, Rabin-Karp, suffix arrays)?
Yes. KMP for pattern matching in O(n plus m) with the failure-function preprocessing step worked out as a 4-row table. Rabin-Karp with rolling hash for multiple-pattern search and plagiarism-detection-style assignments. Aho-Corasick for the multi-pattern version with a trie plus failure links. Suffix arrays with DC3 (Karkkainen-Sanders) or SA-IS construction in O(n), plus LCP array via Kasai algorithm, plus longest-common-substring queries. Z-function for prefix-matching problems. Manacher for longest-palindromic-substring in linear time. Standard work on advanced algorithms problem sets and competitive-programming string-heavy contests.

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