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Algorithms homework help. Code, proofs and complexity.

Dynamic programming, greedy algorithms, graph problems and proofs. Working code plus the correctness argument your grader looks for.

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What we cover

Every part of algorithms your course covers.

Paradigms

Divide and conquer
Dynamic programming
Greedy algorithms
Backtracking

Graphs

Dijkstra and Bellman-Ford
Minimum spanning trees
Network flow
Topological sort

Analysis

Big-O, Θ and Ω
Master theorem
Amortized analysis
Correctness proofs

Advanced

NP-completeness reductions
Approximation algorithms
Randomized algorithms
String algorithms

Example order

One algorithms order, start to finish.

What the student uploaded, what came back, and how the price was set.

01The brief

Introduction to AlgorithmsUndergradDue in 3 days

Minimum edit distance with proof

Compute the edit distance between two strings with dynamic programming, prove the recurrence is correct, and state the time and space complexity.

Requirements

Bottom-up DP table
Insert, delete and replace costs
Proof of the recurrence
Edge cases: empty strings

02The solution

edit_distance.py16 lines

1def edit_distance(a: str, b: str) -> int:

2 m, n = len(a), len(b)

3 # dp[i][j] = cost to turn a[:i] into b[:j]

4 dp = [[0] * (n + 1) for _ in range(m + 1)]

5 for i in range(m + 1): dp[i][0] = i

6 for j in range(n + 1): dp[0][j] = j

8 for i in range(1, m + 1):

9 for j in range(1, n + 1):

10 same = a[i - 1] == b[j - 1]

11 dp[i][j] = min(

12 dp[i - 1][j] + 1, # delete

13 dp[i][j - 1] + 1, # insert

14 dp[i - 1][j - 1] + (0 if same else 1), # replace

15 )

16 return dp[m][n]

12 tests passing · proof included

03The explanation doc

explanation.pdf

The subproblem

dp[i][j] is the cheapest way to turn the first i letters of a into the first j letters of b.

Proof by induction

Any optimal script ends in a delete, an insert or a replace/keep. Each leaves a smaller optimal subproblem.

Complexity

O(mn) time and space; space drops to O(min(m, n)) by keeping two rows.

04The price

AI predicted budget

$80–$150

Level · UndergradIncluded

Deadline · 3 daysStandard

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$110

Delivered 5h early

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Typical orders

Common algorithms assignments and typical budgets.

DP problem set (3–5 problems)

$80–$180

Usually 2–3 days

typical range

Graph algorithm implementation

$90–$200

Usually 2–4 days

typical range

Proof-based problem set

$70–$160

Usually 2–3 days

typical range

NP-completeness reductions

$90–$200

Usually 3–4 days

typical range

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