Course audit report

Algorithm Analysis and Design

Done Role: Backend Engineer 2 Findings Algorithm Analysis And Design — Classical Cs Theory
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2 findings · 2 medium
Incorrect CS 412 - T2311 - Ch 15_part1.pptx, Slide 3

What the slide says

Fibonacci Sequence: '0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 114, ….'

Primary source ✓ Source checked

oeis.org ↗

A000045 · Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. ... 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, ...

What to learn instead

Replace '114' with '144'. The 13th Fibonacci term (F(12) under the convention F(0)=0) is 89+55=144, which is also self-consistent with the F(n)=F(n-1)+F(n-2) recurrence stated on the same slide.

Incorrect CS 412 - T2313 - Ch 4_Part2 _1_.pptx, Slide 5

What the slide says

Each Fibonacci number is the sum of the two previous ones, yielding the Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 114, ….

Primary source ✓ Source checked

oeis.org ↗

A000045 · Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. ... 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...

What to learn instead

Replace '114' with '144'. 89 + 55 = 144, not 114; the term shown contradicts the recurrence definition given immediately below it on the same slide.

This is a well-scoped classical-algorithms course (asymptotic analysis, divide-and-conquer, DP, balanced BSTs, BFS/DFS at the pseudocode level), and every backend skill demanded by ≥30% of postings (SQL, Docker, Postgres, REST APIs, AWS, microservices, Kubernetes, OAuth, Kafka, Redis, etc.) is cross-domain to algorithm theory with 0% partial coverage in the slides — so under the extend-partial-coverage rule there are no in-scope gaps to recommend, even though the gap to the live backend job market is large.

No extendable gaps for this role

Stale only flags gaps that the course already partially covers. It won't push you toward Kubernetes when you're sitting in a Unicode course. For backend, every high-frequency market demand is in a different area from what this course actually teaches.

Try a different target role on the run page, or run Stale on a course whose subject area overlaps the role you're aiming for.

What the curriculum actually teaches (20 skills)
  • Asymptotic notation (Big-O, Big-Theta, Big-Omega, little-o, little-omega) · CS 412 - Ch 3 (Growth of Functions), CS 412 - Ch 2 part 1 (Insertion sort and Analyzing Algorithms)
    Ch 3 slide 8: 'O notation: asymptotic less than ... Ω notation: asymptotic greater than ... Θ notation: asymptotic equality.' Ch 2_part1 slide 57: 'Order of Growth ... We use Θ-notation informally in this chapter, and we will define it precisely in Chapter 3.'
  • Recurrence-solving methods (iteration, substitution with induction, recursion-tree, Master Theorem) · CS 412 - Ch 4 part 1 (Divide-and-Conquer)
    Ch 4_Part1 slide 21: 'This chapter offers four methods for solving recurrences: The iteration method ... The substitution method ... The recursion-tree method ... The master method provides bounds for recurrences of the form: T(n) = aT(n/b) + f(n).' Ch 4_Part1 slide 63: 'Theorem 4.1 (Master theorem) ... three cases.'
  • Divide-and-conquer paradigm (divide / conquer / combine; recurrence formulation) · CS 412 - Ch 2 part 2 (Merge sort), CS 412 - Ch 4 part 1, CS 412 - Ch 4 part 2
    Ch 4_Part1 slide 4: 'The divide-and-conquer design paradigm: Divide the problem (instance) into subproblems. Conquer the subproblems by solving them recursively. Combine subproblem solutions.'
  • Merge sort (recursive split, MERGE auxiliary procedure with sentinels, Θ(n lg n) analysis) · CS 412 - Ch 2 part 2 (Merge sort)
    Ch 2_part2 slide 10: 'Alg.: MERGE-SORT(A, p, r) if p < r then q = (p + r)/2 ; MERGE-SORT(A, p, q); MERGE-SORT(A, q + 1, r); MERGE(A, p, q, r).' Slide 49: 'Total = Θ(n lg n).'
  • Quicksort and randomized quicksort (Lomuto partition; worst-case Θ(n^2), expected Θ(n lg n)) · CS 412 - Ch 7 (Quicksort)
    Ch 7 slide 12: 'PARTITION(A, p, r): x ← A[r] // pivot = A[r]; i ← p-1; for j ← p to r-1: if A[j] ≤ x then i ← i+1; exchange A[i]↔A[j]; exchange A[i+1]↔A[r]; return i+1.' Slide 43: 'Randomized-Quicksort'.
  • Heapsort and binary max-heap (MAX-HEAPIFY, BUILD-MAX-HEAP, array-as-tree representation) · CS 412 - Ch 6 (Heapsort)
    Ch 6 slide 15: 'MAX-HEAPIFY(A, i): l ← LEFT(i); r ← RIGHT(i); ... if largest ≠ i then exchange A[i]↔A[largest]; MAX-HEAPIFY(A, largest).' Slide 25: 'HEAPSORT(A): BUILD-MAX-HEAP(A); for i ← A.length downto 2: exchange A[1]↔A[i]; A.heap-size = A.heap-size - 1; MAX-HEAPIFY(A, 1).'
  • Elementary comparison-based sorts: insertion sort, bubble sort, selection sort (Θ(n^2)) · CS 412 - Ch 2 part 1
    Ch 2_part1 slide 23: 'INSERTION-SORT(A): for j ← 2 to n: do key ← A[j]; i ← j-1; while i>0 and A[i]>key: do A[i+1]←A[i]; i ← i-1; A[i+1] ← key.' Slide 48: 'BUBBLESORT(A) ... ' Slide 52: 'SELECTION-SORT(A) ... '
  • Binary search (recursive halving on a sorted array; T(n) = T(n/2) + Θ(1)) · CS 412 - Ch 4 part 1
    Ch 4_Part1 slide 13: 'BINARY-SEARCH (A, lo, hi, x): if (lo > hi) return FALSE; mid ← (lo+hi)/2; if x = A[mid] return TRUE; if (x < A[mid]) BINARY-SEARCH (A, lo, mid-1, x); if (x > A[mid]) BINARY-SEARCH (A, mid+1, hi, x).'
  • Strassen's algorithm for matrix multiplication (7 recursive multiplies, Θ(n^lg7) ≈ Θ(n^2.81)) · CS 412 - Ch 4 part 2
    Ch 4_Part2 slide 21: 'Multiply 2×2 matrices with only 7 recursive mults. P1 = a × (f – h); P2 = (a + b) × h; ...' Slide 26: 'T(n) = 7 T(n/2) + Θ(n^2) ... T(n) = Θ(n^lg 7).'
  • Dynamic programming (optimal substructure, overlapping subproblems, top-down memoization, bottom-up tabulation) · CS 412 - Ch 15 part 1, CS 412 - Ch 15 part 2
    Ch 15_part1 slide 13: 'How to design a dynamic-programming algorithm? 1. Characterize the structure of an optimal solution ... 2. Recursively define the value of an optimal solution ... 3. Compute the value of an optimal solution typically in a bottom-up fashion. 4. Construct an optimal solution from computed information.'
  • Rod-cutting DP problem (recurrence rn = max(pi + r(n-i)), Θ(n^2)) · CS 412 - Ch 15 part 1
    Ch 15_part1 slide 32: 'Bottom-Up-Cut Rod(p, n): r[0] = 0; for j = 1 to n: q = -∞; for i = 1 to j: q = max(q, p[i] + r[j - i]); r[j] = q; return r[n].'
  • Longest Common Subsequence (LCS) DP (Θ(mn) table c[i,j] with optimal-choice table b[i,j]) · CS 412 - Ch 15 part 2
    Ch 15_part2 slide 33: 'c[i,j] = 0 if i=0 or j=0; c[i-1,j-1]+1 if xi = yj; max(c[i,j-1], c[i-1,j]) if xi ≠ yj.' Slide 35: 'LCS-LENGTH(X, Y, m, n) ... Running time: Θ(mn).'
  • Binary Search Tree (BST) operations: insertion, deletion (3 cases), search, min/max, successor, predecessor in O(h) · CS 412 - Ch 13 part 1&2
    Ch 13 slide 19: 'Operations: insertion, deletion, search, maximum, minimum, successor, predecessor. O(h), h is the height of the tree ... Best case: O(log n). Worst case: O(n).' Slides 14–16 cover the three deletion cases.
  • Red-Black Trees (balanced BST with color invariant, O(lg n) worst-case dynamic-set operations) · CS 412 - Ch 13 part 1&2
    Ch 13 slide 22: 'Properties of red-black tree: Every node is either red or black. The root is black. Every leaf (NIL) is black. If a node is red, then both its children are black ... For each node, all paths from that node to descendant leaves contain the same number of black nodes.'
  • Graph representations: adjacency list (Θ(V+E)) and adjacency matrix (Θ(V^2)); directed/undirected, weighted/unweighted · CS 412 - Ch 22 part 1 (Elementary Graph Algorithms)
    Ch 22_part1 slide 21: 'Two standard ways: Adjacency List — Preferred for sparse graphs (|E| is much less than |V|^2) ... Adjacency Matrix — Preferred for dense graphs (|E| is close to |V|^2).' Slide 24: 'Memory required Θ(V + E).' Slide 28: 'Memory required Θ(V^2).'
  • Breadth-First Search (BFS): queue-based, white/gray/black coloring, BFS tree, shortest-path-in-edges, O(V+E) · CS 412 - Ch 22 part 2
    Ch 22_part2 slide 28: 'Each vertex is enqueued once and dequeued once: O(V) ... the total time spent in scanning adjacency lists is O(E). Total: O(V+E).' Slide 29: 'd[v] = δ(s,v) for all v in V.'
  • Depth-First Search (DFS): recursive, discovery/finish timestamps, edge classification (tree/back/forward/cross), parenthesis theorem, O(V+E) · CS 412 - Ch 22 part 2
    Ch 22_part2 slide 59: 'DFS: Analysis Time complexity: O(V+E).' Slide 60: 'Parenthesis Theorem ... three conditions.' Slide 63: 'Tree edges ... Back edges ... Forward edges ... Cross edges.'
  • Loop-invariant proofs (initialization / maintenance / termination) for algorithm correctness · CS 412 - Ch 2 part 1, CS 412 - Ch 2 part 2
    Ch 2_part1 slide 24: 'We must show three things about a loop invariant: Initialization: It is true prior to the first iteration of the loop. Maintenance: If it is true before an iteration of the loop, it remains true before the next iteration. Termination: When the loop terminates, the invariant gives us a useful property that helps show that the algorithm is correct.'
  • Mathematical induction for asymptotic-bound proofs · CS 412 - Ch 3 (Growth of Functions)
    Ch 3 slide 41: 'Mathematical Induction: Basis step: prove that the statement is true for n = 1. Inductive step: assume that S(n) is true and prove that S(n+1) is true for all n ≥ 1.'
  • RAM (Random-Access Machine) model and primitive-operation step counting · CS 412 - Ch 2 part 1
    Ch 2_part1 slide 30: 'we shall assume a generic one processor, random-access machine (RAM) model of computation ... Arithmetic (such as add, subtract, multiply, divide, remainder, floor, ceiling). Data movement (load, store, copy). Control (conditional and unconditional branch, subroutine call and return).'

No prescriptions are issued. The Market-fit agent surfaced zero in-scope gaps (gap_count = 0) because every backend skill demanded by ≥30% of postings — SQL (100%), Docker (92%), Postgres (92%), REST APIs (92%), AWS (83%), unit testing (83%), Git (75%), Linux (75%), CI/CD (67%), microservices (67%), Kubernetes (58%), OAuth (58%), Redis (58%), GraphQL (50%), JWT (50%), Kafka (50%) — has 0% partial coverage in the slides and is cross-domain to algorithm theory. Under the extend-partial-coverage rule (Rule 1) and the course's depth bound (classical pseudocode-level algorithms, Rule 2), none of these can be honestly grafted onto an existing CS 412 chapter without becoming a new course.

These prescriptions close 0% of the live backend job-market gap, and that is the correct, honest answer for this course. CS 412 is doing exactly what a classical algorithms course should do — asymptotic analysis, divide-and-conquer, DP, balanced BSTs, BFS/DFS at the pseudocode level — and the backend market gap (SQL/Docker/Postgres/REST/AWS/K8s/Kafka/Redis/OAuth/JWT/microservices) is a curriculum-level concern that belongs in a separate Databases, Systems, Networks, or Cloud/DevOps course, not in CS 412. Recommending those topics here would violate the course's stated depth bound and the extend-partial-coverage rule. The top backend-market signals to relay to the program's curriculum committee (not to CS 412) are: SQL + Postgres (~96% combined), containerization with Docker/Kubernetes (~75% combined), REST/GraphQL API design (~71% combined), and AWS cloud deployment (83%) — these warrant dedicated coursework elsewhere in the major.