36 docs tagged with "algorithms"

Capacity-indexed dynamic programming and the direction of one-dimensional updates.

Maximum-cardinality interval scheduling by earliest finish time.

A map for analyzing algorithms, recognizing design patterns, and choosing an appropriate problem-solving family.

Depth-first search over decisions with reversible state and sound pruning.

Single-source shortest paths with negative edges and reachable negative-cycle detection.

Boundary search over sorted random-access data or monotone predicates.

Layered graph traversal and shortest paths by edge count.

Adjacent-swap sorting, its invariant, and its narrow practical role.

Stack-based graph traversal, parent structure, and DFS-specific guarantees.

Single-source shortest paths with nonnegative edge weights.

Independent recursive subproblems, combine costs, and recurrence-based analysis.

A state-first method for problems with reusable subproblem structure.

A small recurrence illustrating repeated subproblems and state compression.

Dynamic programming for all-pairs shortest paths and negative-cycle detection.

Density-ordered selection when items are continuously divisible.

A problem-first map for traversal, shortest paths, and minimum spanning trees.

Local-choice algorithms organized around proof obligations and counterexamples.

In-place sorting with a binary heap and a worst-case n-log-n bound.

Optimal binary prefix codes for known symbol frequencies.

Adaptive stable sorting for small or nearly ordered ranges.

Minimum spanning forests by sorted edges and disjoint-set union.

Sequential lookup without ordering or preprocessing assumptions.

Sequence-alignment dynamic programming with length and reconstruction trade-offs.

Stable divide-and-conquer sorting with predictable runtime and linear array workspace.

The cut property connecting Prim's and Kruskal's safe edge choices.

Position-based enumeration with duplicate-value symmetry pruning.

Growing a minimum spanning tree across the lightest eligible cut edge.

Partition-based sorting, pivot risk, duplicate handling, and stack discipline.

A decision map for lookup, ordered search, and graph traversal.

Minimum-selection sorting with fixed comparison cost and few swaps.

The recurrence view of shortest paths and a bridge to graph-specific algorithms.

A decision map for comparison sorting, stability, adaptiveness, and memory trade-offs.

Peak memory analysis across input, output, auxiliary state, and recursion.

A precise 0/1 subset-sum search and its pruning boundaries.

Asymptotic runtime analysis with explicit input measures, models, and case assumptions.

Profit-maximizing unit jobs scheduled into their latest feasible slots.