Introduction to Algorithms

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2022). Introduction to Algorithms. MIT Press.

Type

Book

Intellectual base

Textbook

Year

2022

ISBN

9780262046305

Link

https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/

Cited by

7 citations across 7 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Disjoint-Set Data Structure
  • The disjoint-set forest is the standard implementation, not the only possible realization.
• Divide-and-conquer algorithm
  • A divide-and-conquer algorithm solves base instances directly and solves larger instances by dividing them into two or more smaller related instances, recursively solving those instances, and combining their answers into one answer for the original instance.
• Held–Karp algorithm
  • … cities and endpoint j, the table stores the cheapest route from city 1 visiting exactly that subset and ending at j, then chooses the cheapest return edge. to An exact benchmark implementation uses bit masks for subsets and predecessor pointers to recover a tour while reporting exponential memory and time limits..
• Hybrid algorithm
  • … between constitutive identity and a convenient observable transfers from Introsort begins with quicksort and switches to heapsort when recursion depth threatens quicksort's worst case. to Design benchmarks selection overhead and adversarial thresholds and proves the fallback retains the advertised complexity..
• Optimal Substructure
  • Greedy correctness requires an additional exchange, cut, matroid, or dominance argument.
• Running total
  • For example, the distinction between constitutive identity and a convenient observable transfers from For inputs five, eight and three, the running totals are five, thirteen and sixteen. to An implementation handles overflow, floating-point error, late corrections and reset boundaries explicitly..

Mechanisms

• Divide-and-Conquer Algorithm
  • When subproblems are genuinely independent and the combine step is cheap relative to the reduction in problem size, divide-and-conquer converts an intractable whole into a shallow recursion tree with a provable running time you can read straight off the recurrence.

    This sourceRepresents divide-and-conquer running time with a recurrence and derives provable asymptotic bounds using the Master Theorem for covered forms.

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