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Document Outline

  • Contents at a Glance
  • Contents
  • About the Author
  • About the Technical Reviewer
  • Acknowledgments
  • Preface
  • Chapter 1: Introduction
    • What’s All This, Then?
    • Why Are You Here?
    • Some Prerequisites
    • What’s in This Book
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 2: The Basics
    • Some Core Ideas in Computing
    • Asymptotic Notation
      • It’s Greek to Me!
      • Rules of the Road
      • Taking the Asymptotics for a Spin
      • Three Important Cases
      • Empirical Evaluation of Algorithms
    • Implementing Graphs and Trees
      • Adjacency Lists and the Like
      • Adjacency Matrices
      • Implementing Trees
      • A Multitude of Representations
    • Beware of Black Boxes
      • Hidden Squares
      • The Trouble with Floats
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 3: Counting 101
    • The Skinny on Sums
      • More Greek
      • Working with Sums
    • A Tale of Two Tournaments
      • Shaking Hands
      • The Hare and the Tortoise
    • Subsets, Permutations, and Combinations
    • Recursion and Recurrences
      • Doing It by Hand
      • A Few Important Examples
      • Guessing and Checking
      • The Master Theorem: A Cookie-Cutter Solution
    • So What Was All That About?
    • Summary
    • If You’re Curious ...
    • Exercises
    • References
  • Chapter 4: Induction and Recursion ... and Reduction
    • Oh, That’s Easy!
    • One, Two, Many
    • Mirror, Mirror
    • Designing with Induction (and Recursion)
      • Finding a Maximum Permutation
      • The Celebrity Problem
      • Topological Sorting
    • Stronger Assumptions
    • Invariants and Correctness
    • Relaxation and Gradual Improvement
    • Reduction + Contraposition = Hardness Proof
    • Problem Solving Advice
    • Summary
    • If You’re Curious ...
    • Exercises
    • References
  • Chapter 5: Traversal: The Skeleton Key of Algorithmics
    • A Walk in the Park
      • No Cycles Allowed
      • How to Stop Walking in Circles
    • Go Deep!
      • Depth-First Timestamps and Topological Sorting (Again)
    • Infinite Mazes and Shortest (Unweighted) Paths
    • Strongly Connected Components
    • Summary
    • If You’re Curious ...
    • Exercises
    • References
  • Chapter 6: Divide, Combine, and Conquer
    • Tree-Shaped Problems: All About the Balance
    • The Canonical D&C Algorithm
    • Searching by Halves
      • Traversing Search Trees ... with Pruning
      • Selection
    • Sorting by Halves
      • How Fast Can We Sort?
    • Three More Examples
      • Closest Pair
      • Convex Hull
      • Greatest Slice
    • Tree Balance ... and Balancing *
    • Summary
    • If You’re Curious ...
    • Exercises
    • References
  • Chapter 7: Greed Is Good? Prove It!
    • Staying Safe, Step by Step
    • The Knapsack Problem
      • Fractional Knapsack
      • Integer Knapsack
    • Huffman’s Algorithm
      • The Algorithm
      • The First Greedy Choice
      • Going the Rest of the Way
      • Optimal Merging
    • Minimum Spanning Trees
      • The Shortest Edge
      • What About the Rest?
      • Kruskal’s Algorithm
      • Prim’s Algorithm
    • Greed Works. But When?
      • Keeping Up with the Best
      • No Worse Than Perfect
      • Staying Safe
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 8: Tangled Dependencies and Memoization
    • Don’t Repeat Yourself
    • Shortest Paths in Directed Acyclic Graphs
    • Longest Increasing Subsequence
    • Sequence Comparison
    • The Knapsack Strikes Back
    • Binary Sequence Partitioning
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 9: From A to B with Edsger and Friends
    • Propagating Knowledge
    • Relaxing like Crazy
    • Finding the Hidden DAG
    • All Against All
    • Far-Fetched Subproblems
    • Meeting in the Middle
    • Knowing Where You’re Going
    • Summary
    • If You’re Curious ...
    • Exercises
    • References
  • Chapter 10: Matchings, Cuts, and Flows
    • Bipartite Matching
    • Disjoint Paths
    • Maximum Flow
    • Minimum Cut
    • Cheapest Flow and the Assignment Problem *
    • Some Applications
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 11: Hard Problems and (Limited) Sloppiness
    • Reduction Redux
    • Not in Kansas Anymore?
    • Meanwhile, Back in Kansas …
    • But Where Do You Start? And Where Do You Go from There?
    • A Ménagerie of Monsters
      • Return of the Knapsack
      • Cliques and Colorings
      • Paths and Circuits
    • When the Going Gets Tough, the Smart Get Sloppy
    • Desperately Seeking Solutions
    • And the Moral of the Story Is …
    • Summary
    • If You’re Curious …
    • Exercises
    • References
  • Chapter 12: Pedal to the Metal: Accelerating Python
  • Chapter 13: List of Problems and Algorithms
    • Problems
    • Algorithms and Data Structures
  • Chapter 14: Graph Terminology
  • Chapter 15: Hints for Exercises
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Chapter 9
    • Chapter 10
    • Chapter 11
  • Index

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