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Algorithm

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  1. Getting Started with Algorithm
    What is an Algorithm?
  2. Characteristics of Algorithm
    1 Topic
  3. Analysis Framework
  4. Performance Analysis
    3 Topics
  5. Mathematical Analysis
    2 Topics
  6. Sorting Algorithm
    Sorting Algorithm
    10 Topics
  7. Searching Algorithm
    6 Topics
  8. Fundamental of Data Structures
    Stacks
  9. Queues
  10. Graphs
  11. Trees
  12. Sets
  13. Dictionaries
  14. Divide and Conquer
    General Method
  15. Binary Search
  16. Recurrence Equation for Divide and Conquer
  17. Finding the Maximum and Minimum
  18. Merge Sort
  19. Quick Sort
  20. Stassen’s Matrix Multiplication
  21. Advantages and Disadvantages of Divide and Conquer
  22. Decrease and Conquer
    Insertion Sort
  23. Topological Sort
  24. Greedy Method
    General Method
  25. Coin Change Problem
  26. Knapsack Problem
  27. Job Sequencing with Deadlines
  28. Minimum Cost Spanning Trees
    2 Topics
  29. Single Source Shortest Paths
    1 Topic
  30. Optimal Tree Problem
    1 Topic
  31. Transform and Conquer Approach
    1 Topic
  32. Dynamic Programming
    General Method with Examples
  33. Multistage Graphs
  34. Transitive Closure
    1 Topic
  35. All Pairs Shortest Paths
    6 Topics
  36. Backtracking
    General Method
  37. N-Queens Problem
  38. Sum of Subsets problem
  39. Graph Coloring
  40. Hamiltonian Cycles
  41. Branch and Bound
    2 Topics
  42. 0/1 Knapsack problem
    2 Topics
  43. NP-Complete and NP-Hard Problems
    1 Topic
Lesson 31 of 43
In Progress

Transform and Conquer Approach

This chapter deals with a group of design methods that are based on the idea of transformation. We call this general technique transform-and-conquer because these methods work as two-stage procedures. First, in the transformation stage, the problem’s instance is modified to be, for one reason or another, more amenable to solution. Then, in the second or conquering stage, it is solved.

There are three major variations of this idea that differ by what we transform a given instance to (Figure 1):

  • Transformation to a simpler or more convenient instance of the same problem—we call it instance simplification.
  • Transformation to a different representation of the same instance—we call it representation change.
  • Transformation to an instance of a different problem for which an algorithm is already available—we call it problem reduction.
KodNest image 2
FIGURE 1: Transform-and-conquer strategy.

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