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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 36 of 43
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General Method

Backtracking is an algorithmic-technique for solving problems recursively by trying to build a solution incrementally, one piece at a time, removing those solutions that fail to satisfy the constraints of the problem at any point of time (by time, here, is referred to the time elapsed till reaching any level of the search tree).

Backtracking algorithm is applied to some specific types of problems,

  • Decision problem used to find a feasible solution of the problem.
  • Optimisation problem used to find the best solution that can be applied.
  • Enumeration problem used to find the set of all feasible solutions of the problem.

In backtracking problem, the algorithm tries to find a sequence path to the solution which has some small checkpoints from where the problem can backtrack if no feasible solution is found for the problem.

Example,

KodNest Capture36

Here,

Green is the start point, blue is the intermediate point, red are points with no feasible solution, dark green is end solution.

Here, when the algorithm propagates to an end to check if it is a solution or not, if it is then returns the solution otherwise backtracks to the point one step behind it to find track to the next point to find solution.

Algorithm

Step 1 − if current_position is goal, return success
Step 2 − else,
Step 3 − if current_position is an end point, return failed.
Step 4 − else, if current_position is not end point, explore and repeat above steps.

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