Problem solving

• Problem-solving strategy


  A plan used to find a solution or overcome a challenge
• Different problem-solving strategies


  • Trial and error
  • Algorithm
  • Heuristic
  • Means-ends analysis
  • Past experience
  • Bring in a facilitator
  • Decision matrix
  • Peer assistance
  • Step away
• Trial and error


  Trying different solutions and ruling out those that don't work
• Algorithm


  Step-by-step problem-solving formula that always produces the same result when followed exactly
• Heuristic


  General problem-solving framework or "rule of thumb" that saves time and energy but is not always the most rational method
• Types of heuristics


  • Working backwards
  • Breaking down tasks
• Means-ends analysis


  Analyzing actions in smaller steps to achieve the goal
• Tower of Hanoi puzzle


  • Move a stack of discs from the leftmost rod to the rightmost rod, following the rules: 1) Move only one disk at a time, 2) Place disks on top of another stack or an empty rod, 3) No larger disk on top of a smaller disk
• Methods for solving the Tower of Hanoi

  • Iterative
  • Recursive
  • Non-recursive
  • Binary and Gray-code
  • Graphical representations
• Brute-force approach


  Lacks sophistication, takes the most direct or obvious route, does not minimize the number of operations required
• Divide and conquer approach


  Problem is solved recursively in three steps: Divide, Conquer, and Combine
• Merge Sort Algorithm


  • Divide an array into two halves, 2) Recursively sort each half, 3) Combine the sorted halves
• Dynamic programming approach


  Similar to divide-and-conquer but reuses results of sub-problems, bottom-up technique that solves smallest sub-problems first
• Fibonacci Series


  • Sequence where each term is the sum of the two preceding ones
• Greedy algorithm approach


  At each step, makes the choice with the smallest immediate cost, does not look ahead to find the global optimum
• Randomized approach


  Depends on input data and values from a random number generator, often more effective when determining the optimal choice is difficult
• Randomized approaches are widely used in computer security and games