Flowcharts in Problem Solving

Flowcharts are visual representations of the steps involved in a process. They help in understanding and organizing the flow of a problem-solving approach. By using symbols and arrows, flowcharts depict the sequence of actions and decisions required to solve a problem.

Flowcharts and the Guess the Number Game

Let's revisit the "Guess the Number" game and see how a flowchart helps in understanding the process:

    flowchart TD
        A(["Start"]) --> B[Guess a number between 1 and 100]
        B --> C{Is the guess correct?}
        C -->|Yes| D(["End - You've guessed the number!"])
        C -->|No| E{Is the guess too high or too low?}
        E -->|Too high| F[Adjust guess lower]
        E -->|Too low| G[Adjust guess higher]
        F --> B
        G --> B
    

This flowchart breaks down the game into its fundamental steps, making it easier to understand and analyze. By following the flowchart, you can see the logical progression of the game and how each decision leads to the next step.

Using Flowcharts to Solve Complex Problems

Flowcharts are not just limited to simple games; they are powerful tools for tackling complex problems. By visually mapping out each step and decision point, you can identify potential issues, optimize processes, and communicate solutions more effectively.

Flowchart Symbols

Here is a table that explains some common flowchart symbols:

                    flowchart TD
                        A(["Start"]) --> B(["End"])
                    

                    flowchart TD
                        A[Process]
                    

                    flowchart TD
                        A{Decision}
                    

                    flowchart TD
                        A[/Input/Output/]
                    

                    flowchart LR
                        A{{Hexagon}}
                    

Introducing Analysis of Algorithms

Understanding the steps and flow of a problem-solving process is just the beginning. Analysing the efficiency and effectiveness of these steps is crucial for optimising solutions. This is where the analysis of algorithms comes into play.

Big O Notation

Big O notation is a way to describe the efficiency of an algorithm. It provides an upper bound on the time complexity or space complexity of an algorithm, helping us understand how the algorithm's performance scales with the size of the input.

For example, an algorithm with a time complexity of O(n) will take linear time to complete, meaning the time required grows linearly with the input size. On the other hand, an algorithm with a time complexity of O(log n) will take logarithmic time, growing much slower as the input size increases.

Reiterating a statement made earlier, when we have a problem, we can use more than one approach to arrive at a solution. Let us see a few different approaches to solve the 'Guess the number' game.

Alternative Method: Binary Search Algorithm

In the "Guess the Number" game, the strategy of starting with the middle number and adjusting based on feedback is similar to the binary search algorithm. This algorithm efficiently narrows down the possible range by repeatedly dividing it in half.

    flowchart TD
        A(["Start"]) --> B[Set low = 1, high = 100]
        B --> C{Is low <= high?}
        C -->|No| D(["End - Number not found"])
        C -->|Yes| E["Set mid = (low + high) / 2"]
        E --> F{Is mid == target?}
        F -->|Yes| G(["End - Number found"])
        F -->|No| H{Is mid < target?}
        H -->|Yes| I[Set low = mid + 1] --> B
        H -->|No| J[Set high = mid - 1] --> B
    

The binary search algorithm is efficient because it reduces the search range by half with each step, leading to a time complexity of O(log n). This makes it significantly faster than a linear search, especially for large datasets.

Alternative Method: Linear Search Algorithm

Another way to find the number is using a linear search, where you start from one end and check each number until you find the target. This method has a time complexity of O(n), making it less efficient for large datasets compared to binary search.

    flowchart TD
        A(["Start"]) --> B[Set index = 1]
        B --> C{Is index <= 100?}
        C -->|No| D(["End - Number not found"])
        C -->|Yes| E[Is number at index == target?]
        E -->|Yes| F(["End - Number found"])
        E -->|No| G[Increment index by 1] --> B
    

Interactive Activity: Guess the Number

By comparing the efforts required in these three methods, you can understand the relative efficiency of each algorithm. Binary search, with a time complexity of O(log n), is more efficient than linear search, which has a time complexity of O(n).

By using flowcharts and analysing algorithms, we can enhance our problem-solving skills and develop more efficient solutions. Whether it's a simple game or a complex real-world problem, these tools and techniques are invaluable for effective problem-solving.