How to apply scientific method to programming? - mmedrano9438/peripheral-brain GitHub Wiki

The base case is the simplest or smallest instance of the problem that can be verified directly. The induction step is the assumption that if the statement or formula holds for some value of the input, then it also holds for the next value.

so for example: Write a JavaScript program to get integers in the range (x, y) using recursion.
Example : range(2, 9) Expected Output : [3, 4, 5, 6, 7, 8]

// Function to generate a range of numbers between start_num and end_num (exclusive). var range = function(start_num, end_num) { // Base case: if the difference between end_num and start_num is 2, // return an array containing the number between them. if (end_num - start_num === 2) { return [start_num + 1]; } else { // Recursive case: generate the range between start_num and end_num - 1, // then push the current end_num - 1 to the array. var list = range(start_num, end_num - 1); list.push(end_num - 1); return list; } };

// Example usage: Generate and print the range of numbers between 2 and 9 (exclusive). console.log(range(2, 9));

Here's a general guide:

  1. Base Case:

    • Identify the smallest input or case for which your algorithm should work.
    • Prove that the algorithm produces the correct output for this base case.

  2. Inductive Hypothesis:

    • Assume that the algorithm works correctly for an arbitrary case, represented by an input size 'k'.

  3. Inductive Step:

    • Show that if the algorithm works for the 'k' case, it will also work for the next case, 'k+1'.
    • This involves demonstrating that, based on the assumption, the algorithm correctly handles the increase in input size or complexity.

  4. Conclusion:

    • Conclude that since the algorithm works for the base case and the inductive step, it is correct for all cases.