To implement a program to find out the largest and smallest number from a list / array using recursive divide and conquer algorithm.
The given program is an implementation of the "maximum and minimum" problem using a divide-and-conquer approach. The goal is to find both the maximum and minimum elements in a given list 'a' within a specified range.
The program defines a function called 'maxmin' that takes three parameters: the list 'a', the starting index 's', and the ending index 'e'. It uses a helper function to recursively divide the list into smaller sub lists until it reaches the base case, which is when 's' is equal to 'e' (indicating a sublist with only one element).
In the base case, the function creates a temporary list 't' with two elements. Both elements are set to the single element in the sub list 'a[s]', representing both the 'maximum' and 'minimum' value. This sub list is then returned as the result.
In the recursive case, the function calculates the middle index 'mid' as the floor division of the sum of 's' and 'e' divided by 2. It then recursively calls 'maxmin' on the left and right halves of the list, i.e., from 's' to 'mid' and from 'mid + 1' to 'e', respectively.
Once the recursive calls return, the function compares the maximum and minimum values of the left and right sub lists. If the maximum value of the left sub list (lmaxmin) is greater than the maximum value of the right sub list (rmaxmin), it checks if the minimum value of the left sub list (lmaxmin) is greater than the minimum value of the right sub list (rmaxmin). If both conditions are true, it sets the result (res) to have the maximum value from the right sub list and the minimum value from the left sub list.
If the maximum value of the left sub list is not greater than the maximum value of the right sub list, it sets the result to have the maximum value from the right sub list and the maximum value from the left sub list.
If the minimum value of the left sublist is not greater than the minimum value of the right sublist, it sets the result to have the minimum value from the left sub list and the maximum value from the right sub list.
Finally, the function returns the result containing the maximum and minimum values found in the given sub list.
It's important to note that the program assumes the existence of a global list 't' and 'a' global list 'res', which are not explicitly defined in the code provided. These lists should be defined before calling the 'maxmin' function in order for the program to work correctly.
The divide and conquer strategy is a problem-solving approach in computer science and mathematics that involves breaking down a complex problem into smaller sub problems, solving them independently, and then combining the solutions to solve the original problem. The name comes from the three main steps involved:
The divide and conquer strategy is often used to solve problems that are difficult to solve directly, such as sorting algorithms, matrix multiplication, and finding the closest pair of points in a set.
The main advantage of the divide and conquer strategy is that it allows for parallel processing of the sub problems, which can result in faster processing times. Additionally, it can be easier to reason about and debug smaller sub problems rather than the original, larger problem.
Some common algorithms that use the Divide and Conquer strategy include:
By learning the Divide and Conquer algorithm to find the maximum value of an array, you can achieve several learning outcomes, including: