Exploring Recursion: A Fundamentally Important Technique in Data Science
Recursion is a fundamental concept in computer science and programming, and is widely used in data science as well. It is a technique where a function calls itself repeatedly until a specific condition is met. Recursion is particularly useful when solving problems that can be broken down into smaller, similar sub-problems.
What is Recursion?
Recursion is a programming technique where a function calls itself. A recursive function can be defined as a function that solves a problem by breaking it down into smaller versions of the same problem. The function calls itself with a smaller version of the original problem, until the problem becomes small enough that it can be solved directly, without further recursion.
Recursion can be used to solve problems that can be broken down into smaller, similar sub-problems. For example, if we want to calculate the factorial of a number, we can use recursion to break down the problem into smaller sub-problems until we reach the base case, where the factorial of 1 is simply 1.
Recursive Functions
A recursive function is a function that calls itself. The function must have a base case, which is the condition that causes the function to stop calling itself. Without a base case, the function will continue to call itself infinitely, resulting in an infinite loop.
Let's take an example of a recursive function that calculates the factorial of a number:
def factorial(n): if n == 1: return 1 else: return n * factorial(n-1)--
In this function, the base case is when
n equals 1. If n is not 1, the function calls itself with n-1, until n becomes 1. Once n is 1, the function returns 1, which is the result of the factorial.Recursion in Data Science
Recursion is widely used in data science to solve problems that can be broken down into smaller sub-problems. For example, in decision trees, each node in the tree represents a sub-problem, and the tree is built recursively by breaking down the problem into smaller sub-problems.
Another example is in the implementation of the k-means clustering algorithm, where the algorithm recursively partitions the data into smaller clusters until the clusters become small enough to be considered as individual clusters.
Recursion can also be used to traverse data structures such as trees, graphs, and linked lists. For example, in a binary tree, we can use recursion to traverse the tree and perform operations on each node.
Problems to Solve with Recursion
1.You are given an array
people where people[i] is the weight of the ith person, and an infinite number of boats where each boat can carry a maximum weight of limit. Each boat carries at most two people at the same time, provided the sum of the weight of those people is at most limit.Return the minimum number of boats to carry every given person.