You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
89 lines
4.3 KiB
89 lines
4.3 KiB
---
|
|
id: recursion
|
|
title: Recursion cheatsheet for coding interviews
|
|
description: Recursion study guide for coding interviews, including practice questions, techniques, time complexity, and recommended resources
|
|
keywords:
|
|
[
|
|
recursion coding interview study guide,
|
|
recursion tips for coding interviews,
|
|
recursion practice questions,
|
|
recursion useful techniques,
|
|
recursion time complexity,
|
|
recursion recommended study resources,
|
|
]
|
|
sidebar_label: Recursion
|
|
toc_max_heading_level: 2
|
|
---
|
|
|
|
<head>
|
|
<meta property="og:image" content="https://www.techinterviewhandbook.org/social/algorithms/algorithms/algorithms-recursion.png" />
|
|
</head>
|
|
|
|
## Introduction
|
|
|
|
Recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem.
|
|
|
|
All recursive functions contains two parts:
|
|
|
|
1. A base case (or cases) defined, which defines when the recursion is stopped - otherwise it will go on forever!
|
|
1. Breaking down the problem into smaller subproblems and invoking the recursive call
|
|
|
|
One of the most common example of recursion is the Fibonacci sequence.
|
|
|
|
- Base cases: `fib(0) = 0` and `fib(1) = 1`
|
|
- Recurrence relation: `fib(i) = fib(i-1) + fib(i-2)`
|
|
|
|
```py
|
|
def fib(n):
|
|
if n <= 1:
|
|
return n
|
|
return fib(n - 1) + fib(n - 2)
|
|
```
|
|
|
|
Many algorithms relevant in coding interviews make heavy use of recursion - binary search, merge sort, tree traversal, depth-first search, etc. In this article, we focus on questions which use recursion but aren't part of other well known algorithms.
|
|
|
|
## Learning resources
|
|
|
|
- Readings
|
|
- [Recursion](https://www.cs.utah.edu/~germain/PPS/Topics/recursion.html), University of Utah
|
|
- Videos
|
|
- [Tail Recursion](https://www.coursera.org/lecture/programming-languages/tail-recursion-YZic1), University of Washington
|
|
|
|
<!-- TODO: Talk about backtracking -->
|
|
|
|
## Things to look out for during interviews
|
|
|
|
- Always remember to always define a base case so that your recursion will end.
|
|
- Recursion is useful for permutation, because it generates all combinations and tree-based questions. You should know how to generate all permutations of a sequence as well as how to handle duplicates.
|
|
- Recursion implicitly uses a stack. Hence all recursive approaches can be rewritten iteratively using a stack. Beware of cases where the recursion level goes too deep and causes a stack overflow (the default limit in Python is 1000). You may get bonus points for pointing this out to the interviewer. Recursion will never be O(1) space complexity because a stack is involved, unless there is [tail-call optimization](https://stackoverflow.com/questions/310974/what-is-tail-call-optimization) (TCO). Find out if your chosen language supports TCO.
|
|
- Number of base cases - In the fibonacci example above, note that one of our recursive calls invoke `fib(n - 2)`. This indicates that you should have 2 base cases defined so that your code covers all possible invocations of the function within the input range. If your recursive function only invokes `fn(n - 1)`, then only one base case is needed
|
|
|
|
## Corner cases
|
|
|
|
- `n = 0`
|
|
- `n = 1`
|
|
- Make sure you have enough base cases to cover all possible invocations of the recursive function
|
|
|
|
## Techniques
|
|
|
|
### Memoization
|
|
|
|
In some cases, you may be computing the result for previously computed inputs. Let's look at the Fibonacci example again. `fib(5)` calls `fib(4)` and `fib(3)`, and `fib(4)` calls `fib(3)` and `fib(2)`. `fib(3)` is being called twice! If the value for `fib(3)` is memoized and used again, that greatly improves the efficiency of the algorithm and the time complexity becomes O(n).
|
|
|
|
## Recommended questions
|
|
|
|
- [Letter Combinations of a Phone Number](https://leetcode.com/problems/letter-combinations-of-a-phone-number/)
|
|
- [Generate Parentheses](https://leetcode.com/problems/generate-parentheses/)
|
|
- [Combinations](https://leetcode.com/problems/combinations/)
|
|
- [Subsets](https://leetcode.com/problems/subsets/)
|
|
- [Subsets II](https://leetcode.com/problems/subsets-ii/)
|
|
- [Permutations](https://leetcode.com/problems/permutations/)
|
|
- [Sudoku Solver](https://leetcode.com/problems/sudoku-solver/)
|
|
- [Strobogrammatic Number II (LeetCode Premium)](https://leetcode.com/problems/strobogrammatic-number-ii/)
|
|
|
|
## Recommended courses
|
|
|
|
import AlgorithmCourses from '../\_courses/AlgorithmCourses.md'
|
|
|
|
<AlgorithmCourses />
|