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96 lines
4.5 KiB
96 lines
4.5 KiB
5 years ago
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---
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id: recursion
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title: Recursion cheatsheet for coding interviews
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description: Recursion study guide for coding interviews, including practice questions, techniques, time complexity, and recommended resources
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keywords:
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[
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recursion coding interview study guide,
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recursion tips for coding interviews,
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recursion practice questions,
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recursion useful techniques,
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recursion time complexity,
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recursion recommended study resources,
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]
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sidebar_label: Recursion
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toc_max_heading_level: 2
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---
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<head>
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<meta property="og:image" content="https://www.techinterviewhandbook.org/social/algorithms/algorithms/algorithms-recursion.png" />
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</head>
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## Introduction
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Recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem.
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All recursive functions contains two parts:
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1. A base case (or cases) defined, which defines when the recursion is stopped - otherwise it will go on forever!
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1. Breaking down the problem into smaller subproblems and invoking the recursive call
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One of the most common example of recursion is the Fibonacci sequence.
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- Base cases: `fib(0) = 0` and `fib(1) = 1`
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- Recurrence relation: `fib(i) = fib(i-1) + fib(i-2)`
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```py
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def fib(n):
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if n <= 1:
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return n
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return fib(n - 1) + fib(n - 2)
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```
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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.
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## Learning resources
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- Readings
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- [Recursion](https://www.cs.utah.edu/~germain/PPS/Topics/recursion.html), University of Utah
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- Videos
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- [Tail Recursion](https://www.coursera.org/lecture/programming-languages/tail-recursion-YZic1), University of Washington
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<!-- TODO: Talk about backtracking -->
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## Things to look out for during interviews
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- Always remember to always define a base case so that your recursion will end.
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- 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.
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- 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.
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- 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
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## Corner cases
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- `n = 0`
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- `n = 1`
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- Make sure you have enough base cases to cover all possible invocations of the recursive function
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## Techniques
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### Memoization
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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).
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## Essential questions
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_These are essential questions to practice if you're studying for this topic._
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- [Generate Parentheses](https://leetcode.com/problems/generate-parentheses/)
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- [Combinations](https://leetcode.com/problems/combinations/)
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- [Subsets](https://leetcode.com/problems/subsets/)
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## Recommended practice questions
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_These are recommended questions to practice after you have studied for the topic and have practiced the essential questions._
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- [Letter Combinations of a Phone Number](https://leetcode.com/problems/letter-combinations-of-a-phone-number/)
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- [Subsets II](https://leetcode.com/problems/subsets-ii/)
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- [Permutations](https://leetcode.com/problems/permutations/)
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- [Sudoku Solver](https://leetcode.com/problems/sudoku-solver/)
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- [Strobogrammatic Number II (LeetCode Premium)](https://leetcode.com/problems/strobogrammatic-number-ii/)
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## Recommended courses
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import AlgorithmCourses from '../\_courses/AlgorithmCourses.md'
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<AlgorithmCourses />
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