Scala algorithm: Binary search in a rotated sorted array

Published

Algorithm goal

This is a variation of BinarySearch, where the input array is rotated (RotateArrayRight).

For example, an input of [1,2,3,4], rotated could become [3,4,1,2].

Binary search runs in \(O(\log{n})\), which is faster than a linear search (\(O(n)\)).

Test cases in Scala

assert(searchIn(Array.empty, 7) == None)
assert(searchIn(Array(7, 1), 7) == Some(0))
assert(searchIn(Array(9, 1, 7), 7) == Some(2))
assert(searchIn(Array(7, 9, 1), 7) == Some(0))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 7) == Some(1))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 1) == Some(4))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 10) == None)
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 9) == Some(3))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 4, 5), 4) == Some(7))
assert(searchIn(Array(6, 7, 8, 9, 1, 2, 3, 5), 5) == Some(7))

Algorithm in Scala

20 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

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Explanation

The Scala implementation uses the Range concept in order to achieve a more terse solution, in particular by defining the range for the next iteration in terms of the previous range, rather than dealing with raw indices.

This is a very powerful concept because you notice that in Scala, algorithms can be quite self-explanatory whereas in some C/Python algorithm implementations one would have to refer to documentation and comments for an explanation. Documentability is crucial in sharing knowledge. (this is © from www.scala-algorithms.com)

The variation requires us to capture the case where our range is still uneven. In this case, the code explains the story

Scala concepts & Hints

  1. Def Inside Def

    A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.

    def exampleDef(input: String): String = {
  def surroundInputWith(char: Char): String = s"$char$input$char"
  surroundInputWith('-')
}

assert(exampleDef("test") == "-test-")

    It is also frequently used in combination with Tail Recursion.

  2. Option Type

    The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!

    assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))

assert(Option(1).flatMap(x => None) == None)

  3. Range

    The (1 to n) syntax produces a "Range" which is a representation of a sequence of numbers.

    assert((1 to 5).toString == "Range 1 to 5")

assert((1 to 5).reverse.toString() == "Range 5 to 1 by -1")

assert((1 to 5).toList == List(1, 2, 3, 4, 5))

  4. Stack Safety

    Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

    This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

    In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

    def sum(from: Int, until: Int): Int =
  if (from == until) until else from + sum(from + 1, until)

def thisWillSucceed: Int = sum(1, 5)

def thisWillFail: Int = sum(1, 300)

  5. Tail Recursion

    In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.

    def fibonacci(n: Int): Int = {
  @scala.annotation.tailrec
  def go(i: Int, previous: Int, beforePrevious: Int): Int =
    if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)

  go(i = 1, previous = 1, beforePrevious = 0)
}

assert(fibonacci(8) == 21)

Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala

How our 100 algorithms look

  1. A description/goal of the algorithm.
  2. An explanation with both Scala and logical parts.
  3. A proof or a derivation, where appropriate.
  4. Links to Scala concepts used in this specific algorithm, also unit-tested.
  5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
  6. Unit tests, with a button to run them immediately in our in-browser IDE.
Screenshot of an example algorithm demonstrating the listed features

Study our 100 Scala Algorithms: 6 fully free, 90 published & 10 upcoming

Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

  1. Compute the length of longest valid parentheses
  2. Check a binary tree is balanced
  3. Remove duplicates from an unsorted List
  4. Make a queue using stacks (Lists in Scala)
  5. Find height of binary tree
  6. Single-elimination tournament tree
  7. Reverse Polish Notation calculator
  8. Quick Sort sorting algorithm in pure immutable Scala
  9. Find minimum missing positive number in a sequence
  10. Least-recently used cache (LRU)
  11. Count pairs of a given expected sum
  12. Binary heap (min-heap)
  13. Compute a Roman numeral for an Integer, and vice-versa
  14. Compute keypad possibilities
  15. Matching parentheses algorithm with foldLeft and a state machine
  16. Traverse a tree Breadth-First, immutably
  17. Read a matrix as a spiral
  18. Remove duplicates from a sorted list (state machine)
  19. Token Bucket Rate Limiter
  20. Leaky Bucket Rate Limiter
  21. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  22. Longest increasing sub-sequence length
  23. Reverse first n elements of a queue
  24. Binary search a generic Array
  25. Game of Life
  26. Merge Sort: in pure immutable Scala
  27. Make a queue using Maps
  28. Is an Array a permutation?
  29. Count number of contiguous countries by colors
  30. Add numbers without using addition (plus sign)
  31. Tic Tac Toe MinMax solve
  32. Run-length encoding (RLE) Encoder
  33. Print Alphabet Diamond
  34. Find kth largest element in a List
  35. Balanced parentheses algorithm with tail-call recursion optimisation
  36. Reverse a String's words efficiently
  37. Count number of changes (manipulations) needed to make an anagram with an efficient foldLeft
  38. Count passing cars
  39. Establish execution order from dependencies
  40. Counting inversions of a sequence (array) using a Merge Sort
  41. Longest common prefix of strings
  42. Check if an array is a palindrome
  43. Compute missing ranges
  44. Check a directed graph has a routing between two nodes (depth-first search)
  45. Compute nth row of Pascal's triangle
  46. Run-length encoding (RLE) Decoder
  47. Check if a number is a palindrome
  48. In a range of numbers, count the numbers divisible by a specific integer
  49. Compute minimum number of Fibonacci numbers to reach sum
  50. Find the index of a substring ('indexOf')
  51. Reshape a matrix
  52. Compute the steps to transform an anagram only using swaps
  53. Compute modulo of an exponent without exponentiation
  54. Closest pair of coordinates in a 2D plane
  55. Find the contiguous slice with the minimum average
  56. Compute maximum sum of subarray (Kadane's algorithm)
  57. Pure-functional double linked list
  58. Binary search in a rotated sorted array
  59. Check if a directed graph has cycles
  60. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  61. Check a binary tree is a search tree
  62. Length of the longest common substring
  63. Sliding Window Rate Limiter
  64. Tic Tac Toe board check
  65. Find an unpaired number in an array
  66. Check if a String is a palindrome
  67. Count binary gap size of a number using tail recursion
  68. Remove duplicates from a sorted list (Sliding)
  69. Monitor success rate of a process that may fail
  70. Least-recently used cache (MRU)
  71. Find sub-array with the maximum sum
  72. Find the minimum absolute difference of two partitions
  73. Find maximum potential profit from an array of stock price
  74. Fibonacci in purely functional immutable Scala
  75. Fizz Buzz in purely functional immutable Scala
  76. Find triplets that sum to a target ('3Sum')
  77. Find combinations adding up to N (non-unique)
  78. Find the minimum item in a rotated sorted array
  79. Make a binary search tree (Red-Black tree)
  80. Mars Rover
  81. Find combinations adding up to N (unique)
  82. Find indices of tuples that sum to a target (Two Sum)
  83. Count factors/divisors of an integer
  84. Compute single-digit sum of digits
  85. Fixed Window Rate Limiter
  86. Traverse a tree Depth-First
  87. Reverse bits of an integer
  88. Find k closest elements to a value in a sorted Array
  89. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  90. Rotate a matrix by 90 degrees clockwise

Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

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