Scala algorithm: Check a binary tree is a search tree


Algorithm goal

A binary tree is a tree that can only have at most 2 children. A search tree is a tree in which all the children to the left of the node are < than the value of this node, and all items of the right are >=, and this property also applies to their children nodes as well.

This property enables very fast lookups (hence the name a search tree) due to the ordering guarantees.

Test cases in Scala

  !BinaryTree.of(2).withLeft(1).withRight(3, _.withRight(0)).isSearchTree
  BinaryTree.of(2).withLeft(1).withRight(3, _.withRight(5)).isSearchTree

Algorithm in Scala

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

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A common mistake in implementing this algorithm is to think that comparing a node's value with the value of its direct child is enough.

In fact, one has to ensure that the property applies to all the children. While it is possible to verify this by traversing the tree top-down, in fact a better approach is to perform an in-order traversal of the tree and check that it is sorted. In this algorithm, we do exactly that using LazyLists and implicit classes provided by Scala. (this is © from

Scala concepts & Hints

  1. Lazy List

    The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').

  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. Ordering

    In Scala, the 'Ordering' type is a 'type class' that contains methods to determine an ordering of specific types.

    assert(List(3, 2, 1).sorted == List(1, 2, 3))
    assert(List(3, 2, 1).sorted(Ordering[Int].reverse) == List(3, 2, 1))
    assert(Ordering[Int].lt(1, 2))
    assert(!Ordering[Int].lt(2, 1))
  4. Sliding / Sliding Window

    Get fixed-length sliding sub-sequences (sliding windows) from another sequence

  5. Type Class

    Type classes are one of Scala's most important super-powers: they enable you to add new behaviour to existing classes, without modifying those classes. In many languages, to add a behaviour to a class, you would typically extend it with an interface, and then implement methods against this interface.This, however, does not scale: especially when you have older libraries, you would be forced to make them depend on a new interface, and have to re-build everything.

    Type classes are used heavily in Apple's SwiftUI as "extensions" to enable powerful abstraction capabilities.

    Type classes enable you to do things like this:

    import Ordering.Implicits._
    type CommonType = (Int, String, Option[String])
    val a: CommonType = (1, "X", None)
    val b: CommonType = (2, "A", Some("B"))
    assert(a < b, "We can order tuples using Scala-provided type classes")

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  13. Matching parentheses algorithm with foldLeft and a state machine
  14. Traverse a tree Breadth-First, immutably
  15. Read a matrix as a spiral
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  17. Token Bucket Rate Limiter
  18. Leaky Bucket Rate Limiter
  19. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  20. Longest increasing sub-sequence length
  21. Reverse first n elements of a queue
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  33. Balanced parentheses algorithm with tail-call recursion optimisation
  34. Reverse a String's words efficiently
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  36. Count passing cars
  37. Establish execution order from dependencies
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  39. Longest common prefix of strings
  40. Check if an array is a palindrome
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  42. Check a directed graph has a routing between two nodes (depth-first search)
  43. Compute nth row of Pascal's triangle
  44. Run-length encoding (RLE) Decoder
  45. Check if a number is a palindrome
  46. In a range of numbers, count the numbers divisible by a specific integer
  47. Compute minimum number of Fibonacci numbers to reach sum
  48. Find the index of a substring ('indexOf')
  49. Reshape a matrix
  50. Compute the steps to transform an anagram only using swaps
  51. Compute modulo of an exponent without exponentiation
  52. Closest pair of coordinates in a 2D plane
  53. Find the contiguous slice with the minimum average
  54. Compute maximum sum of subarray (Kadane's algorithm)
  55. Pure-functional double linked list
  56. Binary search in a rotated sorted array
  57. Check if a directed graph has cycles
  58. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  59. Check a binary tree is a search tree
  60. Length of the longest common substring
  61. Sliding Window Rate Limiter
  62. Tic Tac Toe board check
  63. Find an unpaired number in an array
  64. Check if a String is a palindrome
  65. Count binary gap size of a number using tail recursion
  66. Remove duplicates from a sorted list (Sliding)
  67. Monitor success rate of a process that may fail
  68. Least-recently used cache (MRU)
  69. Find sub-array with the maximum sum
  70. Find the minimum absolute difference of two partitions
  71. Find maximum potential profit from an array of stock price
  72. Fibonacci in purely functional immutable Scala
  73. Fizz Buzz in purely functional immutable Scala
  74. Find triplets that sum to a target ('3Sum')
  75. Find combinations adding up to N (non-unique)
  76. Find the minimum item in a rotated sorted array
  77. Make a binary search tree (Red-Black tree)
  78. Remove duplicates from an unsorted List
  79. Mars Rover
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  81. Find indices of tuples that sum to a target (Two Sum)
  82. Count factors/divisors of an integer
  83. Compute single-digit sum of digits
  84. Fixed Window Rate Limiter
  85. Traverse a tree Depth-First
  86. Reverse bits of an integer
  87. Find k closest elements to a value in a sorted Array
  88. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  89. 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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