From b6ea63d12f67bb64fbf3e5ea9a87899780714a67 Mon Sep 17 00:00:00 2001
From: Chris Kolonas <ckolonas@csd.auth.gr>
Date: Sat, 18 Jan 2020 22:06:25 +0200
Subject: [PATCH] InterpolationSearch and test cases

---
 .../scala/Search/InterpolationSearch.scala    | 45 +++++++++++++++++++
 .../Search/InterpolationSearchSpec.scala      | 17 +++++++
 2 files changed, 62 insertions(+)
 create mode 100644 src/main/scala/Search/InterpolationSearch.scala
 create mode 100644 src/test/scala/Search/InterpolationSearchSpec.scala

diff --git a/src/main/scala/Search/InterpolationSearch.scala b/src/main/scala/Search/InterpolationSearch.scala
new file mode 100644
index 0000000..6e51587
--- /dev/null
+++ b/src/main/scala/Search/InterpolationSearch.scala
@@ -0,0 +1,45 @@
+package Search
+
+/*
+  An implementation of the Interpolation algorithm to search an
+  element in a sorted list of uniformly distributed values.
+  Interpolation algorithm is based on the binary search algorithm but instead of going to
+  the middle element, it checks elements closer to the edges.
+ */
+object InterpolationSearch {
+  /**
+   *
+   * @param arr  a sequence of uniformly distributed values
+   * @param elem an integer to search for in @arr
+   * @return index of the @elem else -1
+   */
+  def interpolationSearch(arr: List[Int], elem: Int): Int = {
+    var low = 0
+    var high = arr.size - 1
+
+    while (low <= high && elem>=arr(low) && elem <=arr(high)) {
+      //The interpolation formula that decides the next position keeping the uniform distribution in mind.
+      var pos = low + ((elem - arr(low)) * (high - low) / (arr(high) - arr(low)))
+      //Target index found
+      if (arr(pos) == elem) {
+        return pos
+      }
+      //If target is bigger, search right part of list.
+      else if (arr(pos) < elem) {
+        low = pos + 1
+      }
+      //If target is lower, search left part of list.
+      else {
+        high = pos - 1
+      }
+    }
+    //If element is not found.
+    -1
+  }
+  def main(args:Array[String]):Unit ={
+    val arr = List(10, 12, 13, 16, 18, 19, 20, 21,
+      22, 23, 24, 33, 35, 42, 47)
+
+    println(interpolationSearch(arr,48))
+  }
+}
diff --git a/src/test/scala/Search/InterpolationSearchSpec.scala b/src/test/scala/Search/InterpolationSearchSpec.scala
new file mode 100644
index 0000000..1dfc0e6
--- /dev/null
+++ b/src/test/scala/Search/InterpolationSearchSpec.scala
@@ -0,0 +1,17 @@
+package Search
+
+import org.scalatest.FlatSpec
+
+class InterpolationSearchSpec extends FlatSpec {
+  "An Interpolation Search" should "return the index of an element in an array" in{
+    val l = List.range(1,10)
+    assert(InterpolationSearch.interpolationSearch(l,2)===1)
+    assert(InterpolationSearch.interpolationSearch(l,9)===8)
+  }
+
+  it should "return -1 if the element is not found in the list" in{
+    val l = List(10, 12, 13, 16, 18, 19, 20, 21,
+      22, 23, 24, 33, 35, 42, 47)
+    assert(InterpolationSearch.interpolationSearch(l,48) === -1)
+  }
+}