update ExponentialSearch and added TernarySearch

Added ExponentialSearch and TernarySearch to Test/Searches and updated Directory.md

Searches/ExponentialSearch.php

@@ -7,14 +7,6 @@
  **** if it were in the list.
  * In the second stage, a binary search is performed on this range.
  */
- 
- 
- 
- 
- 
- 
- 
- 
  /**
   * @param Array $arr
   * @param int $value
@@ -25,18 +17,12 @@
 function binarySearch ($arr, $value, $floor, $ceiling) {
   // Get $middle index
   $mid = floor(($floor + $ceiling) / 2);
-
   // Return position if $value is at the $mid position
   if ($arr[$mid] === $value) {
     return (int) $mid;
   }
-  
   //Return -1 is range is wrong
   if ($floor > $ceiling) return -1;
-
-
-
-
   // search the left part of the $array
   // If the $middle element is great than the $value
   if ($arr[$mid] > $value) {
@@ -48,22 +34,13 @@ function binarySearch ($arr, $value, $floor, $ceiling) {
     return binarySearch($arr, $value, $mid + 1, $ceiling);
   }
 }
-
-
-
-
-
-
-
-
- 
  /**
   * @param Array $arr
   * @param int $length
   * @param int $value
   * @return int
   **/
-function exponentialSearch ($arr, $length, $value) {
+function exponentialSearch ($arr, $value) {
   // If $value is the first element of the $array return this position
   if ($arr[0] === $value) {
     return 0;
@@ -71,6 +48,7 @@ function exponentialSearch ($arr, $length, $value) {
 
   // Find range for binary search
   $i = 1;
+  $length = count($arr);
   while ($i < $length && $arr[$i] <= $value) {
     $i = $i * 2;
   }
@@ -79,21 +57,4 @@ function exponentialSearch ($arr, $length, $value) {
 
   // Call binary search for the range found above
   return binarySearch($arr, $value, $floor, $ceiling);
-}
-
-
-
-
-
-
-
-
-
-function Test(){
- $arr = [2, 3, 4, 7, 28, 35, 63, 98];
- $value = 35;
- $result = exponentialSearch($arr, count($arr), $value);
- 
- var_dump($result);
-}
-//Test();
+}

Searches/TernarySearch.php

@@ -0,0 +1,83 @@
+<?php
+/* Ternary search is similar to binary search
+ * It rather divides the sorted array into three parts rather than.two parts by using two middle points, $mid1  $mid2.
+ * The value of the $key will first be compared with the two $mid points, the value will be returned if there is a match.
+ * Then, if the value of the $key is less than $mid1, narrow the interval to the first part.
+ * Else, if the value of the $key is greater than $mid2, narrow the interval to the third part.
+ * Otherwise, narrow the interval to the $middle part.
+ * Repeat the steps until the value is found or the interval is empty (value not found after checking all elements).
+ */
+
+function ternarySearchByRecursion ($arr, $key, $low, $high) {
+  
+    //Return -1 if high lesser than low, we can't find item in the whole array
+    if ($high < $low) {
+      return -1;
+    }
+    
+    
+    //get $mid1 and $mid2
+    $mid1 = floor($low + ($high - $low) / 3);
+    $mid2 = floor($high - ($high - $low) / 3);
+    // check if $key is found at any $mid
+    if ($arr[$mid1] === $key) {
+      // return index of $key if found
+      return $mid1;
+    }
+    if ($arr[$mid2] === $key) {
+      // return index of $key if found
+      return $mid2;
+    }
+    
+    // since the $key is not found at $mid,
+    // check in which region it is present
+    // and repeat the Search operation
+    // in that region
+    if ($key < $arr[$mid1]) {
+      // the $key lies in between $low and $mid1
+      return ternarySearchByRecursion($arr, $key, $low, $mid1 - 1);
+    } else if ($key > $arr[$mid2]) {
+      // the $key lies in between $mid2 and $high
+      return ternarySearchByRecursion($arr, $key, $mid2 + 1, $high);
+    } else {
+      // the $key lies in between $mid1 and $mid2
+      return ternarySearchByRecursion($arr, $key, $mid1 + 1, $mid2 - 1);
+    }
+}
+
+function ternarySearchIterative ($arr, $key) {
+  $low = 0; $high = count($arr) - 1;
+  while ($high >= $low) {
+    // find the $mid1 and $mid2
+    $mid1 = floor($low + ($high - $low) / 3);
+    $mid2 = floor($high - ($high - $low) / 3);
+
+    // check if $key is found at any $mid
+    if ($arr[$mid1] === $key) {
+      // return index of $key if found
+      return $mid1;
+    }
+    if ($arr[$mid2] === $key) {
+      // return index of $key if found
+      return $mid2;
+    }
+
+    // since the $key is not found at $mid,
+    // check in which region it is present
+    // and repeat the Search operation
+    // in that region
+    if ($key < $arr[$mid1]) {
+      // the $key lies in between $low and $mid1
+      $high = $mid1 - 1;
+    } else if ($key > $arr[$mid2]) {
+      // the $key lies in between $mid2 and $high
+      $low = $mid2 + 1;
+    } else {
+      // the $key lies in between $mid1 and $mid2
+      $low = $mid1 + 1;
+      $high = $mid2 - 1;
+    }
+  }
+  // the $key was not found
+  return -1;
+}