add ExponentialSearch Algorithm

Searches/ExponentialSearch.php

@@ -0,0 +1,101 @@
+<?php
+
+/*
+ * Exponential Search
+ *
+ * The algorithm consists of two stages. The first stage determines a
+ * range in which the search key would reside if it were in the list.
+ * In the second stage, a binary search is performed on this range.
+ *
+ *
+ */
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ /**
+  * @param Array $arr
+  * @param int $value
+  * @param int $floor
+  * @param int $ceiling
+  * @return int
+  **/
+function binarySearch ($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] > $value) {
+    return binarySearch($arr, $value, $floor, $mid - 1);
+  }
+  // search the right part of the $array
+  // If the $middle element is lower than the $value
+  else {
+    return binarySearch($arr, $value, $mid + 1, $ceiling);
+  }
+}
+
+
+
+
+
+
+
+
+ 
+ /**
+  * @param Array $arr
+  * @param int $length
+  * @param int $value
+  * @return int
+  **/
+function exponentialSearch ($arr, $length, $value) {
+  // If $value is the first element of the $array return this position
+  if ($arr[0] === $value) {
+    return 0;
+  }
+
+  // Find range for binary search
+  $i = 1;
+  while ($i < $length && $arr[$i] <= $value) {
+    $i = $i * 2;
+  }
+  $floor = $i/2;
+  $ceiling = min($i, $length);
+
+  // Call binary search for the range found above
+  return binarySearch($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/index.php

@@ -0,0 +1,23 @@
+<?php
+
+/*
+ * Function to find nth number in Fibonacci sequence.
+ * Uses a version of memoization and runs very fast!
+ */
+
+/**
+ * @param int $n position to check
+ * @param array $m array to store solved trees
+ */
+function fibonacciPosition(int $n, array &$m = [])
+{
+    if(isset($m[$n])) return $m[$n];
+    if($n < 2) return $n;
+
+    $m[$n] = fibonacciPosition($n - 1, $m) + fibonacciPosition($n - 2, $m);
+
+    return $m[$n];
+
+}
+
+print fibonacciPosition(59);