Two Pointers Algorithm added in PHP/Searches/TwoPointers.php

DIRECTORY.md

@@ -67,6 +67,7 @@
   * [Lowerbound](./Searches/LowerBound.php)
   * [Ternarysearch](./Searches/TernarySearch.php)
   * [Upperbound](./Searches/UpperBound.php)
+  * [TwoPointers](./Searches/TwoPointers.php)
 
 ## Sorting
   * [Arraykeyssort](./Sorting/ArrayKeysSort.php)

Searches/TwoPointers.php

@@ -0,0 +1,61 @@
+<?php
+/**
+ * Two Pointers Approach
+ * This method is designed to improve the efficiency of algorithms by processing two elements per
+ * loop instead of just one, thereby reducing both time and space complexity
+ * The technique involves using two pointers, which can start from the beginning and the end of the array
+ * or list, or one pointer moving at a slower pace while the other moves at a faster pace.
+ */
+
+/**
+ * To understand the technique let's solve a simple problem,
+ * Problem Statement:
+ *     There is an array of distinct integers "$list" and a target integer "$target". We have to find how many pairs
+ *     of elements of $list sum up to $target.
+ *     For example: $list = [2,4,3,8,6,9,10], $target = 12
+ *     in this array 2+10 = 12, 4+8 = 12, 3+9 = 12, therefore, there are 3 pairs which sum up to 12.
+ *
+ * If we solve this problem using two nested loops, the time complexity would be O(n^2),
+        for($i=0; $i<sizeof($list); ++$i){
+            for($j=$i+1; $j<sizeof($list); ++$j){
+                if($list[$i] + $list[$j] == $target)
+                    $ans++;
+            }
+        }
+ * To reduce the time complexity to O(n), we need Two Pointers technique.
+ */
+
+// Two Pointers step by step solution to that problem is given below:
+function twoPointers($list, $target)
+{
+    // First we need to sort the array so that we can take advantage of the order
+    sort($list);
+    // Now we are having two pointers "$left" and "$right"
+    // $left at the start and $right at the end of the array
+    $n = sizeof($list);
+    $left = 0;
+    $right = $n - 1;
+
+    $ans = 0; # we will store the number of pairs in $ans
+
+    // Now we will scan the array until $left and $right meet
+    while ($left < $right) {
+        # Now carefully understand how we move one of our pointers
+        if ($list[$left] + $list[$right] < $target) {
+            // it means the sum is less than $target and we need to increase our sum
+            // to increase the sum we will move $left pointer to the right
+            $left++;
+        } else if ($list[$left] + $list[$right] > $target) {
+            // the sum is greater than the target, so we need to decrease the sum
+            // to decrease the sum we will move our $right pointer to the left
+            $right--;
+        } else if ($list[$left] + $list[$right] == $target) {
+            // if it's true, we have found a pair
+            $ans++;
+            // now we will move one of our pointers, otherwise it'll run forever
+            $left++; # doesn't matter which one we move
+        }
+        // The loop will go until the pointers point to the same element
+    }
+    return $ans; # returning the number of pairs
+}

tests/Searches/SearchesTest.php

@@ -12,6 +12,7 @@
 require_once __DIR__ . '/../../Searches/ExponentialSearch.php';
 require_once __DIR__ . '/../../Searches/TernarySearch.php';
 require_once __DIR__ . '/../../Searches/InterpolationSearch.php';
+require_once __DIR__ . '/../../Searches/TwoPointers.php';
 
 
 class SearchesTest extends TestCase
@@ -202,4 +203,18 @@ public function testInterpolationSearch()
         $result = interpolationSearch($list, $target);
         $this->assertEquals(12, $result);
     }
+
+    public function testTwoPointers()
+    {
+        $list = [1, 2, 4, 7, 8, 10, 11, 12, 15];
+        $target = 3;
+        $result = twoPointers($list, $target);
+        $this->assertEquals(1, $result);
+        $target = 12;
+        $result = twoPointers($list, $target);
+        $this->assertEquals(3, $result);
+        $target = 18;
+        $result = twoPointers($list, $target);
+        $this->assertEquals(2, $result);
+    }
 }