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