From d6ea21bbd5bc2fbd456803beac1471f245060b9e Mon Sep 17 00:00:00 2001
From: JasbirCodeSpace <shikhawat.jasbir@gmail.com>
Date: Tue, 12 May 2020 17:23:23 +0530
Subject: [PATCH 1/3] Added Karatsuba_Algorithm.php

---
 Karatsuba_Algorithm/Karatsuba_Algorithm.php | 50 +++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 Karatsuba_Algorithm/Karatsuba_Algorithm.php

diff --git a/Karatsuba_Algorithm/Karatsuba_Algorithm.php b/Karatsuba_Algorithm/Karatsuba_Algorithm.php
new file mode 100644
index 0000000000..7934fb7417
--- /dev/null
+++ b/Karatsuba_Algorithm/Karatsuba_Algorithm.php
@@ -0,0 +1,50 @@
+<?php
+/*
+The Karatsuba Algorithm implements faster multiplication, 
+than the traditional approach.
+*/
+function karatsuba($num1,$num2){
+
+    // for single digit number multiply directly
+    if ($num1 < 10 || $num2 < 10) {
+        return $num1 * $num2;
+    }
+
+    $num1Str = strval($num1);
+    $num2Str = strval($num2);
+
+    $n = min(strlen($num1Str),strlen($num2Str));
+    $half = round($n / 2);
+
+    // divide num1 into two halves
+    $num1_H = intval(substr($num1Str,0, strlen($num1Str) - $half));
+    $num1_L = intval(substr($num1Str,strlen($num1Str) - $half, strlen($num1Str)));
+
+    // divide num2 into two halves
+    $num2_H = intval(substr($num2Str,0, strlen($num2Str) - $half));
+    $num2_L = intval(substr($num2Str,strlen($num2Str) - $half, strlen($num2Str)));
+
+    // using the KaratSuba Definition
+    $s1 = karatSuba($num1_L, $num2_L);
+    $s2 = karatSuba($num1_L + $num1_H, $num2_L + $num2_H);
+    $s3 = karatSuba($num1_H, $num2_H);
+
+    $s4 = $s2 - $s3 -$s1;
+
+    // karatsuba formula for finding product
+    $result = $s3 * pow(10, 2 * $half) + $s4 * pow(10, $half) + $s1;
+
+    return $result;
+}
+
+$num1 = 23984;
+$num2 = 183672;
+echo "\nInputs are: ".$num1." ".$num2;
+$result = karatSuba($num1,$num2);
+echo "\nThe result is: ".$result;
+
+// Input :
+// 23984 183672
+// Output: 
+// 4405189248
+?>
\ No newline at end of file

From 5e952a0714fdda0ca9cf8097171204fb650685f3 Mon Sep 17 00:00:00 2001
From: JasbirCodeSpace <shikhawat.jasbir@gmail.com>
Date: Sun, 17 May 2020 19:08:38 +0530
Subject: [PATCH 2/3] Segment_Tree_RMQ in PHP

---
 Segment_Tree_RMQ/Segment_Tree_RMQ.php | 46 +++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)
 create mode 100644 Segment_Tree_RMQ/Segment_Tree_RMQ.php

diff --git a/Segment_Tree_RMQ/Segment_Tree_RMQ.php b/Segment_Tree_RMQ/Segment_Tree_RMQ.php
new file mode 100644
index 0000000000..ea689ea303
--- /dev/null
+++ b/Segment_Tree_RMQ/Segment_Tree_RMQ.php
@@ -0,0 +1,46 @@
+<?php
+function RMQ($segArr, $segStart, $segEnd, $start, $end, $index)
+{
+
+    if ($start <= $segStart && $end >= $segEnd) return $segArr[$index];
+
+    if ($segEnd < $start || $segStart > $end) return PHP_INT_MAX;
+
+    $mid = floor($segStart + ($segEnd - $segStart) / 2);
+
+    $left = RMQ($segArr, $segStart, $mid, $start, $end, 2 * $index + 1);
+    $right = RMQ($segArr, $mid + 1, $segEnd, $start, $end, 2 * $index + 2);
+    return ($left <= $right ? $left : $right);
+}
+
+function buildSegmentTree(&$arr, $start, $end, &$segArray, $index)
+{
+    if ($start == $end)
+    {
+        $segArray[$index] = $arr[$start];
+        return $arr[$start];
+    }
+
+    $mid = floor($start + ($end - $start) / 2);
+    $left = buildSegmentTree($arr, $start, $mid, $segArray, $index * 2 + 1);
+    $right = buildSegmentTree($arr, $mid + 1, $end, $segArray, $index * 2 + 2);
+
+    $segArray[$index] = ($left <= $right ? $left : $right);
+
+    return $segArray[$index];
+}
+
+$arr = array(1,3,2,7,9,11,8,4,20,15);
+$size = count($arr);
+
+$height = ceil(log($size, 2));
+$segtree_size = 2 * (pow(2, $height) - 1);
+$segArray = new SplFixedArray($segtree_size);
+
+buildSegmentTree($arr, 0, $size - 1, $segArray, 0);
+
+$start = 1;
+$end = 5;
+
+echo "Minimum value in index range $start to $end is " . RMQ($segArray, 0, $size - 1, $start, $end, 0);
+?>

From 01bd8e4652c2dfbfac7a1131b5d861bf0c2f4bdb Mon Sep 17 00:00:00 2001
From: Jasbir <shikhawat.jasbir@gmail.com>
Date: Wed, 20 May 2020 11:20:14 +0530
Subject: [PATCH 3/3] Delete Karatsuba_Algorithm.php

---
 Karatsuba_Algorithm/Karatsuba_Algorithm.php | 50 ---------------------
 1 file changed, 50 deletions(-)
 delete mode 100644 Karatsuba_Algorithm/Karatsuba_Algorithm.php

diff --git a/Karatsuba_Algorithm/Karatsuba_Algorithm.php b/Karatsuba_Algorithm/Karatsuba_Algorithm.php
deleted file mode 100644
index 7934fb7417..0000000000
--- a/Karatsuba_Algorithm/Karatsuba_Algorithm.php
+++ /dev/null
@@ -1,50 +0,0 @@
-<?php
-/*
-The Karatsuba Algorithm implements faster multiplication, 
-than the traditional approach.
-*/
-function karatsuba($num1,$num2){
-
-    // for single digit number multiply directly
-    if ($num1 < 10 || $num2 < 10) {
-        return $num1 * $num2;
-    }
-
-    $num1Str = strval($num1);
-    $num2Str = strval($num2);
-
-    $n = min(strlen($num1Str),strlen($num2Str));
-    $half = round($n / 2);
-
-    // divide num1 into two halves
-    $num1_H = intval(substr($num1Str,0, strlen($num1Str) - $half));
-    $num1_L = intval(substr($num1Str,strlen($num1Str) - $half, strlen($num1Str)));
-
-    // divide num2 into two halves
-    $num2_H = intval(substr($num2Str,0, strlen($num2Str) - $half));
-    $num2_L = intval(substr($num2Str,strlen($num2Str) - $half, strlen($num2Str)));
-
-    // using the KaratSuba Definition
-    $s1 = karatSuba($num1_L, $num2_L);
-    $s2 = karatSuba($num1_L + $num1_H, $num2_L + $num2_H);
-    $s3 = karatSuba($num1_H, $num2_H);
-
-    $s4 = $s2 - $s3 -$s1;
-
-    // karatsuba formula for finding product
-    $result = $s3 * pow(10, 2 * $half) + $s4 * pow(10, $half) + $s1;
-
-    return $result;
-}
-
-$num1 = 23984;
-$num2 = 183672;
-echo "\nInputs are: ".$num1." ".$num2;
-$result = karatSuba($num1,$num2);
-echo "\nThe result is: ".$result;
-
-// Input :
-// 23984 183672
-// Output: 
-// 4405189248
-?>
\ No newline at end of file