From db95b02de89180572d7b21b584399d1c3b400e04 Mon Sep 17 00:00:00 2001
From: Ayush Shah <shahayush2507@gmail.com>
Date: Mon, 5 Oct 2020 08:46:43 +0530
Subject: [PATCH 1/2] Create Segment_Tree_Template.cpp

---
 Data-Structures/Segment_Tree_Template.cpp | 69 +++++++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 Data-Structures/Segment_Tree_Template.cpp

diff --git a/Data-Structures/Segment_Tree_Template.cpp b/Data-Structures/Segment_Tree_Template.cpp
new file mode 100644
index 0000000..5adabd6
--- /dev/null
+++ b/Data-Structures/Segment_Tree_Template.cpp
@@ -0,0 +1,69 @@
+// Name : Segment tree for range sum queries and point updates.
+// Time complexity : build : nlogn
+//                   query : logn
+//                   update : logn
+// Space Complexity : n
+
+struct segtree {
+    vector<int> arr;
+    int sz = 1;
+    void  init(int n) {
+        while(sz < n) sz *= 2;
+        arr.assign(2*sz,0);
+    }
+    void update(int pos, int val, int curr_node, int l, int r) {
+        if(r-l == 1) {
+            // here the curr_node will become = to i;
+            
+            
+            arr[curr_node] = val;
+            return;
+        }
+        // now decide where to go - left subtree or right subtree
+        
+        
+        int m = (l+r)/2;
+        if(pos < m) {
+            // go left
+            
+            update(pos,val,2*curr_node+1,l,m);
+            
+            // curr_node becomes the left child of x i.e 2*x+1;
+        } else {
+            // go right
+            
+            update(pos,val,2*curr_node+2,m,r);
+            
+            // curr_node becomes the right child of x i.e 2*x+2;
+        }
+        // and here the sum of curr_node = sum of left child and right child
+        
+        
+        arr[curr_node] = arr[2*curr_node+1]+arr[2*curr_node+2];
+        return;
+    }
+
+    void update(int pos, int val) {
+        update(pos,val,0,0,sz);
+        
+        
+        // 0 means the root; we start update with the root
+    }
+
+    /*------------
+    this is where all the changes will be made for point updates;
+    -------------*/
+    
+    
+    int sum(int l, int r, int curr_node, int currL, int currR) {
+        if(currL >= r || currR <= l) return 0; // outside the segment
+        if(currL >= l && currR <= r) return arr[curr_node]; // totally inside the segment
+        int m = (currL+currR)/2;
+        int ans = sum(l,r,2*curr_node+1,currL,m) + sum(l,r,2*curr_node+2,m,currR);
+        return ans;
+    }
+
+    int sum(int l, int r) {
+        return sum(l,r,0,0,sz);
+    }
+};

From 5607ce177e44d51115f3dfd80c658a1550880835 Mon Sep 17 00:00:00 2001
From: Ayush Shah <shahayush2507@gmail.com>
Date: Mon, 5 Oct 2020 09:00:11 +0530
Subject: [PATCH 2/2] gcd of 2 numbers in logarithmic time

---
 Algebra-and-Numerical-Methods/GCD.cpp | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)
 create mode 100644 Algebra-and-Numerical-Methods/GCD.cpp

diff --git a/Algebra-and-Numerical-Methods/GCD.cpp b/Algebra-and-Numerical-Methods/GCD.cpp
new file mode 100644
index 0000000..dd79e61
--- /dev/null
+++ b/Algebra-and-Numerical-Methods/GCD.cpp
@@ -0,0 +1,23 @@
+// Name : GCD of two numbers in log(max(a,b)) time.
+// Time Complexity : log(max(a,b));
+// Space Complexity : constant
+
+#include <bits/stdc++.h>
+#define int long long
+using namespace std;
+
+int gcd(int a, int b) {
+    // use the result that gcd(a,b) = gcd(b%a,a) recursively;
+    if(b == 0) return a;
+    if(a == 0) return b;
+    return gcd(b%a,a);
+}
+
+signed main()
+{
+    int a, b;
+    // Enter the 2 numbers to calculate the gcd;
+    cin>>a>>b;
+    cout<<gcd(a,b);
+    return 0;   
+}