From d45ea564b29a6c09c33a86307f13492bd60b2715 Mon Sep 17 00:00:00 2001
From: "Md. Zarif Ul Alam" <zarif98sjs@gmail.com>
Date: Wed, 2 Dec 2020 14:29:51 +0600
Subject: [PATCH] LIS Segment Tree Added

---
 .../05.3 LIS (Segment Tree).cpp               | 238 ++++++++++++++++++
 README.md                                     |   2 +-
 2 files changed, 239 insertions(+), 1 deletion(-)
 create mode 100644 Dynamic Programming/05.3 LIS (Segment Tree).cpp

diff --git a/Dynamic Programming/05.3 LIS (Segment Tree).cpp b/Dynamic Programming/05.3 LIS (Segment Tree).cpp
new file mode 100644
index 0000000..0db5f0a
--- /dev/null
+++ b/Dynamic Programming/05.3 LIS (Segment Tree).cpp	
@@ -0,0 +1,238 @@
+
+/*
+ * Problem : Longest Increasing Subsequence (using Segment Tree)
+ * */
+
+/** Which of the favors of your Lord will you deny ? **/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define F first
+#define S second
+
+#define ALL(x)      (x).begin(), (x).end()
+#define READ        freopen("alu.txt", "r", stdin)
+#define WRITE       freopen("vorta.txt", "w", stdout)
+
+#ifndef ONLINE_JUDGE
+#define DBG(x)      cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#else
+#define DBG(x)
+#endif
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
+
+inline void optimizeIO()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+const LL LINF = 1e17;
+
+/**
+Segment Tree (Point Update , Range Query)
+=========================================
+1 based indexing
+**/
+
+struct Node
+{
+    int mx;
+
+    Node() /// change here
+    {
+        mx = 0;
+    }
+
+    void create_leaf(int val) /// change here
+    {
+        mx = val;
+    }
+};
+
+Node merge_nodes(Node &a,Node &b) /// change here
+{
+    Node temp;
+    temp.mx = max(a.mx,b.mx);
+
+    return temp;
+}
+
+struct SegTree
+{
+    int n;
+    vector<int>data;
+    vector<Node>Tree;
+
+    SegTree(int n)
+    {
+        this->n = n;
+        int len = n+1;
+
+        data = vector<int>(len);
+        Tree = vector<Node>(len<<2);
+    }
+
+    void build()
+    {
+        build(1,1,n);
+        return;
+    }
+
+    void build(int cur,int start,int end)
+    {
+        if(start==end)
+        {
+            Tree[cur].create_leaf(data[start]);
+            return;
+        }
+
+        int mid = (start+end)>>1;
+        int lc = cur<<1 , rc = lc|1;
+
+        build(lc,start,mid);
+        build(rc,mid+1,end);
+
+        Tree[cur] = merge_nodes(Tree[lc],Tree[rc]);
+    }
+
+    void update(int updex,int val)
+    {
+        update(1,1,n,updex,val);
+    }
+
+    void update(int cur,int start,int end,int updex,int val)
+    {
+        if(start==end)
+        {
+            Tree[cur].create_leaf(val);
+            return;
+        }
+
+        int mid = (start+end)>>1;
+        int lc = cur<<1 , rc = lc|1;
+
+        /// binary search
+        if(updex<=mid) update(lc,start,mid,updex,val);
+        else update(rc,mid+1,end,updex,val);
+
+        Tree[cur] = merge_nodes(Tree[lc],Tree[rc]); /// bottom up correction after update
+    }
+
+    Node query(int ql,int qr)
+    {
+        return query(1,1,n,ql,qr);
+    }
+
+    Node query(int cur,int start,int end,int ql,int qr)
+    {
+        if(ql>qr) return Node();
+
+        if(end<ql || start>qr) return Node();
+
+        if(start>=ql && end<=qr)
+        {
+            return Tree[cur];
+        }
+
+        int mid = (start+end)>>1;
+        int lc = cur<<1 , rc = lc|1;
+
+        /// query on both child
+        Node ansL = query(lc,start,mid,ql,qr);
+        Node ansR = query(rc,mid+1,end,ql,qr);
+
+        return merge_nodes(ansL,ansR);
+    }
+};
+
+int solveLIS(vector<PII>&v)
+{
+    int n = v.size();
+
+    vector<PII> sorted = v;
+    sort(ALL(sorted));
+
+    SegTree s(n);
+    s.build();
+
+    for(auto el:sorted)
+    {
+        int id = -el.second;
+
+        int mx_till_now = s.query(1,id-1).mx;
+
+        s.update(id,mx_till_now+1);
+    }
+
+    int lis = s.query(1,n).mx;
+    return lis;
+}
+
+int main()
+{
+    optimizeIO();
+
+    int n;
+    cin>>n;
+
+    vector<PII>v(n);
+
+    for(int i=0; i<n; i++)
+    {
+        int x;
+        cin>>x;
+
+        v[i] = {x,-(i+1)}; /* minus to handle overcounting for duplicates after sorting , so that the latter ones are calculated first */
+    }
+
+    int ans = solveLIS(v);
+    cout<<ans<<endl;
+
+    return 0;
+}
+/**
+5
+1 6 2 3 5
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+    os<<"{"<<p.first<<", "<<p.second<<"} ";
+    return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" " ;
+    }
+    os<<" ]";
+    return os;
+}
+
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" ";
+    }
+    os<<" ]";
+    return os;
+}
diff --git a/README.md b/README.md
index b5a1fc4..f1f6be8 100644
--- a/README.md
+++ b/README.md
@@ -306,7 +306,7 @@
   * Longest Increasing Subsequence
     - [O(N^2)](Dynamic%20Programming/05%20LIS.cpp)
     - [O( NlogN )](Dynamic%20Programming/05.2%20LIS%20(Binary%20Search).cpp) **Binary Search**
-    - [O( NlogN )]() **Segment Tree** //code not added
+    - [O( NlogN )](/Dynamic%20Programming/05.3%20LIS%20(Segment%20Tree).cpp) **Segment Tree**
   * [Longest Bitonic Subsequence](Dynamic%20Programming/09%20Longest%20Bitonic%20Subsequence.cpp)
   * [Increasing Subsequence with Maximum Sum](Dynamic%20Programming/10%20Increasing%20Subsequence%20with%20Maximum%20Sum.cpp)
   * [Longest Increasing Index-Dividing Subsequence](Dynamic%20Programming/32%20Longest%20increasing%20index%20dividing%20subsequence.cpp)