From cf76ecc1f0a65038adf40ae2189dd2dde8a5dd6c Mon Sep 17 00:00:00 2001
From: zscoder <zisong.yeoh@gmail.com>
Date: Fri, 7 Oct 2016 17:22:24 +0800
Subject: [PATCH] Added Treap

---
 Data Structures Class Template.cpp | 102 +++++++++++++++++++++++++++--
 1 file changed, 96 insertions(+), 6 deletions(-)

diff --git a/Data Structures Class Template.cpp b/Data Structures Class Template.cpp
index 4b92a03..d0540f2 100644
--- a/Data Structures Class Template.cpp	
+++ b/Data Structures Class Template.cpp	
@@ -1035,13 +1035,12 @@ struct ConvexHull
             return m * x + c;
         }
     };
-    #define sz(x) (int)(x).size()
     deque<Line> d;
     bool irrelevant(Line Z) 
     {
-        if (sz(d) < 2) return false;
+        if (int(d.size()) < 2) return false;
     
-        Line X = d[sz(d)-2], Y = d[sz(d)-1];
+        Line X = d[int(d.size())-2], Y = d[int(d.size())-1];
 
         return (X.c - Z.c) * (Y.m - X.m) <= (X.c - Y.c) * (Z.m - X.m);
     }
@@ -1052,7 +1051,7 @@ struct ConvexHull
         d.push_back(l);
     }
     ll query(ll x) {
-        while (sz(d) > 1 && (d[0].c - d[1].c <= x * (d[1].m - d[0].m))) d.pop_front();
+        while (int(d.size()) > 1 && (d[0].c - d[1].c <= x * (d[1].m - d[0].m))) d.pop_front();
         return d.front().pass(x);
     }
 };
@@ -1534,10 +1533,102 @@ struct Tree
 };
 //End Tree
 
+//Start Treap (see https://threads-iiith.quora.com/Treaps-One-Tree-to-Rule-em-all-Part-2)
+struct Treap
+{
+	struct node
+	{
+		int prior,siz;
+		ll val;//value stored in the array
+		ll sum;//whatever info you want to maintain in segtree for each node
+		ll lazy;//whatever lazy update you want to do
+		struct node *l,*r;
+	};
+	
+	typedef node* pnode;
+	
+	int sz(pnode t)
+	{
+		return t?t->siz:0;
+	}
+	void upd_sz(pnode t)
+	{
+		if(t)t->siz=sz(t->l)+1+sz(t->r);
+	}
+	void lazy(pnode t)
+	{
+		if(!t || !t->lazy)return;
+		t->val+=t->lazy;//operation of lazy
+		t->sum+=t->lazy*sz(t);
+		if(t->l)t->l->lazy+=t->lazy;//propagate lazy
+		if(t->r)t->r->lazy+=t->lazy;
+		t->lazy=0;
+	}
+	void reset(pnode t)
+	{
+		if(t)t->sum = t->val;//no need to reset lazy coz when we call this lazy would itself be propagated
+	}
+	void combine(pnode& t,pnode l,pnode r){//combining two ranges of segtree
+		if(!l || !r)return void(t = l?l:r);
+		t->sum = l->sum + r->sum;
+	}
+	void operation(pnode t){//operation of segtree
+		if(!t)return;
+		reset(t);//reset the value of current node assuming it now represents a single element of the array
+		lazy(t->l);lazy(t->r);//imp:propagate lazy before combining t->l,t->r;
+		combine(t,t->l,t);
+		combine(t,t,t->r);
+	}
+	void split(pnode t,pnode &l,pnode &r,int pos,int add=0){
+		if(!t)return void(l=r=NULL);
+		lazy(t);
+		int curr_pos = add + sz(t->l);
+		if(curr_pos<=pos)//element at pos goes to left subtree(l)
+			split(t->r,t->r,r,pos,curr_pos+1),l=t;
+		else 
+			split(t->l,l,t->l,pos,add),r=t;
+		upd_sz(t);
+		operation(t);
+	}
+	void merge(pnode &t,pnode l,pnode r){ //l->leftarray,r->rightarray,t->resulting array
+		lazy(l);lazy(r);
+		if(!l || !r) t = l?l:r;
+		else if(l->prior>r->prior)merge(l->r,l->r,r),t=l;
+		else    merge(r->l,l,r->l),t=r;
+		upd_sz(t);
+		operation(t);
+	}
+	pnode init(int val){
+		pnode ret = (pnode)malloc(sizeof(node));
+		ret->prior=rand();ret->siz=1;
+		ret->val=val;
+		ret->sum=val;ret->lazy=0;
+		return ret;
+	}
+	int range_query(pnode t,int l,int r){//[l,r]
+		pnode L,mid,R;
+		split(t,L,mid,l-1);
+		split(mid,t,R,r-l);//note: r-l!!
+		int ans = t->sum;
+		merge(mid,L,t);
+		merge(t,mid,R);
+		return ans;
+	}
+	void range_update(pnode t,int l,int r,ll val){//[l,r]
+		pnode L,mid,R;
+		split(t,L,mid,l-1);
+		split(mid,t,R,r-l);//note: r-l!!
+		t->lazy+=val; //lazy_update
+		merge(mid,L,t);
+		merge(t,mid,R);
+	}
+};
+//End Treap
+
 /* TO-DO LIST :
 1. SQRT DECOMP (MO)
 2. SQRT DECOMP (REAL)
-3. TREE (LCA, HLD)
+3. TREE (HLD, centroid?)
 12. OTHER STRING STRUCTS SUCH AS PALINDROMIC TREE, MANACHAR, Z?
 14. FFT
 15. Karatsuba
@@ -1545,7 +1636,6 @@ struct Tree
 17. KMP
 18. Trie
 19. Suffix Tree (?)
-20. Treap
 */
 int main() //Testing Zone
 {