add CHT

Author: snuke

README.md

@@ -17,7 +17,8 @@ AtCoder解説放送ライブラリ集
 |名前|コード|説明|
 |:--|:--|:--|
 |BIT|[bit.cpp](bit.cpp)|Binary Indexed Tree (Fenwick Tree)|
-|UnionFind|[uf.cpp](uf.cpp)|Union Find|
+|UnionFind|[uf.cpp](uf.cpp)|Union Find (DSU)|
+|CHT|[cht.cpp](cht.cpp)|Convex Hull Trick|
 
 ### 数学
 |名前|コード|説明|

cht.cpp

@@ -0,0 +1,31 @@
+// Convex Hull Trick (max)
+// https://youtu.be/TSvXG35mmRE?t=7853
+struct CHT {
+  struct Linear {
+    ll a, b;
+    Linear(ll a=0, ll b=0): a(a), b(b) {}
+    ll operator()(ll x) const { return a*x+b;}
+  };
+  deque<Linear> ls;
+  void add(ll a, ll b) {
+    Linear l(a,b);
+    assert(ls.size() == 0 || ls.back().a <= l.a);
+    while (ls.size() >= 2) {
+      const Linear& l1 = ls[ls.size()-2];
+      const Linear& l2 = ls.back();
+      if ((l.a-l2.a)*(l1.b-l2.b) < (l2.a-l1.a)*(l2.b-l.b)) break;
+      ls.pop_back();
+    }
+    ls.push_back(l);
+  }
+  ll operator()(ll x) { // x: asc
+    ll res = ls[0](x);
+    while (ls.size() >= 2) {
+      ll now = ls[1](x);
+      if (now < res) break;
+      res = now;
+      ls.pop_front();
+    }
+    return res;
+  }
+};