Add dynamic Li-Chao Tree

Author: ekzhang

files.json

@@ -118,5 +118,13 @@
   {
     "title": "Wavelet Tree for K-th Order Statistics",
     "name": "mkthnum.cpp"
+  },
+  {
+    "title": "Li-Chao Segment Tree",
+    "name": "li_chao.cpp"
+  },
+  {
+    "title": "Dynamic Li-Chao Segment Tree",
+    "name": "li_chao_dynamic.cpp"
   }
 ]

li_chao_dynamic.cpp

@@ -0,0 +1,71 @@
+// li_chao_dynamic.cpp
+// Eric K. Zhang; Jul. 3, 2018
+
+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long LL;
+
+#define MAXLC 1000000000
+#define INF (1LL<<60)
+
+inline LL f(LL m, LL b, int x) {
+	return m * x + b;
+}
+
+struct lc_node {
+	LL m = 0, b = INF;
+	lc_node *l = nullptr, *r = nullptr;
+	
+	lc_node() {}
+	lc_node(LL m, LL b) : m(m), b(b) {}
+	~lc_node() { delete l; delete r; }
+
+	void add_line(LL nm, LL nb, int lo=0, int hi=MAXLC) {
+		int mid = (lo + hi) / 2;
+		bool bl = f(nm, nb, lo) < f(m, b, lo);
+		bool bm = f(nm, nb, mid) < f(m, b, mid);
+		if (bm) {
+			swap(nm, m);
+			swap(nb, b);
+		}
+		if (lo == hi || nb == INF)
+			return;
+		else if (bl != bm) {
+			if (!l) l = new lc_node;
+			l->add_line(nm, nb, lo, mid - 1);
+		}
+		else {
+			if (!r) r = new lc_node;
+			r->add_line(nm, nb, mid + 1, hi);
+		}
+	}
+
+	LL get(int x, int lo=0, int hi=MAXLC) {
+		int mid = (lo + hi) / 2;
+		LL ret = f(m, b, x);
+		if (l && x < mid)
+			ret = min(ret, l->get(x, lo, mid - 1));
+		if (r && x > mid)
+			ret = min(ret, r->get(x, mid + 1, hi));
+		return ret;
+	}
+
+	void clear() {
+		delete l; delete r;
+		m = 0, b = INF, l = nullptr, r = nullptr;
+	}
+
+} lc;
+
+int main() {
+	lc.add_line(2, -1); // y = 2x - 1
+	lc.add_line(-1, 9); // y = 9 - x
+
+	cout << lc.get(0) << " = " << -1 << endl;
+	cout << lc.get(1) << " = " << 1 << endl;
+	cout << lc.get(3) << " = " << 5 << endl;
+	cout << lc.get(4) << " = " << 5 << endl;
+	cout << lc.get(5) << " = " << 4 << endl;
+	cout << lc.get(100) << " = " << -91 << endl;
+}