Optimize li_chao

Author: ekzhang

li_chao.cpp

@@ -0,0 +1,60 @@
+// li_chao.cpp
+// Eric K. Zhang; Jul. 3, 2018
+
+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long LL;
+typedef pair<LL, LL> pll;
+inline LL f(pll a, int x) {
+	return a.first * x + a.second;
+}
+
+#define MAXLC 1000000
+#define INF (1LL<<60)
+pll line[MAXLC << 1];
+
+void lc_init(int lo=0, int hi=MAXLC, int node=0) {
+	if (lo > hi || line[node].second == INF)
+		return;
+	line[node] = { 0, INF };
+	int mid = (lo + hi) / 2;
+	lc_init(lo, mid - 1, 2 * node + 1);
+	lc_init(mid + 1, hi, 2 * node + 2);
+}
+
+void add_line(pll ln, int lo=0, int hi=MAXLC, int node=0) {
+	int mid = (lo + hi) / 2;
+	bool l = f(ln, lo) < f(line[node], lo);
+	bool m = f(ln, mid) < f(line[node], mid);
+	if (m) swap(line[node], ln);
+	if (lo == hi || ln.second == INF)
+		return;
+	else if (l != m)
+		add_line(ln, lo, mid - 1, 2 * node + 1);
+	else
+		add_line(ln, mid + 1, hi, 2 * node + 2);
+}
+
+LL get(int x, int lo=0, int hi=MAXLC, int node=0) {
+	int mid = (lo + hi) / 2;
+	LL ret = f(line[node], x);
+	if (x < mid)
+		ret = min(ret, get(x, lo, mid - 1, 2 * node + 1));
+	if (x > mid)
+		ret = min(ret, get(x, mid + 1, hi, 2 * node + 2));
+	return ret;
+}
+
+int main() {
+	lc_init();
+	add_line({ 2, -1 }); // y = 2x - 1
+	add_line({ -1, 9 }); // y = 9 - x
+
+	cout << get(0) << " = " << -1 << endl;
+	cout << get(1) << " = " << 1 << endl;
+	cout << get(3) << " = " << 5 << endl;
+	cout << get(4) << " = " << 5 << endl;
+	cout << get(5) << " = " << 4 << endl;
+	cout << get(100) << " = " << -91 << endl;
+}