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source/DS/LiChaoTree.cpp

@@ -0,0 +1,47 @@
+const ll L = 1e9+7, inf = 2*L*L+7;
+struct Line {
+    ll a, b;
+    ll operator()(ll x){return a*x+b;}
+    Line():a(0),b(-inf){}
+    Line(ll a, ll b):a(a), b(b){}
+};
+struct Node {ll l, r; Line v; Node():l(-1), r(-1), v(){}};
+using LiChao = vector<Node>;
+
+// add Line v in [l, r]
+void update(LiChao& seg, Line v, ll l, ll r, ll s=-L, ll e=L, ll i=0) {
+    if(e < l or r < s) return;
+    if(s == e) { seg[i].v = (seg[i].v(s) > v(s))?seg[i].v:v; return; }
+    
+    ll mid=(s+e)>>1;
+    if(l <= s && e <= r) {
+        Line A = seg[i].v, B = v; if(A(s) < B(s)) swap(A, B);
+        if(A(e) >= B(e)) seg[i].v = A;
+        else if(A(mid) >= B(mid)) {
+            seg[i].v = A;
+            if(seg[i].r == -1) seg[i].r = seg.size(), seg.pb(Node());
+            update(seg, B, mid+1, e, mid+1, e, seg[i].r);
+        }
+        else {
+            seg[i].v = B;
+            if(seg[i].l == -1) seg[i].l = seg.size(), seg.pb(Node());
+            update(seg, A, s, mid, s, mid, seg[i].l);
+        }
+        return;
+    }
+if(seg[i].l == -1) seg[i].l = seg.size(), seg.pb(Node());
+if(seg[i].r == -1) seg[i].r = seg.size(), seg.pb(Node());
+    update(seg, v, l, r, s, mid, seg[i].l);
+    update(seg, v, l, r, mid+1, e, seg[i].r);
+}
+// query max_{l_i <= x <= r_i} (a_i*x + b_i)
+ll query(LiChao& seg, ll x, ll s=-L, ll e=L, ll i=0) {
+    if(i == -1 or x < s or e < x) return -inf;
+    if(s == e) return seg[i].v(x);
+    ll mid = (s+e)>>1;
+    return max({query(seg, x, s, mid, seg[i].l), query(seg, x, mid+1, e, seg[i].r), seg[i].v(x)});
+}
+
+// LiChao seg(1, Node());
+// update(seg, {a, b}, l, r);
+// ll v = query(seg, x);