Create LiChao Tree (Sparse).cpp

DP/DP Optimization/LiChao Tree (Sparse).cpp

@@ -0,0 +1,62 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define ll long long int
+
+const int maxk = 105;
+const int maxn = 10005;
+const int maxX = 1000005;
+const ll inf = 1e12;
+
+struct Poly{
+    vector<ll> co;
+    Poly() {}
+    void add(ll c) {co.push_back(c);}
+    ll f(ll x){
+        if(co.size() == 0) return inf;
+
+        ll ans = 0;
+        ll mul = 1;
+        for(ll c : co) {ans += mul * c; mul = mul * x;}
+        return ans;
+    }
+};
+
+struct lc{
+    Poly S;
+    lc *lft, *rgt;
+
+    lc() {lft = rgt = NULL; S = Poly();}
+
+    void Del(){
+        if(lft) lft->Del();
+        if(rgt) rgt->Del();
+        delete this;
+    }
+
+    void add(int lo, int hi, Poly upd){
+        if(upd.f(lo) > S.f(lo) && upd.f(hi) > S.f(hi)) return;
+
+        int mid = (lo + hi) / 2;
+        bool bame  = upd.f(lo) < S.f(lo);
+        bool majhe = upd.f(mid) < S.f(mid);
+        if(majhe) swap(S, upd);
+        if(lo == hi) return;
+
+        if(bame != majhe){
+            if(!lft) lft = new lc();
+            lft->add(lo, mid, upd);
+        }
+        else{
+            if(!rgt) rgt = new lc();
+            rgt->add(mid+1, hi, upd);
+        }
+    }
+
+    ll query(int lo, int hi, ll x){
+        ll Curr = S.f(x);
+        if(lo == hi) return Curr;
+        int mid = (lo + hi) / 2;
+        if(x <= mid) return min(Curr, lft ? lft->query(lo, mid, x) : inf);
+        else return min(Curr, rgt ? rgt->query(mid+1, hi, x) : inf);
+    }
+};