#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
long long w[100005] , h[100005];
long long n;
long long dp[100005];
struct line{
long long x , y;
line(long long x , long long y){
this->x = x , this->y = y;
}
};
bool operator < (line a , line b){
return a.x > b.x;
}
template <class type>
class CHT{
public :
bool cmp(type a , type b , type c){
double f1 = ((c.y) - (a.y)) * ((a.x) - (b.x)) , f2 = ((b.y) - (a.y)) * ((a.x) - (c.x));
return ((long double) (c.y) - (a.y)) * ((long double) (a.x) - (b.x)) <= ((long double) (a.x) - (c.x) )* ((long double) (b.y) - (a.y)) ;
return f1 <= f2;
}
int returnsize(){
return (int) cht.size();
}
void addLINE(type a){
while(cht.size() >= 2 && (a.x == cht.back().x || cmp(cht[cht.size() - 2] , cht[cht.size() - 1] , a))){
cht.pop_back();
}
cht.push_back(a);
}
long long eval(type b , int a){
int w = (b.x) * a + (b.y);
return w;
}
long long querymin(int x){
if(cht.size() == 0) return ((long long) 1e18);
if(cht.size() <= 5){
int bestvalue = (int) 1e18;
for(int i = 0 ; i < cht.size() ; i++) bestvalue = min(bestvalue , eval(cht[i] , x));
return bestvalue;
}
int l = 0 , r = cht.size() - 1;
r--;
int ansj = -1;
while(l<=r){
int mid = (l+r)/2;
if(eval(cht[mid] , x) >= eval(cht[mid + 1] , x)){
l = mid + 1;
ansj = mid;
}
else r = mid - 1;
}
long long bestvalue = eval(cht.front() , x);
if(ansj != -1) bestvalue = min(bestvalue , eval(cht[ansj] , x));
ansj ++;
if(ansj < cht.size()) bestvalue = min(bestvalue , eval(cht[ansj] , x));
for(int i = ansj - 20 ; i <= ansj + 20 ; i++){
if(cht.size() > i && i >=0) bestvalue = min(bestvalue , eval(cht[i] , x));
}
return bestvalue;
}
void mergev(vector<type> nhcht){
vector<type> newcht;
reverse(nhcht.begin() , nhcht.end());
reverse(cht.begin() , cht.end());
while(cht.size() && nhcht.size()){
if(cht.back().x == nhcht.back().x){
if(cht.back().y > nhcht.back().y) newcht.pb(cht.back()) , cht.pop_back();
else newcht.pb(nhcht.back()) , nhcht.pop_back();
}
else if(cht.back().x >= nhcht.back().x) newcht.pb(cht.back()) , cht.pop_back();
else newcht.pb(nhcht.back()) , nhcht.pop_back();
}
while(cht.size()){
newcht.pb(cht.back()) , cht.pop_back();
}
while(nhcht.size()) newcht.pb(nhcht.back()) , nhcht.pop_back();
for(int i = 0 ; i < ((int)newcht.size()) - 1 ; i++){
assert(newcht[i].x >= newcht[i+1].x);
}
for(int i = 0 ; i < newcht.size() ; i++) addLINE(newcht[i]);
}
vector<type> mergefunc(){
return cht;
}
void clearv(){
cht.clear();
}
long long querymax(int x){
if(cht.size() == 0) return -(int) 1e18;
int l = 0 , r = cht.size() - 1;
r--;
int ansj = -1;
while(l<=r){
int mid = (l+r)/2;
if(eval(cht[mid] , x) <= eval(cht[mid+1],x)){
l = mid + 1;
ansj = mid;
}
else r = mid - 1;
}
long long bestvalue = eval(cht.front() , x);
if(ansj != -1) bestvalue = max(bestvalue , eval(cht[ansj] , x));
ansj++;
if(ansj < cht.size()) bestvalue = max(bestvalue ,eval(cht[ansj] , x));
return bestvalue;
}
// private :
vector<type> cht;
};
CHT<line> chts[32];
void addline(line a){
vector<line> newcht;
newcht.pb(a);
chts[0].mergev(newcht);
for(int i = 0 ; i < 32 ; i++){
int z = (1LL<<i);
if((chts[i].returnsize()) >= z){
chts[i+1].mergev(chts[i].mergefunc());
chts[i].clearv();
}
}
}
long long query(int x){
long long bestvalue = (long long) 1e18;
for(int i = 0 ; i < 32 ; i++){
if(chts[i].returnsize() != 0)
bestvalue = min(bestvalue , chts[i].querymin(x));
}
return bestvalue;
}
int32_t main(){
scanf("%lld" , &n);
dp[0] = 0;
for(int i = 1 ; i <=n ;i ++){
scanf("%lld" , &h[i]);
}
w[0] = 0;
for(int i = 1 ; i <=n ;i ++){
scanf("%lld" , &w[i]);
w[i] += w[i-1];
}
dp[1] = 0;
addline(line(-2*h[1] , h[1]*h[1] - w[1] ));
for(int i = 2 ; i <= n ;i ++){
dp[i] = query(h[i]) + h[i]*h[i] + w[i-1];
addline(line(-2*h[i] , h[i]*h[i] - w[i] + dp[i]));
}
printf("%lld\n" , dp[n]);
}
Compilation message
building.cpp: In instantiation of 'void CHT<type>::mergev(std::vector<_Tp>) [with type = line]':
building.cpp:122:23: required from here
building.cpp:85:24: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0 ; i < newcht.size() ; i++) addLINE(newcht[i]);
building.cpp: In instantiation of 'long long int CHT<type>::querymin(long long int) [with type = line]':
building.cpp:138:49: required from here
building.cpp:42:28: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0 ; i < cht.size() ; i++) bestvalue = min(bestvalue , eval(cht[i] , x));
building.cpp:59:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if(ansj < cht.size()) bestvalue = min(bestvalue , eval(cht[ansj] , x));
building.cpp:61:24: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if(cht.size() > i && i >=0) bestvalue = min(bestvalue , eval(cht[i] , x));
building.cpp: In function 'int32_t main()':
building.cpp:145:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%lld" , &n);
~~~~~^~~~~~~~~~~~~
building.cpp:148:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%lld" , &h[i]);
~~~~~^~~~~~~~~~~~~~~~
building.cpp:152:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%lld" , &w[i]);
~~~~~^~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
376 KB |
Output is correct |
| 3 |
Correct |
3 ms |
428 KB |
Output is correct |
| 4 |
Correct |
3 ms |
432 KB |
Output is correct |
| 5 |
Correct |
3 ms |
444 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
195 ms |
2936 KB |
Output is correct |
| 2 |
Correct |
194 ms |
4088 KB |
Output is correct |
| 3 |
Correct |
194 ms |
5112 KB |
Output is correct |
| 4 |
Correct |
176 ms |
5892 KB |
Output is correct |
| 5 |
Correct |
170 ms |
8868 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
376 KB |
Output is correct |
| 3 |
Correct |
3 ms |
428 KB |
Output is correct |
| 4 |
Correct |
3 ms |
432 KB |
Output is correct |
| 5 |
Correct |
3 ms |
444 KB |
Output is correct |
| 6 |
Correct |
195 ms |
2936 KB |
Output is correct |
| 7 |
Correct |
194 ms |
4088 KB |
Output is correct |
| 8 |
Correct |
194 ms |
5112 KB |
Output is correct |
| 9 |
Correct |
176 ms |
5892 KB |
Output is correct |
| 10 |
Correct |
170 ms |
8868 KB |
Output is correct |
| 11 |
Correct |
179 ms |
8868 KB |
Output is correct |
| 12 |
Correct |
193 ms |
9160 KB |
Output is correct |
| 13 |
Correct |
120 ms |
10036 KB |
Output is correct |
| 14 |
Correct |
192 ms |
11508 KB |
Output is correct |
| 15 |
Correct |
186 ms |
18516 KB |
Output is correct |
| 16 |
Correct |
159 ms |
18516 KB |
Output is correct |
| 17 |
Correct |
77 ms |
18516 KB |
Output is correct |
| 18 |
Correct |
100 ms |
18516 KB |
Output is correct |
