Submission #48422

#	Time	Username	Problem	Language	Result	Execution time	Memory
48422		wzy	Building Bridges (CEOI17_building)	C++11	100 / 100	195 ms	18516 KiB

building

#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 (stderr)

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]);
   ~~~~~^~~~~~~~~~~~~~~~

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40