Submission #1014888

#	Time	Username	Problem	Language	Result	Execution time	Memory
1014888		ByeWorld	Building Bridges (CEOI17_building)	C++14	100 / 100	88 ms	14192 KiB

building

#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
#define ll long long
#define int long long
#define pb push_back
#define fi first
#define se second
#define lf (id<<1)
#define rg ((id<<1)|1)
#define md ((l+r)/2)
#define ld long double
using namespace std;
typedef pair<int,int> pii;
typedef pair<pii, int> ipii;
const int MAXN = 1e5+10;
const int MAXA = 1e9+10;
const int INF = 1e18+10;
const int INF2 = 1e18+10;
const int LOG = 19;
const int MOD = 1e9+7;
const int SQRT = 450;
const vector<int> NOL = {};
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const vector<int> dx = {1, -1, 0, 0};
const vector<int> dy = {0, 0, 1, -1};
void chmn(int &a, int b){ a = min(a, b); }
int n;
int h[MAXN], w[MAXN], pr[MAXN], dp[MAXN];

struct line {
    int m, c;
    int y(int x){ return m*x+c; }
};

struct seg {
    seg *le, *ri; line val;
    int l, r, mid;

    void bd(int x, int y){
        l = x; r = y; mid = md;
        val.m = 0; val.c = INF2;
        le = NULL; ri = NULL;
    }
    void ADD(line add){
        if(add.c==INF2) return;

        if(val.y(mid) > add.y(mid)) swap(val, add);
        if(val.m == add.m) return; // kalah
        if(val.m < add.m){ 
            if(le==NULL){ le = new seg(); le->bd(l, mid); }
            le->ADD(add); return; 
        }
            if(ri==NULL){ ri = new seg(); ri->bd(mid+1, r); }
            ri->ADD(add); return; 
    }
    void upd(int x, int y, line add){
        if(x<=l && r<=y){ ADD(add); return; }
        if(r<x || y<l) return;

        if(le==NULL){ le = new seg(); le->bd(l, mid); }
        le->upd(x, y, add);
        if(ri==NULL){ ri = new seg(); ri->bd(mid+1, r); }
        ri->upd(x, y, add);
    }
    int que(int x){
        int te = val.y(x);
        if(x < mid){
            if(le!=NULL) chmn(te, le->que(x));
        } else {
            if(ri!=NULL) chmn(te, ri->que(x));
        }
        return te;
    }
} *A;

signed main(){
    cin >> n;
    for(int i=1; i<=n; i++) cin >> h[i];
    for(int i=1; i<=n; i++){
        cin >> w[i]; pr[i] = pr[i-1]+w[i];
    }
    A = new seg(); A->bd(-MAXA, MAXA);
    dp[1] = 0;
    int i = 1;
    line nw; 
    nw.m = -2*h[i]; 
    nw.c = dp[i] - pr[i] + h[i]*h[i];
    // cout << "pp\n";
    A->upd(-MAXA, MAXA, nw);

    for(int i=2; i<=n; i++){
        dp[i] = h[i]*h[i] + pr[i-1];
        dp[i] += A->que(h[i]);

        line nw; 
        nw.m = -2*h[i]; 
        nw.c = dp[i] - pr[i] + h[i]*h[i];
        A->upd(-MAXA, MAXA, nw);
        // cout << i<< ' ' << dp[i] << " pp\n";
        // for(int j=1; j<=i-1; j++){
        //     int te = dp[j] + pr[i-1]-pr[j] + (h[j]-h[i])*(h[j]-h[i]);
        //     chmn(dp[i], te);
        // }
    }
    cout << dp[n] << '\n';
}
/*
Rumus:
dp[i] = min:
(dp[j]-pr[j]+hj^2 +  hi -2hj) + hi^2 + pr[i-1]
( c                   x   m ) +  k
m gk monotonic -> dynamic CHT
6
3 8 7 1 6 6
0 -1 9 1 2 0
->17
*/

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