Submission #585526

#	Time	Username	Problem	Language	Result	Execution time	Memory
585526		talant117408	Building Bridges (CEOI17_building)	C++17	100 / 100	169 ms	80284 KiB

building

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
 
#define pb                  push_back
#define mp                  make_pair
#define all(v)              (v).begin(),(v).end()
#define rall(v)             (v).rbegin(),(v).rend()
#define lb                  lower_bound
#define ub                  upper_bound
#define sz(v)               int((v).size())
#define do_not_disturb      ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define endl                '\n'

const int N = 1e6 + 7;

struct line {
    ll m, b;
    line() {
        m = 0;
        b = 1e18;
    }
    line(ll _m, ll _b) {
        m = _m; 
        b = _b;
    }
    ll operator()(ll x) {
        return m * x + b;
    }
} tree[N * 4];

void update(int v, int l, int r, line seg) {
    if (l == r - 1) {
        if (seg(l) < tree[v](l))
            tree[v] = seg;
        return;
    }
    int mid = (l + r) >> 1;
    if (seg.m > tree[v].m) 
        swap(seg, tree[v]);
    if (tree[v](mid) > seg(mid)) {
        swap(seg, tree[v]);
        update(v * 2, l, mid, seg);
    }
    else {
        update(v * 2 + 1, mid, r, seg);
    }
}

ll get(int v, int l, int r, ll x) {
    if (l == r - 1) {
        return tree[v](x);
    }
    int mid = (l + r) >> 1;
    if (x < mid) return min(tree[v](x), get(v * 2, l, mid, x));
    else return min(tree[v](x), get(v * 2 + 1, mid, r, x));
}

void solve() {
    int n;
    cin >> n;
    vector <ll> h(n), w(n), pref(n);
    for (auto &to : h) cin >> to;
    for (auto &to : w) cin >> to;
    pref[0] = w[0];
    for (int i = 1; i < n; i++) {
        pref[i] = pref[i - 1] + w[i];
    }
    
    vector <vector <ll>> dp(n, vector <ll> (2, 2e18));
    dp[0][1] = 0;
    multiset <ll> st;
    st.insert(-pref[0]);
    /*
    m = -2 * h[j]
    x = h[i]
    b = dp[j][1] - pref[j] + h[j]^2 
    c = pref[i - 1] + h[i]^2
    */
    update(1, 0, N, line(-2 * h[0], dp[0][1] - pref[0] + h[0] * h[0]));
    for (int i = 1; i < n; i++) {
        dp[i][0] = (*st.begin()) + pref[i];
        dp[i][1] = get(1, 0, N, h[i]) + pref[i - 1] + h[i] * h[i];
        st.insert(dp[i][0] - pref[i]);
        st.insert(dp[i][1] - pref[i]);
        update(1, 0, N, line(-2 * h[i], dp[i][1] - pref[i] + h[i] * h[i]));
    }
    cout << dp[n - 1][1];
}

// (h[i] - h[j]) ^ 2 = h[i] ^ 2 - 2 * h[i] * h[j] + h[j] ^ 2

/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/

int main() {
    do_not_disturb
    
    int t = 1;
    //~ cin >> t;
    while (t--) {
        solve();
    }
    
    return 0;
}

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