oj.uz

Submission #911345

# Submission time Handle Problem Language Result Execution time Memory
911345 2024-01-18T18:58:52 Z danikoynov Meetings (IOI18_meetings) C++14
100 / 100
 3182 ms 396404 KB 
#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const int maxn = 7.5e5 + 10;

int n, q;
ll h[maxn];

/// Cartesian tree data
int left_child[maxn], right_child[maxn];
int left_border[maxn], right_border[maxn];
int root, depth[maxn];

void cartesian_tree()
{
    stack < int > lf;
    for (int i = 1; i <= n; i ++)
    {
        left_child[i] = -1;
        while(!lf.empty() && h[lf.top()] <= h[i])
        {
            left_child[i] = lf.top();
            lf.pop();
        }

        if (lf.empty())
            left_border[i] = 1;
        else
            left_border[i] = lf.top() + 1;

        lf.push(i);
    }

    stack < int > rf;
    for (int i = n; i >= 1; i --)
    {
        right_child[i] = -1;
        while(!rf.empty() && h[rf.top()] < h[i])
        {
            right_child[i] = rf.top();
            rf.pop();
        }

        if (rf.empty())
            right_border[i] = n;
        else
            right_border[i] = rf.top() - 1;

        rf.push(i);
    }

    for (int i = 1; i <= n; i ++)
    {
        if (left_border[i] == 1 && right_border[i] == n)
        {
            root = i;
            break;
        }
    }
}

void calc_depth(int ver)
{
    //cout << "vertex " << ver << endl;
    //cout << "left border " << left_border[ver] << " right border " << right_border[ver] << endl;
    if (left_child[ver] != -1)
    {
        depth[left_child[ver]] = depth[ver] + 1;
        calc_depth(left_child[ver]);
    }
    if (right_child[ver] != -1)
    {
        depth[right_child[ver]] = depth[ver] + 1;
        calc_depth(right_child[ver]);
    }
}


struct query
{
    int l, r, idx;

    query(int _l = 0, int _r = 0, int _idx = 0)
    {
        l = _l;
        r = _r;
        idx = _idx;
    }
};

query task[maxn];
vector < query > spot[maxn];

struct line
{
    ll k, m;

    line (ll _k = 0, ll _m = 0)
    {
        k = _k;
        m = _m;
    }

    ll get(ll x)
    {
        return k * x + m;
    }
};




const ll inf = 1e18;

void chmin(ll &var, ll val)
{
    var = min(var, val);
}


struct li_chao_tree
{
    struct node
    {
        line cur;
        ll lazy;
        bool act;
        node *lc, *rc;

        node()
        {
            cur = line();
            act = false;
            lc = NULL;
            rc = NULL;
            lazy = 0;
        }
    };


    node *root = NULL;

    li_chao_tree()
    {
        root = new node();
    }
    void push_lazy(node *ver)
    {
        if (ver -> act)
            ver -> cur.m += ver -> lazy;

        if (ver -> lc != NULL)
            ver -> lc -> lazy += ver -> lazy;
        if (ver -> rc != NULL)
            ver -> rc -> lazy += ver -> lazy;

        ver -> lazy = 0;
    }

    void add_line_conscious(node *ver, ll left, ll right, line target)
    {
        push_lazy(ver);

        if (ver -> act == false)
        {
            ver -> act = true;
            ver -> cur = target;
            return;
        }

        ll mid = (left + right) / 2;
        if (ver -> cur.get(mid) > target.get(mid))
            swap(ver -> cur, target);

        if (left == right)
            return;

        if (ver -> cur.get(left) > target.get(left))
            add_line_conscious(ver -> lc, left, mid, target);
        if (ver -> cur.get(right) > target.get(right))
            add_line_conscious(ver -> rc, mid + 1, right, target);
    }

    void add_line(node *ver, ll left, ll right, ll qleft, ll qright, line target)
    {
        push_lazy(ver);

        if (left > qright || right < qleft || qright < qleft)
            return;

        if (left >= qleft && right <= qright)
        {
            add_line_conscious(ver, left, right, target);
            return;
        }

        ll mid = (left + right) / 2;
        add_line(ver -> lc, left, mid, qleft, qright, target);
        add_line(ver -> rc, mid + 1, right, qleft, qright, target);
    }

    void range_update(node *ver, ll left, ll right, ll qleft, ll qright, ll val)
    {

        push_lazy(ver);
        if (left > qright || right < qleft || qright < qleft)
            return;

        if (left >= qleft && right <= qright)
        {
            ver -> lazy += val;
            push_lazy(ver);
            return;
        }

        ll mid = (left + right) / 2;
        if (left != right && ver -> act)
        {
            ///cout << "add conscious " << " " << left << " " << mid << " " <<
            add_line_conscious(ver -> lc, left, mid, ver -> cur);
            add_line_conscious(ver -> rc, mid + 1, right, ver -> cur);
            ver -> act = false;
        }
        range_update(ver -> lc, left, mid, qleft, qright, val);
        range_update(ver -> rc, mid + 1, right, qleft, qright, val);
        ///cout << "range update " << left << " " << right << " " << qleft << " " << qright << " " << ver -> act << endl;
    }

    ll query_pivot(node *ver, ll left, ll right, ll pivot)
    {
        push_lazy(ver);
        ll mx = inf;
        if (ver -> act)
            chmin(mx, ver -> cur.get(pivot));
        if (left == right)
            return mx;

        ll mid = (left + right) / 2;
        if (pivot <= mid)
            chmin(mx, query_pivot(ver -> lc, left, mid, pivot));
        else
            chmin(mx, query_pivot(ver -> rc, mid + 1, right, pivot));

        return mx;

    }

    void build(node *ver, ll left, ll right)
    {
        if (left == right)
            return;

        ver -> lc = new node();
        ver -> rc = new node();

        ll mid = (left + right) / 2;
        build(ver -> lc, left, mid);
        build(ver -> rc, mid + 1, right);
    }

    ll get_pivot(ll pivot)
    {
        return query_pivot(root, 1, n, pivot);
    }

    void insert_line(int left, int right, line cur)
    {
        add_line(root, 1, n, left, right, cur);
    }

    void add_to_range(int left, int right, ll val)
    {
        range_update(root, 1, n, left, right, val);
    }
};
ll left_price[maxn], right_price[maxn];
li_chao_tree li_left_price, li_right_price;

ll answer[maxn];



void conquer(ll root)
{
    line left_line(h[root], - (root - 1) * h[root]), right_line(- h[root], + (root + 1) * h[root]);
    if (root != left_border[root])
    {
        ///left_line.m += left_price[root - 1];
        left_line.m += li_left_price.get_pivot(root - 1);
    }
    if (root != right_border[root])
    {
        ///right_line.m += right_price[root + 1];
        right_line.m += li_right_price.get_pivot(root + 1);
    }


    if (root == left_border[root])
    {
        ///cout << "conquer " << h[root] << endl;
        li_left_price.insert_line(root, root, line(0, h[root]));
        ///left_price[root] = h[root];
    }
    else
    {
        li_left_price.insert_line(root, root, line(0, li_left_price.get_pivot(root - 1) + h[root]));
        ///left_price[root] = left_price[root - 1] + h[root];
    }


        //if (root == 1)
        //cout << "first " << li_left_price.get_pivot(2) << endl;

    li_left_price.add_to_range(root + 1, right_border[root], (root - left_border[root] + 1) * h[root]);
    li_left_price.insert_line(root + 1, right_border[root], left_line);

    /**for (int pivot = root + 1; pivot <= right_border[root]; pivot ++)
    {

        left_price[pivot] += (root - left_border[root] + 1) * h[root];
        chmin(left_price[pivot], left_line.get(pivot));
    }*/

    if (root == right_border[root])
    {
        li_right_price.insert_line(root, root, line(0, h[root]));
        ///right_price[root] = h[root];
    }
    else
    {
        li_right_price.insert_line(root, root, line(0, li_right_price.get_pivot(root + 1) + h[root]));
        ///right_price[root] = right_price[root + 1] + h[root];
    }


    li_right_price.add_to_range(left_border[root], root - 1, (right_border[root] - root + 1) * h[root]);
    li_right_price.insert_line(left_border[root], root - 1, right_line);
    /**for (int pivot = root - 1; pivot >= left_border[root]; pivot --)
    {
        right_price[pivot] += (right_border[root] - root + 1) * h[root];
        chmin(right_price[pivot], right_line.get(pivot));
    }*/
}
void divide(int root)
{
    if (left_child[root] != -1)
        divide(left_child[root]);
    if (right_child[root] != -1)
        divide(right_child[root]);

    for (query cur : spot[root])
    {

        ///cout << "answer " << left_border[root] << " " << right_border[root] << " " << cur.idx << endl;
        ll left_opt = (ll)(cur.r - root + 1) * h[root];
        if (root != cur.l)
            left_opt += li_right_price.get_pivot(cur.l);

        //ll left_opt = right_price[cur.l] + (ll)(cur.r - root + 1) * h[root];
        ll right_opt = (ll)(root - cur.l + 1) * h[root];
        if (root != cur.r)
            right_opt += + li_left_price.get_pivot(cur.r);;
        ///ll right_opt = (ll)(root - cur.l + 1) * h[root] + left_price[cur.r];
        chmin(answer[cur.idx], min(left_opt, right_opt));
    }

    conquer(root);

    /**cout << "range " << left_border[root] << " " << right_border[root] << endl;
    for (int i = left_border[root]; i <= right_border[root]; i ++ )
        cout << li_left_price.get_pivot(i) << " ";
    cout << endl;
    for (int i = left_border[root]; i <= right_border[root]; i ++ )
        cout << li_right_price.get_pivot(i) << " ";
    cout << endl;
    cout << "-------------" << endl;
        for (int i = left_border[root]; i <= right_border[root]; i ++ )
        cout << left_price[i] << " ";
    cout << endl;
    for (int i = left_border[root]; i <= right_border[root]; i ++ )
        cout << right_price[i] << " ";
    cout << endl;*/

}

vector < ll > get_result()
{
    vector < ll > res;
    for (int i = 1; i <= q; i ++)
        res.push_back(answer[i]);
    return res;
}

void build_li_chao()
{
    li_left_price.build(li_left_price.root, 1, n);
    li_right_price.build(li_right_price.root, 1, n);
}

int tree[4 * maxn];

void build_tree(int root, int left, int right)
{
    if (left == right)
    {
        tree[root] = left;
        return;
    }

    int mid = (left + right) / 2;
    build_tree(root * 2, left, mid);
    build_tree(root * 2 + 1, mid + 1, right);

    tree[root] = tree[root * 2];
    if (depth[tree[root * 2 + 1]] < depth[tree[root]])
        tree[root] = tree[root * 2 + 1];
}

int query_depth(int root, int left, int right, int qleft, int qright)
{
    if (left > qright || right < qleft)
        return 0;

    if (left >= qleft && right <= qright)
        return tree[root];

    int mid = (left + right) / 2;
    int lf = query_depth(root * 2, left, mid, qleft, qright);
    int rf = query_depth(root * 2 + 1, mid + 1, right, qleft, qright);

    if (depth[lf] < depth[rf])
        return lf;
    return rf;
}


void assign_queries()
{
    for (int i = 1; i <= q; i ++)
    {
        int mx = query_depth(1, 1, n, task[i].l, task[i].r);
        /**for (int j = task[i].l; j <= task[i].r; j ++)
        {
            if (mx == -1 || depth[j] < depth[mx])
                mx = j;
        }*/
        spot[mx].push_back(task[i]);
    }
}
vector<long long> minimum_costs(vector<int> H, vector<int> L,
                                vector<int> R)
{
    n = H.size();
    q = L.size();
    for (int i = 1; i <= n; i ++)
    {
        h[i] = H[i - 1];
    }

    for (int i = 1; i <= q; i ++)
    {
        task[i] = query(L[i - 1] + 1, R[i - 1] + 1, i);
        answer[i] = inf;
    }

    cartesian_tree();
    calc_depth(root);
    depth[0] = 1e6 + 10;
    build_tree(1, 1, n);
    assign_queries();
    build_li_chao();
    divide(root);
    vector < ll > res = get_result();
    return res;
}
/**
5 1
3 1 5 4 3
1 4

*/

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 43356 KB Output is correct
2 Correct 15 ms 44124 KB Output is correct
3 Correct 13 ms 44120 KB Output is correct
4 Correct 14 ms 44124 KB Output is correct
5 Correct 13 ms 44124 KB Output is correct
6 Correct 12 ms 44380 KB Output is correct
7 Correct 16 ms 44380 KB Output is correct
8 Correct 13 ms 44500 KB Output is correct
9 Correct 13 ms 44376 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 43356 KB Output is correct
2 Correct 15 ms 44124 KB Output is correct
3 Correct 13 ms 44120 KB Output is correct
4 Correct 14 ms 44124 KB Output is correct
5 Correct 13 ms 44124 KB Output is correct
6 Correct 12 ms 44380 KB Output is correct
7 Correct 16 ms 44380 KB Output is correct
8 Correct 13 ms 44500 KB Output is correct
9 Correct 13 ms 44376 KB Output is correct
10 Correct 19 ms 45148 KB Output is correct
11 Correct 19 ms 45148 KB Output is correct
12 Correct 19 ms 45056 KB Output is correct
13 Correct 19 ms 45148 KB Output is correct
14 Correct 19 ms 45376 KB Output is correct
15 Correct 19 ms 45020 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 43352 KB Output is correct
2 Correct 51 ms 48332 KB Output is correct
3 Correct 249 ms 87696 KB Output is correct
4 Correct 239 ms 84172 KB Output is correct
5 Correct 200 ms 91048 KB Output is correct
6 Correct 241 ms 91552 KB Output is correct
7 Correct 254 ms 92636 KB Output is correct

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 43352 KB Output is correct
2 Correct 51 ms 48332 KB Output is correct
3 Correct 249 ms 87696 KB Output is correct
4 Correct 239 ms 84172 KB Output is correct
5 Correct 200 ms 91048 KB Output is correct
6 Correct 241 ms 91552 KB Output is correct
7 Correct 254 ms 92636 KB Output is correct
8 Correct 245 ms 84728 KB Output is correct
9 Correct 199 ms 84328 KB Output is correct
10 Correct 210 ms 84692 KB Output is correct
11 Correct 230 ms 84208 KB Output is correct
12 Correct 200 ms 83656 KB Output is correct
13 Correct 212 ms 84428 KB Output is correct
14 Correct 242 ms 89740 KB Output is correct
15 Correct 226 ms 83984 KB Output is correct
16 Correct 269 ms 89980 KB Output is correct

Subtask #5
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 43356 KB Output is correct
2 Correct 15 ms 44124 KB Output is correct
3 Correct 13 ms 44120 KB Output is correct
4 Correct 14 ms 44124 KB Output is correct
5 Correct 13 ms 44124 KB Output is correct
6 Correct 12 ms 44380 KB Output is correct
7 Correct 16 ms 44380 KB Output is correct
8 Correct 13 ms 44500 KB Output is correct
9 Correct 13 ms 44376 KB Output is correct
10 Correct 19 ms 45148 KB Output is correct
11 Correct 19 ms 45148 KB Output is correct
12 Correct 19 ms 45056 KB Output is correct
13 Correct 19 ms 45148 KB Output is correct
14 Correct 19 ms 45376 KB Output is correct
15 Correct 19 ms 45020 KB Output is correct
16 Correct 11 ms 43352 KB Output is correct
17 Correct 51 ms 48332 KB Output is correct
18 Correct 249 ms 87696 KB Output is correct
19 Correct 239 ms 84172 KB Output is correct
20 Correct 200 ms 91048 KB Output is correct
21 Correct 241 ms 91552 KB Output is correct
22 Correct 254 ms 92636 KB Output is correct
23 Correct 245 ms 84728 KB Output is correct
24 Correct 199 ms 84328 KB Output is correct
25 Correct 210 ms 84692 KB Output is correct
26 Correct 230 ms 84208 KB Output is correct
27 Correct 200 ms 83656 KB Output is correct
28 Correct 212 ms 84428 KB Output is correct
29 Correct 242 ms 89740 KB Output is correct
30 Correct 226 ms 83984 KB Output is correct
31 Correct 269 ms 89980 KB Output is correct
32 Correct 2593 ms 314576 KB Output is correct
33 Correct 1620 ms 316820 KB Output is correct
34 Correct 1811 ms 312708 KB Output is correct
35 Correct 2325 ms 310376 KB Output is correct
36 Correct 1579 ms 313812 KB Output is correct
37 Correct 1850 ms 311852 KB Output is correct
38 Correct 2560 ms 356028 KB Output is correct
39 Correct 2610 ms 355768 KB Output is correct
40 Correct 2531 ms 316340 KB Output is correct
41 Correct 2655 ms 395712 KB Output is correct
42 Correct 3182 ms 396404 KB Output is correct
43 Correct 3111 ms 396336 KB Output is correct
44 Correct 2983 ms 355036 KB Output is correct