Submission #918229

#	Time	Username	Problem	Language	Result	Execution time	Memory
918229		borisAngelov	Divide and conquer (IZhO14_divide)	C++17	100 / 100	80 ms	11864 KiB

divide

#include <bits/stdc++.h>

using namespace std;

const int maxn = 100005;
const long long inf = 1e17;

int n;

struct Element
{
    int pos;
    long long gold;
    long long energy;
};

Element a[maxn];

long long prefEenrgy[maxn];
long long prefGold[maxn];

struct SegmentTree
{
    long long tree[maxn * 4];
    long long lazy[maxn * 4];

    void build(int node, int l, int r)
    {
        lazy[node] = 0;

        if (l == r)
        {
            tree[node] = prefEenrgy[l] - a[l].pos;
            return;
        }

        int mid = (l + r) / 2;

        build(2 * node, l, mid);
        build(2 * node + 1, mid + 1, r);

        tree[node] = max(tree[2 * node], tree[2 * node + 1]);
    }

    void pushLazy(int node, int l, int r)
    {
        tree[node] += lazy[node];

        if (l != r)
        {
            lazy[2 * node] += lazy[node];
            lazy[2 * node + 1] += lazy[node];
        }

        lazy[node] = 0;
    }

    void update(int node, int l, int r, int ql, int qr, long long delta)
    {
        pushLazy(node, l, r);

        if (l > qr || r < ql)
        {
            return;
        }

        if (ql <= l && r <= qr)
        {
            lazy[node] += delta;
            pushLazy(node, l, r);
            return;
        }

        int mid = (l + r) / 2;

        update(2 * node, l, mid, ql, qr, delta);
        update(2 * node + 1, mid + 1, r, ql, qr, delta);

        tree[node] = max(tree[2 * node], tree[2 * node + 1]);
    }

    int walk(int node, int l, int r)
    {
        pushLazy(node, l, r);

        if (l == r)
        {
            if (tree[node] >= 0)
            {
                return l;
            }
            else
            {
                return -1;
            }
        }

        int mid = (l + r) / 2;

        if (tree[2 * node + 1] + lazy[2 * node + 1] >= 0)
        {
            return walk(2 * node + 1, mid + 1, r);
        }
        else
        {
            return walk(2 * node, l, mid);
        }
    }

    void build()
    {
        build(1, 1, n);
    }

    void update(int l, int r, long long delta)
    {
        update(1, 1, n, l, r, delta);
    }
};

SegmentTree tree;

void fastIO()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}

int main()
{
    fastIO();

    cin >> n;

    for (int i = 1; i <= n; ++i)
    {
        cin >> a[i].pos >> a[i].gold >> a[i].energy;
        prefEenrgy[i] = prefEenrgy[i - 1] + a[i].energy;
        prefGold[i] = prefGold[i - 1] + a[i].gold;
    }

    for (int i = 2; i <= n; ++i)
    {
        a[i].pos -= a[1].pos;
    }

    a[1].pos = 0;

    tree.build();

    long long ans = -inf;

    for (int i = 1; i <= n; ++i)
    {
        ans = max(ans, a[i].gold);
    }

    for (int i = 1; i <= n; ++i)
    {
        int pos = tree.walk(1, 1, n);

        if (pos != -1)
        {
            ans = max(ans, prefGold[pos] - prefGold[i - 1]);
        }

        if (i + 1 <= n)
        {
            tree.update(i + 1, n, (a[i + 1].pos - a[i].pos) - a[i].energy);
        }

        tree.update(i, i, -inf);
    }

    cout << ans << endl;

    return 0;
}

/*
4
0 5 1
1 7 2
4 4 1
7 15 1

4
1 5 1
2 7 2
5 4 1
8 15 1

2
2 4 1
5 5 1
*/

• Subtask 1: 17 / 17
• Subtask 2: 31 / 31
• Subtask 3: 52 / 52