Submission #927379

#	Time	Username	Problem	Language	Result	Execution time	Memory
927379		boris_mihov	Two Dishes (JOI19_dishes)	C++17	10 / 100	10084 ms	42892 KiB

dishes

#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>

#define int long long
typedef long long llong;
const int MAXN = 200000 + 10;
const int MAXLOG = 20;
const llong INF = 1e18;

int n, m;
template <typename T>
struct Fenwick
{
    T tree[MAXN];
    void update(int pos, T val)
    {
        for (int idx = pos ; idx <= m ; idx += idx & (-idx))
        {
            tree[idx] += val;
        }
    }

    T query(int pos)
    {
        T res = 0;
        for (int idx = pos ; idx > 0 ; idx -= idx & (-idx))
        {
            res += tree[idx];
        }

        return res;
    }

    int findKthZero(int k)
    {
        int idx = 0;
        for (int log = MAXLOG - 1 ; log >= 0 ; --log)
        {
            if (idx + (1 << log) <= m && (1 << log) - tree[idx + (1 << log)] < k)
            {
                idx += (1 << log);
                k -= (1 << log) - tree[idx];
            }
        }

        return idx + 1;
    }

    int findKthOne(int k)
    {
        int idx = 0;
        for (int log = MAXLOG - 1 ; log >= 0 ; --log)
        {
            if (idx + (1 << log) <= m && tree[idx + (1 << log)] < k)
            {
                idx += (1 << log);
                k -= tree[idx];
            }
        }

        return idx + 1;
    }
};

Fenwick <int> fenwickNext;
Fenwick <llong> fenwickActive;

struct Dish
{
    int time;
    llong limit;
    int reward;
    int idx;
    bool type;
};

Dish a[MAXN];
Dish b[MAXN];
llong prefixA[MAXN];
llong prefixB[MAXN];
bool isNext[MAXN];
bool isActive[MAXN];
llong dpBorderM[MAXN];
llong dp[MAXN];

int globalRow;
llong findValue(int col)
{
    if (col == m + 1)
    {
        return dp[m + 1];
    }

    int cnt = col - 1 - fenwickNext.query(col - 1);
    int pos = m;
    
    if (cnt != m - fenwickNext.query(m))
    {
        // std::cout << "IN THE FUCKING IF: " << cnt << ' ' << m << ' ' << fenwickNext.query(m) << '\n';
        // std::cout << "next is\n";
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << fenwickNext.query(i) - fenwickNext.query(i - 1);
        // }

        // std::cout << '\n';

        // std::cout << "lapai\n";
        pos = fenwickNext.findKthZero(cnt + 1);
    }

    // if (col == 3) std::cout << "\n\n      value: " << col << ' ' << m - fenwickNext.query(m) << ' ' << cnt << ' ' << pos << ' ' << fenwickActive.query(pos - 1) - fenwickActive.query(col - 1) + dp[pos] << '\n';
    return fenwickActive.query(pos - 1) - fenwickActive.query(col - 1) + dp[pos];
}

void fix(int col)
{
    assert(col <= m);
    llong prevVal = findValue(col);
    llong curr = dp[col];
    llong next = findValue(col + 1) + fenwickActive.query(col) - fenwickActive.query(col - 1);
    // std::cout << "here: " << curr << ' ' << next << '\n';
    int res = fenwickNext.query(col) - fenwickNext.query(col - 1);
    fenwickNext.update(col, -res);

    int nextVal = 0;
    if (curr > next) 
    {
        fenwickNext.update(col, 0); // unessesary
    } else 
    {
        nextVal = 1;
        fenwickNext.update(col, 1);
    }

    // std::cout << "set: " << col << " = " << curr << ' ' << next << '\n';
    dp[col] = std::max(curr, next);
    if (res != nextVal)
    {
        if (prevVal < dp[col])
        {
            int cntBefore = col - 1 - fenwickNext.query(col - 1);
            // std::cout << "cnt before: " << cntBefore << '\n';
            if (cntBefore > 0)
            {
                fix(fenwickNext.findKthZero(cntBefore));
            }
        } else
        {
            // assert(false);
            int cntBefore = fenwickNext.query(col - 1);
            // std::cout << "cnt before: " << cntBefore << '\n';
            if (cntBefore > 0)
            {
                fix(fenwickNext.findKthOne(cntBefore));
            }
        }
    }
}

void applyUpdate(int to, int val)
{
    for (int i = 1 ; i <= to ; ++i)
    {
        dp[i] += val;
    }
}

std::vector <int> activateAt[MAXN];
void solve()
{
    for (int i = 1 ; i <= n ; ++i)
    {
        prefixA[i] = prefixA[i - 1] + a[i].time;
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        prefixB[i] = prefixB[i - 1] + b[i].time;
    }

    for (int aPos = n ; aPos >= 1 ; --aPos)
    {
        dpBorderM[aPos] = dpBorderM[aPos + 1] + (prefixA[aPos - 1] + prefixB[m] + a[aPos].time <= a[aPos].limit ? a[aPos].reward : 0);
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        int l = 0, r = n + 2, mid;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (prefixA[mid - 1] + prefixB[i] <= b[i].limit) l = mid;
            else r = mid;
        }

        activateAt[l].push_back(i);
        // std::cout << "here: " << i << ' ' << l << '\n';
    }

    globalRow = n + 1;
    for (int i = 1 ; i <= n ; ++i)
    {
        fenwickNext.update(i, 1);
        isNext[i] = true;
    }

    std::sort(activateAt[n + 1].begin(), activateAt[n + 1].end(), std::greater <int> ());
    for (const int &idx : activateAt[globalRow])
    {
        // std::cout << "activate: " << idx << '\n';
        fenwickActive.update(idx, b[idx].reward);
        fix(idx);
    }

    // std::cout << "dp after: " << n + 1 << '\n';
    // for (int i = 1 ; i <= m ; ++i)
    // {
    //     std::cout << findValue(i) << ' ';
    // } 

    // std::cout << '\n';

    for (globalRow = n ; globalRow >= 1 ; --globalRow)
    {
        // std::cout << "      global: " << globalRow << '\n';
        for (const int &idx : activateAt[globalRow])
        {
            dp[idx] = findValue(idx);
        }
    
        int l = 0, r = m + 1, mid;
        while (l < r - 1)
        {
            mid = (l + r) / 2;
            if (prefixA[globalRow] + prefixB[mid - 1] <= a[globalRow].limit) l = mid;
            else r = mid;
        }

        if (l > 0)
        {
            dp[l] = findValue(l);
        }

        for (const int &idx : activateAt[globalRow])
        {
            // std::cout << "      activate: " << idx << '\n';
            fenwickActive.update(idx, b[idx].reward);
        }

        if (l > 0) activateAt[globalRow].push_back(l);
        applyUpdate(l, a[globalRow].reward);

        dp[m + 1] = dpBorderM[globalRow];
        activateAt[globalRow].push_back(m);
        std::sort(activateAt[globalRow].begin(), activateAt[globalRow].end(), std::greater <int> ());

        // std::cout << "after applying\n";
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << findValue(i) << ' ';
        // } 

        // std::cout << '\n';

        // std::cout << "next is\n";
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << fenwickNext.query(i) - fenwickNext.query(i - 1);
        // }

        // std::cout << '\n';
        for (const int &idx : activateAt[globalRow])
        {
            // std::cout << "fix: " << idx << '\n';
            fix(idx);
            if (idx > 1) fix(idx - 1);
        }

        for (int idx = m ; idx >= 1 ; --idx)
        {
            fix(idx);
        }

        // std::cout << "dp after: " << globalRow << '\n';
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << findValue(i) << ' ';
        // } 

        // std::cout << '\n';
        // std::cout << "active\n";
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << isActive[i] << ' ';
        // }

        // std::cout << '\n';
        // std::cout << "next\n";
        // for (int i = 1 ; i <= m ; ++i)
        // {
        //     std::cout << isNext[i] << ' ';
        // }

        // std::cout << '\n';
    }

    globalRow++;
    std::cout << findValue(1) << '\n';
}

void input()
{
    std::cin >> n >> m;
    for (int i = 1 ; i <= n ; ++i)
    {
        std::cin >> a[i].time >> a[i].limit >> a[i].reward;
        a[i].idx = i;
        a[i].type = false;
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        std::cin >> b[i].time >> b[i].limit >> b[i].reward;
        b[i].idx = i;
        a[i].type = true;
    }
}

void fastIOI()
{
    std::ios_base :: sync_with_stdio(0);
    std::cout.tie(nullptr);
    std::cin.tie(nullptr);
}

signed main()
{
    fastIOI();
    input();
    solve();

    return 0;
}

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