Submission #934508

#	Time	Username	Problem	Language	Result	Execution time	Memory
934508		boris_mihov	Chorus (JOI23_chorus)	C++17	100 / 100	1661 ms	44052 KiB

chorus

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

typedef long long llong;
const int MAXN = 1000000 + 10;
const llong INF = 1e18;

int n, k;
struct ConvexHullTrick
{
    struct Line
    {
        llong a, b;
        int cntPenalties;
        llong to;

        std::pair <llong,int> at(llong x)
        {
            return {x * a + b, cntPenalties};
        }
    };

    std::deque <Line> cht;
    llong intersect(Line x, Line y)
    {
        assert(x.a > y.a);
        assert(x.b < y.b);  
        return (y.b - x.b) / (x.a - y.a) - (((y.b - x.b) % (y.a - x.a) == 0) && x.cntPenalties < y.cntPenalties);
    }

    void push(Line l)
    {
        while (cht.size() && cht.back().at(cht.back().to) > l.at(cht.back().to))
        {
            cht.pop_back();
        }

        if (cht.empty()) cht.push_back(l);
        else if (cht.back().at(0) > l.at(0)) cht.push_back({l.a, l.b, l.cntPenalties, intersect(l, cht.back())});
    }
    
    std::pair <llong,int> query(llong x)
    { 
        assert(cht.size());
        while (cht.size() > 1 && x <= cht[1].to)
        {
            cht.pop_front();
        }

        return cht[0].at(x);
    }
};

int h[MAXN];
int next[MAXN];
llong prefix[MAXN];
std::pair <llong,int> dp[MAXN];
char s[2 * MAXN];

std::pair <llong,int> calc(llong penalty)
{
    dp[n + 1] = {0, 0};
    ConvexHullTrick cht;
    cht.push({-(n + 1), dp[n + 1].first + prefix[n], dp[n + 1].second, n});
    int ptr = n + 1;

    for (int pos = n ; pos >= 1 ; --pos)
    {
        dp[pos] = {INF, 0};
        if (pos < next[pos])
        {
            dp[pos] = dp[next[pos]];
            dp[pos].first += penalty;
            dp[pos].second++;
        }

        while (ptr - 1 > std::max(pos, next[pos]))
        {
            ptr--;
            cht.push({-ptr, prefix[ptr - 1] + dp[ptr].first, dp[ptr].second, n});
        }

        llong addedValue = 1LL * (next[pos] - pos + 1) * (pos - 1) + 1LL * pos * (pos - 1) - prefix[next[pos]] + penalty;
        std::pair <llong,int> res = cht.query(pos - 1);
        res.first += addedValue;
        res.second += 1;

        dp[pos] = std::min(dp[pos], res);
    }

    return dp[1];
}

void solve()
{
    int cntA = 0;
    int cntB = 0;
    for (int i = 1 ; i <= 2 * n ; ++i)
    {
        if (s[i] == 'B')
        {
            cntB++;
        } else
        {
            cntA++;
            h[cntA] = cntB;
        }
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        prefix[i] = prefix[i - 1] + h[i];
    }

    next[n + 1] = n + 1;
    h[n + 1] = n + 1;
    for (int i = n ; i >= 1 ; --i)
    {
        next[i] = next[i + 1];
        while (next[i] >= i && h[next[i]] >= i)
        {
            next[i]--;
        }
    }

    llong l = -1, r = 1LL * n * n, mid;
    while (l < r - 1)
    {
        mid = (l + r) / 2;
        if (calc(mid).second > k) l = mid;
        else r = mid;
    }

    auto [fL, groupsL] = calc(l);
    auto [fR, groupsR] = calc(r); 
    fL -= groupsL * l;
    fR -= groupsR * r;

    if (groupsR == k)
    {
        std::cout << fR << '\n';
        return;
    }

    std::cout << fL + (fR - fL) * (groupsL - k) / (groupsL - groupsR) << '\n';
}

void input()
{
    std::cin >> n >> k;
    std::cin >> s + 1;
}

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

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

    return 0;
}

Compilation message (stderr)

chorus.cpp: In function 'void input()':
chorus.cpp:155:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  155 |     std::cin >> s + 1;
      |                 ~~^~~

• Subtask 1: 16 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 26 / 26
• Subtask 5: 13 / 13