Submission #291854

#	Time	Username	Problem	Language	Result	Execution time	Memory
291854		Kastanda	Sails (IOI07_sails)	C++11	100 / 100	121 ms	8920 KiB

sails

// M
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
struct CHT
{
        typedef pair < ll , ll > Line;
        vector < pair < ll , Line > > A;
        vector < vector < pair < ll , Line > > > U;
        ll INF = 1e18;
        inline void Add(Line X)
        {
                vector < pair < ll , Line > > nwu;
                while (A.size() && Intersection(A.back().second, X) <= A.back().first)
                        nwu.push_back(A.back()), A.pop_back();
                if (A.size())
                        A.push_back({Intersection(A.back().second, X), X});
                else
                        A.push_back({-INF, X});
                U.push_back(nwu);
        }
        inline ll GetMax(ll X)
        {
                int lb = upper_bound(A.begin(), A.end(), pair < ll , Line > {X, {INF, INF}}) - A.begin() - 1;
                return (A[lb].second.first * X + A[lb].second.second);
        }
        inline ll Intersection(Line X, Line Y)
        {
                if (X.first == Y.first)
                        return X.second <= Y.second ? -INF : INF;
                return ((X.second - Y.second) / (Y.first - X.first)) + ((X.second - Y.second) % (Y.first - X.first) > 0);
        }
        inline void Undo()
        {
                assert(A.size() && U.size());
                vector < pair < ll , Line > > nwu = U.back();
                U.pop_back(); A.pop_back();
                while (nwu.size())
                        A.push_back(nwu.back()), nwu.pop_back();
        }
};
const int N = 100005;
int n, H[N], K[N], C[N];
ll PS[N];
CHT Cht;
/*inline bool Solve(int md)
{
        memset(C, 0, sizeof(C));
        for (int i = 1; i <= n; i ++)
                C[H[i] - K[i] + 1] ++, C[H[i] + 1] --;
        for (int i = 1; i < N; i ++)
                C[i] += C[i - 1];
        ll LeftOver = 0;
        for (int i = N - 1; i; i --)
        {
                int tmp = min(LeftOver, (ll)md - C[i]);
                LeftOver -= tmp;
                C[i] += tmp;
                assert(C[i] <= md);
        }
        return !LeftOver;
}*/
int main()
{
        scanf("%d", &n);
        for (int i = 1; i <= n; i ++)
                scanf("%d%d", &H[i], &K[i]);

        for (int i = 1; i <= n; i ++)
                C[H[i] - K[i] + 1] ++, C[H[i] + 1] --;
        for (int i = 1; i < N; i ++)
                C[i] += C[i - 1];
        for (int i = 1; i < N; i ++)
                PS[i] = PS[i - 1] + C[i];
        for (int i = N - 1; i; i --)
                Cht.Add({-i, PS[i]});

        for (int i = 1; i + 1 < N; i ++)
        {
                int le = max(C[i], 0) - 1, ri = n, md;
                while (ri - le > 1)
                {
                        md = (le + ri) >> 1;
                        if (Cht.GetMax(md) <= PS[i - 1] - (ll)md * (i - 1))
                                ri = md;
                        else
                                le = md;
                }
                PS[i] += ri - C[i];
                C[i + 1] -= ri - C[i];
                C[i] = ri;
                Cht.Undo();
        }

        /* LOL, this was pure nonsense and it got 90 points! XD
        int le = 0, ri = N, md;
        while (ri - le > 1)
        {
                md = (le + ri) >> 1;
                if (Solve(md))
                        ri = md;
                else
                        le = md;
        }

        // How to do it with ri you ask? I don't know either ...
        Solve(ri);
        int ptr = 1;
        for (int i = N - 1; i; i --)
                if (C[i] == ri)
                {
                        while (ptr < i && C[ptr] == ri)
                                ptr ++;
                        if (ptr >= i)
                                break;
                        C[i] --;
                        C[ptr] ++;
                }
        vector < int > A;
        for (int i = 1; i < N; i ++)
        {
                vector < int > Tbo = {C[i]};
                while (Tbo.size())
                {
                        if (!A.size() || A.back() >= Tbo.back())
                        {
                                A.push_back(Tbo.back());
                                Tbo.pop_back();
                                continue;
                        }
                        int nd = (Tbo.back() - A.back() + 1) / 2;
                        Tbo.back() -= nd;
                        Tbo.push_back(A.back() + nd);
                        A.pop_back();
                }
        }
        assert((int)A.size() == N - 1);
        for (int i = 1; i < N; i ++)
                C[i] = A[i - 1];*/
        /*for (int i = 1; i < N; i ++)
                assert(C[i] <= ri);
        bool Fail = 1;
        for (int i = 1; i < N; i ++)
                if (C[i] == ri)
                        Fail = 0;
        assert(!Fail);*/
        for (int i = 2; i < N; i ++)
                assert(C[i - 1] >= C[i]);
        ll tot = 0;
        for (int i = 1; i < N; i ++)
                tot += (ll)C[i] * (C[i] - 1) / 2;
        printf("%lld\n", tot);
        return 0;
}

Compilation message (stderr)

sails.cpp: In function 'int main()':
sails.cpp:65:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   65 |         scanf("%d", &n);
      |         ~~~~~^~~~~~~~~~
sails.cpp:67:22: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   67 |                 scanf("%d%d", &H[i], &K[i]);
      |                 ~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 10 / 10
• Subtask 3: 10 / 10
• Subtask 4: 5 / 5
• Subtask 5: 10 / 10
• Subtask 6: 10 / 10
• Subtask 7: 10 / 10
• Subtask 8: 10 / 10
• Subtask 9: 10 / 10
• Subtask 10: 10 / 10
• Subtask 11: 10 / 10