Submission #1033289

#	Time	Username	Problem	Language	Result	Execution time	Memory
1033289		borisAngelov	Trains (BOI24_trains)	C++17	71 / 100	192 ms	3164 KiB

Main

#include <bits/stdc++.h>

using namespace std;

const int maxn = 100005;
const int BLOCK_SIZE = 355;
const int mod = 1e9 + 7;

int n;
int d[maxn], x[maxn];
int dp[maxn];
int pref[maxn];

int prefSmall[BLOCK_SIZE][BLOCK_SIZE];

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 >> d[i] >> x[i];
    }

    if (n <= 10000)
    {
        dp[1] = 1;
        int ans = 1;

        for (int i = 2; i <= n; ++i)
        {
            for (int j = i - 1; j >= 1; --j)
            {
                if (d[j] != 0 && (i - j) % d[j] == 0 && (i - j) / d[j] <= x[j])
                {
                    dp[i] += dp[j];
                    //cout << "from " << j << " to " << i << endl;
                    if (dp[i] >= mod) dp[i] -= mod;
                }
            }

            ans += dp[i];
            if (ans >= mod) ans -= mod;

            //cout << "here " << i << " :: " << dp[i] << endl;
        }

        cout << ans << endl;
        return 0;
    }

    bool allD = true, allX = true;

    for (int i = 1; i <= n; ++i)
    {
        allD &= (d[i] == 1);
        allX &= (x[i] == 1000000000);
    }

    if (allD == true)
    {
        for (int i = 1; i <= n; ++i)
        {
            x[i] = min(x[i], n);
        }

        dp[1] = 1;
        pref[1] = 1;
        pref[x[1] + 2] = mod - 1;

        int ans = 1;

        for (int i = 2; i <= n; ++i)
        {
            pref[i] += pref[i - 1];
            if (pref[i] >= mod) pref[i] -= mod;

            dp[i] = pref[i];
            ans += dp[i];
            if (ans >= mod) ans -= mod;

            pref[i + 1] += dp[i];
            if (pref[i + 1] >= mod) pref[i + 1] -= mod;

            pref[min(n + 1, i + x[i] + 1)] -= dp[i];
            if (pref[min(n + 1, i + x[i] + 1)] < 0) pref[min(n + 1, i + x[i] + 1)] += mod;

            //cout << i << " :: " << dp[i] << endl;
            //cout << min(n + 1, i + x[i] + 1) << endl;
        }

        cout << ans << endl;
        return 0;
    }

    if (allX == true)
    {
        int big = sqrt(n);
        int ans = 0;

        for (int i = 1; i <= n; ++i)
        {
            if (i == 1)
            {
                dp[i] = 1;
            }
            else
            {
                for (int small = 1; small < big; ++small)
                {
                    dp[i] += prefSmall[small][i % small];
                    if (dp[i] >= mod) dp[i] -= mod;
                }
            }

            if (d[i] >= big)
            {
                for (int j = i + d[i]; j <= n; j += d[i])
                {
                    dp[j] += dp[i];
                    if (dp[j] >= mod) dp[j] -= mod;
                }
            }
            else
            {
                prefSmall[d[i]][i % d[i]] += dp[i];
                if (prefSmall[d[i]][i % d[i]] >= mod) prefSmall[d[i]][i % d[i]] -= mod;
            }

            ans += dp[i];
            if (ans >= mod) ans -= mod;

            //cout << i << " :: " << dp[i] << endl;
        }

        cout << ans << endl;
    }

    return 0;
}

/*
5
1 3
1 1
1 2
1 2
1 2
2 :: 1
3 :: 2
4 :: 3
5 :: 5

12
3 1000000000
5 1000000000
2 1000000000
7 1000000000
4 1000000000
1 1000000000
1 1000000000
5 1000000000
2 1000000000
1 1000000000
1 1000000000
3 1000000000
here 2 :: 0
here 3 :: 0
here 4 :: 1
here 5 :: 0
here 6 :: 0
here 7 :: 1
here 8 :: 1
here 9 :: 1
here 10 :: 2
here 11 :: 5
here 12 :: 8
*/

• Subtask 1: 8 / 8
• Subtask 2: 13 / 13
• Subtask 3: 16 / 16
• Subtask 4: 34 / 34
• Subtask 5: 0 / 29