Submission #1316294

#TimeUsernameProblemLanguageResultExecution timeMemory
1316294chithanhnguyenModsum (NOI12_modsum)C++20
25 / 25
1 ms332 KiB
/*
Author: Nguyen Chi Thanh - High School for the Gifted - VNU.HCM (i2528)
*/
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ull unsigned long long
#define ld long double
#define pii pair<int, int>
#define fi first
#define se second
#define __builtin_popcount __builtin_popcountll
#define all(x) (x).begin(), (x).end()
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) ((1ll << (x)))

#define debug(a, l, r) for (int _i = (l); _i <= (r); ++_i) cout << (a)[_i] << ' '; cout << '\n';

const int MAXN = 1005;
int n, dp[MAXN][5];
pii intervals[MAXN];

void init() {
    cin >> n;
    for (int i = 1; i <= n; ++i) {
        pii &cur = intervals[i];
        cin >> cur.fi >> cur.se;
    }
}

int floor_div(int a, int b) {
    if (b < 0) a = -a, b = -b;
    if (a >= 0) return a / b;
    return - ((-a + b - 1) / b);
}

int ceil_div(int a, int b) {
    if (b < 0) a = -a, b = -b;
    if (a >= 0) return (a + b - 1) / b;
    return - ((-a) / b);
}

// Count numer of a_i in [l, r] such that a_i % m = k
int cnt_div(int l, int r, int m, int k) { 
    assert(k < m && l <= r);

    int t_min = ceil_div(l - k, m);
    int t_max = floor_div(r - k, m);

    if (t_min > t_max) return 0;
    return t_max - t_min + 1;
}

void solve() {
    for (int j = 0; j < 5; ++j)
        dp[1][j] = cnt_div(intervals[1].fi, intervals[1].se, 5, j);
    
    for (int i = 1; i < n; ++i) {
        for (int j = 0; j < 5; ++j) {
            for (int cur_rem = 0; cur_rem < 5; ++cur_rem) {
                int nxt_rem = (j + cur_rem) % 5;
                int mul = cnt_div(intervals[i + 1].fi, intervals[i + 1].se, 5, cur_rem);
                dp[i + 1][nxt_rem] += dp[i][j] * mul;

            }
        }
    }
    
    // debug(dp[n], 0, 4);

    int res = 0;
    for (int i = 0; i < 5; ++i) {
        int mul = i * i * i * i + 2 * i * i;
        mul %= 5;
        res += (mul + 1) * dp[n][i];
    }

    cout << res;
}

signed main() {
    #ifdef NCTHANH
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr); cout.tie(nullptr);

    init();
    solve();

    return 0;
}
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