Submission #1272423

#	Time	Username	Problem	Language	Result	Execution time	Memory
1272423		Art	Relativnost (COCI15_relativnost)	C++20	56 / 140	779 ms	49812 KiB

relativnost

//      - Art -
#include <bits/stdc++.h>

#define el              cout << '\n'

#define FOR(i, a, b)    for (int i = (a), _b = (b); i <= _b; ++i)
#define REV(i, b, a)    for (int i = (b), _a = (a); i >= _a; --i)
#define REP(i, c)       for (int i = 0, _c = (c); i < _c; ++i)

const int N = 1e5 + 7;
const int MOD = 1e4 + 7;
const int BLOCKSIZE = 578;
const int NUMBLOCK = N / BLOCKSIZE + 7;

using namespace std;

int a[N], b[N];

namespace naive {
    int dp[N][22];

    void solve(int n, int k) {
        int q;
        cin >> q;
        while (q--) {
            int id, na, nb;
            cin >> id >> na >> nb;
            na %= MOD;
            nb %= MOD;
            a[id] = na;
            b[id] = nb;

            dp[0][0] = 1;
            FOR (i, 1, n) REP (j, k) {
                dp[i][j] = dp[i - 1][j] * b[i] % MOD;
                if (j > 0) {
                    dp[i][j] = (dp[i][j] + dp[i - 1][j - 1] * a[i]) % MOD;
                }
            }

            int tot = 1;
            FOR (i, 1, n) {
                tot = (a[i] + b[i]) * tot % MOD;
            }
            REP (i, k) {
                tot = (tot - dp[n][i] + MOD) % MOD;
            }
            cout << tot, el;
        }
    }
}

int inverse(int a) {
    int b = MOD - 2, res = 1;
    while (b) {
        if (b & 1) {
            res = res * a % MOD;
        }
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}

namespace blocksqrt {
    int block[N];
    int dp[NUMBLOCK][22];
    int pre[NUMBLOCK][22];

    void solve(int n, int k) {
        int tot = 1;
        REP (i, n) {
            block[i] = i / BLOCKSIZE;
            a[i] = a[i + 1];
            b[i] = b[i + 1];
            tot = (a[i] + b[i]) * tot % MOD;
        }

        FOR (x, 0, block[n - 1]) {
            int l = x * BLOCKSIZE;
            int r = min(n, l + BLOCKSIZE) - 1;
            dp[x][0] = b[l];
            dp[x][1] = a[l];
            FOR (i, l + 1, r) REV (j, k - 1, 0) {
                dp[x][j] = (dp[x][j] * b[i]) % MOD;
                if (j > 0) {
                    dp[x][j] = (dp[x][j] + dp[x][j - 1] * a[i]) % MOD;
                }
            }
            if (x > 0) {
                REP (j, k) REP (o, j + 1) {
                    pre[x][j] = (pre[x][j] + pre[x - 1][o] * dp[x][j - o]) % MOD;
                }
            }
            else {
                REP (j, k) {
                    pre[x][j] = dp[x][j];
                }
            }
        }

        int q;
        cin >> q;
        while (q--) {
            int id, na, nb;
            cin >> id >> na >> nb;
            na %= MOD;
            nb %= MOD;
            --id;
            tot = tot * inverse(a[id] + b[id]) % MOD;
            tot = tot * (na + nb) % MOD;
            a[id] = na;
            b[id] = nb;

            int x = block[id];
            int l = x * BLOCKSIZE;
            int r = min(n, l + BLOCKSIZE) - 1;
            memset(dp[x], 0, sizeof dp[x]);
            dp[x][0] = b[l];
            dp[x][1] = a[l];
            FOR (i, l + 1, r) {
                REV (j, k - 1, 0) {
                    dp[x][j] = dp[x][j] * b[i] % MOD;
                    if (j > 0) {
                        dp[x][j] = (dp[x][j] + dp[x][j - 1] * a[i]) % MOD;
                    }
                }
            }

            int res = tot;
            for (; x <= block[n - 1]; ++x) {
                if (x > 0) {
                    memset(pre[x], 0, sizeof pre[x]);
                    REP (j, k) {
                        REP (o, j + 1) {
                            pre[x][j] = (pre[x][j] + pre[x - 1][o] * dp[x][j - o]) % MOD;
                        }
                    }
                }
                else {
                    REP (j, k) {
                        pre[x][j] = dp[x][j];
                    }
                }
            }

            REP (j, k) {
                res = (res - pre[block[n - 1]][j] + MOD) % MOD;
            }
            cout << res, el;
        }
    }
}

struct SegmentTree {
    int n, k;
    vector<vector<int>> st;

    SegmentTree(int _n, int _k) {
        n = _n; k = _k;
        st.assign(4 * _n + 7, vector<int>(_k + 7, 0));

        build(1, 1, n);
    }

    void build(int id, int l, int r) {
        if (l == r) {
            st[id][0] = b[l];
            st[id][1] = a[l];
            return;
        }

        int m = (l + r) / 2;
        build(id * 2, l, m);
        build(id * 2 + 1, m + 1, r);

        REP (i, k) REP (j, i + 1) {
            st[id][i] = (st[id][i] + st[id * 2][j] * st[id * 2 + 1][i - j]) % MOD;
        }
    }

    void update(int id, int l, int r, int i) {
        if (i < l || i > r) {
            return;
        }
        if (l == r) {
            st[id][0] = b[l];
            st[id][1] = a[l];
            return;
        }

        int m = (l + r) / 2;
        update(id * 2, l, m, i);
        update(id * 2 + 1, m + 1, r, i);

        REP (i, k) {
            st[id][i] = 0;
            REP (j, i + 1) {
                st[id][i] = (st[id][i] + st[id * 2][j] * st[id * 2 + 1][i - j]) % MOD;
            }
        }
    }
    void update(int i) {
        update(1, 1, n, i);
    }
};

int main() {

    #define name "art"
    if (fopen(name".inp", "r")) {
        freopen(name".inp", "r", stdin);
        freopen(name".out", "w", stdout);
    }

    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    int n, k;
    cin >> n >> k;
    FOR (i, 1, n) {
        cin >> a[i];
        a[i] %= MOD;
    }
    FOR (i, 1, n) {
        cin >> b[i];
        b[i] %= MOD;
    }

    if (n <= 5000) {
        naive::solve(n, k);
        return 0;
    }

    if (n <= 5e4) {
        blocksqrt::solve(n, k);
        return 0;
    }

    int tot = 1;
    FOR (i, 1, n) {
        tot = (a[i] + b[i]) * tot % MOD;
    }

    SegmentTree seg(n, k);

    int q;
    cin >> q;
    while (q--) {
        int id, na, nb;
        cin >> id >> na >> nb;
        na %= MOD;
        nb %= MOD;
        tot = tot * inverse(a[id] + b[id]) % MOD;
        tot = tot * (na + nb) % MOD;
        a[id] = na;
        b[id] = nb;

        seg.update(id);
        int res = tot;
        REP (i, k) {
            res = (res - seg.st[1][i] + MOD) % MOD;
        }
        cout << res, el;
    }

    return 0;
}

Compilation message (stderr)

relativnost.cpp: In function 'int main()':
relativnost.cpp:212:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  212 |         freopen(name".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
relativnost.cpp:213:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  213 |         freopen(name".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 56 / 140