結果

問題 No.1417 100の倍数かつ正整数(2)
ユーザー mjtaimjtai
提出日時 2021-03-05 22:50:32
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 5 ms / 3,000 ms
コード長 12,075 bytes
コンパイル時間 2,751 ms
コンパイル使用メモリ 227,440 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-07 03:50:42
合計ジャッジ時間 3,831 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,820 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 3 ms
6,816 KB
testcase_03 AC 2 ms
6,820 KB
testcase_04 AC 3 ms
6,820 KB
testcase_05 AC 2 ms
6,816 KB
testcase_06 AC 2 ms
6,816 KB
testcase_07 AC 2 ms
6,816 KB
testcase_08 AC 3 ms
6,816 KB
testcase_09 AC 2 ms
6,816 KB
testcase_10 AC 2 ms
6,820 KB
testcase_11 AC 2 ms
6,816 KB
testcase_12 AC 2 ms
6,820 KB
testcase_13 AC 2 ms
6,820 KB
testcase_14 AC 3 ms
6,820 KB
testcase_15 AC 2 ms
6,816 KB
testcase_16 AC 2 ms
6,816 KB
testcase_17 AC 2 ms
6,816 KB
testcase_18 AC 3 ms
6,820 KB
testcase_19 AC 2 ms
6,820 KB
testcase_20 AC 2 ms
6,816 KB
testcase_21 AC 3 ms
6,816 KB
testcase_22 AC 3 ms
6,816 KB
testcase_23 AC 2 ms
6,820 KB
testcase_24 AC 3 ms
6,816 KB
testcase_25 AC 2 ms
6,820 KB
testcase_26 AC 3 ms
6,816 KB
testcase_27 AC 2 ms
6,820 KB
testcase_28 AC 2 ms
6,816 KB
testcase_29 AC 2 ms
6,816 KB
testcase_30 AC 3 ms
6,820 KB
testcase_31 AC 3 ms
6,816 KB
testcase_32 AC 3 ms
6,820 KB
testcase_33 AC 3 ms
6,820 KB
testcase_34 AC 5 ms
6,816 KB
testcase_35 AC 5 ms
6,816 KB
testcase_36 AC 5 ms
6,820 KB
testcase_37 AC 5 ms
6,816 KB
testcase_38 AC 5 ms
6,816 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define S static

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef __int128_t ll128;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
void incr_m(map<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(V<ll> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(V<t2> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(V<t3> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(V<t4> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(V<ll> &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

t2 _ext_gcd(ll a, ll b, ll g)
{
    if (!b) return t2(1, 0);
    ll q = a / b;
    ll r = a % b;
    t2 sol = _ext_gcd(b, r, g);
    ll sx = get<0>(sol);
    ll sy = get<1>(sol);
    ll x = sy;
    ll y = sx - q * sy;
    return t2(x, y);
}

t2 ext_gcd(ll a, ll b)
{
    return _ext_gcd(a, b, gcd(a, b));
}

// x and mod must be coprime
ll mod_inv(ll x, ll mod)
{
    t2 result = ext_gcd(x, mod);
    ll ret = get<0>(result);
    while (ret < 0) ret += mod;
    ret %= mod;
    return ret;
}

ll msec()
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    ll ret = 0;
    ret += tv.tv_sec * 1000LL;
    ret += tv.tv_usec / 1000LL;
    return ret;
}


template <typename T>
void _debug_print(T x)
{
    cout << x << " ";
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "(" << x1 << ", " << x2 << ") ";
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "(" << x1 << ", " << x2 << ", " << x3 << ") ";
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "(" << x1 << ", " << x2 << ", " << x3 << ", " << x4 << ") ";
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
    cout << endl;
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) _debug_print(x);
    cout << endl;
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) _debug_print(x);
    cout << endl;
}

template <typename TT, typename T>
void _debug_print(const map<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "K=";
        _debug_print(k);
        cout << " V=";
        _debug_print(v);
        cout << endl;
    }
}





#define MOD   (1000000007LL)
// #define MOD   (998244353LL)

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// returns t2(solution, mod)
t2 chinese_remainder(ll a1, ll m1, ll a2, ll m2)
{
    assert(a1 >= 0);
    assert(m1 > 0);
    assert(a2 >= 0);
    assert(m2 > 0);

    ll mgcd = gcd(m1, m2);
    if (a1 % mgcd != a2 % mgcd) return t2(0, 0);
    ll mlcm = m1 * m2 / mgcd;
    t2 z = ext_gcd(m1, m2);
    ll z1 = get<0>(z);
    ll z2 = get<1>(z);

    // ll x = a1 + ((a2 - a1) / mgcd) * m1 * z1;

    ll x = z1;
    while (x < 0) x += mlcm;

    x = mod_mlt(x, m1, mlcm);

    ll coef = (a2 - a1) / mgcd;
    while (coef < 0) coef += mlcm;
    x = mod_mlt(x, coef, mlcm);

    x += a1;
    x %= mlcm;

    return t2(x, mlcm);
}

void get_divisors(V<ll> &retlist, ll x)
{
    for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
        if (x % i == 0LL) {
            retlist.push_back(i);
            retlist.push_back(x / i);
        }
    }
}

// returns factors and 1
void get_factors(V<ll> &retlist, ll x)
{
    retlist.pb(1LL);
    for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
        while (x % i == 0LL) {
            retlist.pb(i);
            x /= i;
        }
    }
    retlist.pb(x);
}

bool is_prime(ll x)
{
    V<ll> factors, factors2;

    get_factors(factors, x);

    for (auto factor : factors) {
        if (factor > 1) factors2.pb(factor);
    }

    return factors2.size() == 1 && x == factors2[0];
}

void eratosthenes(set<ll> &primes, ll n)
{
    bool *is_not_prime = new bool[n+3LL];
    memset(is_not_prime, 0, sizeof(bool) * (n+3LL));

    srep (v, 2LL, (ll)sqrt(n)+10LL) {
        if (is_not_prime[v]) continue;
        for (ll vv = v * 2LL; vv <= n; vv += v) {
            is_not_prime[vv] = true;
        }
    }

    srep (v, 2LL, n+1LL) if (!is_not_prime[v]) primes.insert(v);

    delete [] is_not_prime;
}

// p must be prime
ll mod_root(ll p)
{
    if (p == 2) return 1;
    if (p == 3) return 2;

    V<ll> flist;
    get_factors(flist, p-1LL);
    set<ll> fs;
    for (auto f : flist) if (f > 1) fs.insert(f);

    srep (a, 2, p) {
        bool ok = true;
        for (auto f : fs) {
            if (mod_pow(a, (p-1LL) / f, p) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return a;
    }

    assert(false);
}

ull combination(ll x, ll y)
{
    if (y > x / 2LL) y = x - y;

    ull ret = 1LL;
    for (ll i = 0LL; i < y; ++i) {
        ret *= x--;
        ret /= (i + 1LL);
    }

    return ret;
}

void make_factorial(ll factorials[], ll inv_factorials[], ll size, ll mod)
{
    factorials[0] = 1LL;
    srep (i, 1, size) {
        factorials[i] = factorials[i-1] * i;
        factorials[i] %= mod;
    }

    inv_factorials[size-1] = mod_inv(factorials[size-1], mod);
    rrep (i, size-1) {
        inv_factorials[i] = inv_factorials[i+1LL] * (i+1LL);
        inv_factorials[i] %= mod;
    }
}

#if 0
S ll factorials[200010];
S ll inv_factorials[200010];
make_factorial(factorials, inv_factorials, 200010, MOD);
#endif




///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

void _main()
{
    string sn; CIN(sn);

    ll ans = 0;

    S ll dp1[10010][3][3];
    memset(dp1, 0, sizeof(dp1));
    dp1[0][0][0] = 1;
    srep (len, 1, sn.size()) {
        dp1[len][0][0] += dp1[len-1][0][0] * 4LL;
        dp1[len][0][0] %= MOD;

        dp1[len][0][1] += dp1[len-1][0][0];
        dp1[len][0][1] += dp1[len-1][0][1] * 4LL;
        dp1[len][0][1] %= MOD;

        dp1[len][0][2] += dp1[len-1][0][1];
        dp1[len][0][2] += dp1[len-1][0][2] * 5LL;
        dp1[len][0][2] %= MOD;

        dp1[len][1][0] += dp1[len-1][0][0] * 2LL;
        dp1[len][1][0] += dp1[len-1][1][0] * 4LL;
        dp1[len][1][0] %= MOD;

        dp1[len][1][1] += dp1[len-1][1][0];
        dp1[len][1][1] += dp1[len-1][0][1] * 2LL;
        dp1[len][1][1] += dp1[len-1][1][1] * 4LL;
        dp1[len][1][1] %= MOD;

        dp1[len][1][2] += dp1[len-1][0][2] * 2LL;
        dp1[len][1][2] += dp1[len-1][1][1];
        dp1[len][1][2] += dp1[len-1][1][2] * 5LL;
        dp1[len][1][2] %= MOD;

        dp1[len][2][0] += dp1[len-1][0][0] * 2LL;
        dp1[len][2][0] += dp1[len-1][1][0] * 4LL;
        dp1[len][2][0] += dp1[len-1][2][0] * 8LL;
        dp1[len][2][0] %= MOD;

        dp1[len][2][1] += dp1[len-1][0][1] * 2LL;
        dp1[len][2][1] += dp1[len-1][1][1] * 4LL;
        dp1[len][2][1] += dp1[len-1][2][1] * 8LL;
        dp1[len][2][1] += dp1[len-1][2][0];
        dp1[len][2][1] %= MOD;

        dp1[len][2][2] += dp1[len-1][0][2] * 2LL;
        dp1[len][2][2] += dp1[len-1][1][2] * 4LL;
        dp1[len][2][2] += dp1[len-1][2][1];
        dp1[len][2][2] += dp1[len-1][2][2] * 9LL;
        dp1[len][2][2] %= MOD;
    }

    rep (len, 4) {
        ll cnt = 0;
        rep (i, 3) rep (j, 3) cnt += dp1[len][i][j];
        debug_printf("---- len=%lld cnt=%lld\n", len, cnt);
    }

    rep (len, sn.size()) {
        ans += dp1[len][2][2];
        ans %= MOD;
    }
    debug_printf("---- ans 1 = %lld\n", ans);

    S ll dp2[3][3];  // (just, 2cnt, 5cnt)
    memset(dp2, 0, sizeof(dp2));
    ll just2 = 0;
    ll just5 = 0;
    bool just_valid = true;

    for (auto c : sn) {
        ll dp2_prev[3][3];
        memcpy(dp2_prev, dp2, sizeof(dp2_prev));
        memset(dp2, 0, sizeof(dp2));

        if (just_valid) {
            srep (d, '1', c) {
                if (d == '2' || d == '6') {
                    dp2[min(2LL, just2+1LL)][just5]++;
                    dp2[min(2LL, just2+1LL)][just5] %= MOD;
                }
                else if (d == '4' || d == '8') {
                    dp2[2][just5]++;
                    dp2[2][just5] %= MOD;
                }
                else if (d == '5') {
                    dp2[just2][min(2LL, just5+1LL)]++;
                    dp2[just2][min(2LL, just5+1LL)] %= MOD;
                }
                else {
                    dp2[just2][just5]++;
                    dp2[just2][just5] %= MOD;
                }
            }
        }

        srep (d, '1', '9'+1) rep (cnt2, 3) rep (cnt5, 3) {
            if (d == '2' || d == '6') {
                dp2[min(2LL, cnt2+1LL)][cnt5] += dp2_prev[cnt2][cnt5];
                dp2[min(2LL, cnt2+1LL)][cnt5] %= MOD;
            }
            else if (d == '4' || d == '8') {
                dp2[2][cnt5] += dp2_prev[cnt2][cnt5];
                dp2[2][cnt5] %= MOD;
            }
            else if (d == '5') {
                dp2[cnt2][min(2LL, cnt5+1LL)] += dp2_prev[cnt2][cnt5];
                dp2[cnt2][min(2LL, cnt5+1LL)] %= MOD;
            }
            else {
                dp2[cnt2][cnt5] += dp2_prev[cnt2][cnt5];
                dp2[cnt2][cnt5] %= MOD;
            }
        }

        if (c == '2' || c == '6') just2 = min(2LL, just2+1LL);
        if (c == '4' || c == '8') just2 = 2;
        if (c == '5') just5 = min(2LL, just5+1LL);
        if (c == '0') just_valid = false;

        debug_printf("------------------\n");
        rep (x2, 3) rep (x5, 3) debug_printf("dp2[%lld][%lld] = %lld\n", x2, x5, dp2[x2][x5]);
    }

    ans += dp2[2][2];
    if (just_valid && just2 == 2 && just5 == 2) ans++;
    ans %= MOD;


    debug_printf("---- ans\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////
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