結果
| 問題 | No.1417 100の倍数かつ正整数(2) |
| ユーザー |
 mjtai
|
| 提出日時 | 2021-03-05 22:50:32 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 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 | 2,607 ms |
| コンパイル使用メモリ | 219,920 KB |
| 最終ジャッジ日時 | 2025-01-19 11:44:07 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 36 |
ソースコード
///////////////////////////////////////////////////////////////////////////////
#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;
}
///////////////////////////////////////////////////////////////////////////////