/*
author: Maksim1744
created: 09.12.2021 00:29:14
*/
#include "bits/stdc++.h"
using namespace std;
using ll = long long;
using ld = long double;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define sum(a) ( accumulate ((a).begin(), (a).end(), 0ll))
#define mine(a) (*min_element((a).begin(), (a).end()))
#define maxe(a) (*max_element((a).begin(), (a).end()))
#define mini(a) ( min_element((a).begin(), (a).end()) - (a).begin())
#define maxi(a) ( max_element((a).begin(), (a).end()) - (a).begin())
#define lowb(a, x) ( lower_bound((a).begin(), (a).end(), (x)) - (a).begin())
#define uppb(a, x) ( upper_bound((a).begin(), (a).end(), (x)) - (a).begin())
template<typename T> vector<T>& operator-- (vector<T> &v){for (auto& i : v) --i; return v;}
template<typename T> vector<T>& operator++ (vector<T> &v){for (auto& i : v) ++i; return v;}
template<typename T> istream& operator>>(istream& is, vector<T> &v){for (auto& i : v) is >> i; return is;}
template<typename T> ostream& operator<<(ostream& os, vector<T> v){for (auto& i : v) os << i << ' '; return os;}
template<typename T, typename U> pair<T,U>& operator-- (pair<T, U> &p){--p.first; --p.second; return p;}
template<typename T, typename U> pair<T,U>& operator++ (pair<T, U> &p){++p.first; ++p.second; return p;}
template<typename T, typename U> istream& operator>>(istream& is, pair<T, U> &p){is >> p.first >> p.second; return is;}
template<typename T, typename U> ostream& operator<<(ostream& os, pair<T, U> p){os << p.first << ' ' << p.second; return os;}
template<typename T, typename U> pair<T,U> operator-(pair<T,U> a, pair<T,U> b){return mp(a.first-b.first, a.second-b.second);}
template<typename T, typename U> pair<T,U> operator+(pair<T,U> a, pair<T,U> b){return mp(a.first+b.first, a.second+b.second);}
template<typename T, typename U> void umin(T& a, U b){if (a > b) a = b;}
template<typename T, typename U> void umax(T& a, U b){if (a < b) a = b;}
#ifdef HOME
#define SHOW_COLORS
#include "/mnt/c/Libs/tools/print.cpp"
#else
#define show(...) void(0)
#define debugf(fun) fun
#define debugv(var) var
#define mclock void(0)
#define shows void(0)
#define debug if (false)
#endif
namespace mint_ns {
template<auto P>
struct Modular {
using value_type = decltype(P);
value_type value;
Modular(long long k = 0) : value(norm(k)) {}
friend Modular<P>& operator += ( Modular<P>& n, const Modular<P>& m) { n.value += m.value; if (n.value >= P) n.value -= P; return n; }
friend Modular<P> operator + (const Modular<P>& n, const Modular<P>& m) { Modular<P> r = n; return r += m; }
friend Modular<P>& operator -= ( Modular<P>& n, const Modular<P>& m) { n.value -= m.value; if (n.value < 0) n.value += P; return n; }
friend Modular<P> operator - (const Modular<P>& n, const Modular<P>& m) { Modular<P> r = n; return r -= m; }
friend Modular<P> operator - (const Modular<P>& n) { return Modular<P>(-n.value); }
friend Modular<P>& operator *= ( Modular<P>& n, const Modular<P>& m) { n.value = n.value * 1ll * m.value % P; return n; }
friend Modular<P> operator * (const Modular<P>& n, const Modular<P>& m) { Modular<P> r = n; return r *= m; }
friend Modular<P>& operator /= ( Modular<P>& n, const Modular<P>& m) { return n *= m.inv(); }
friend Modular<P> operator / (const Modular<P>& n, const Modular<P>& m) { Modular<P> r = n; return r /= m; }
Modular<P>& operator ++ ( ) { return *this += 1; }
Modular<P>& operator -- ( ) { return *this -= 1; }
Modular<P> operator ++ (int) { Modular<P> r = *this; *this += 1; return r; }
Modular<P> operator -- (int) { Modular<P> r = *this; *this -= 1; return r; }
friend bool operator == (const Modular<P>& n, const Modular<P>& m) { return n.value == m.value; }
friend bool operator != (const Modular<P>& n, const Modular<P>& m) { return n.value != m.value; }
explicit operator int() const { return value; }
explicit operator bool() const { return value; }
explicit operator long long() const { return value; }
constexpr static value_type mod() { return P; }
value_type norm(long long k) {
if (!(-P <= k && k < P)) k %= P;
if (k < 0) k += P;
return k;
}
Modular<P> inv() const {
value_type a = value, b = P, x = 0, y = 1;
while (a != 0) { value_type k = b / a; b -= k * a; x -= k * y; swap(a, b); swap(x, y); }
return Modular<P>(x);
}
};
template<auto P> Modular<P> pow(Modular<P> m, long long p) {
Modular<P> r(1);
while (p) {
if (p & 1) r *= m;
m *= m;
p >>= 1;
}
return r;
}
template<auto P> ostream& operator << (ostream& o, const Modular<P>& m) { return o << m.value; }
template<auto P> istream& operator >> (istream& i, Modular<P>& m) { long long k; i >> k; m.value = m.norm(k); return i; }
template<auto P> string to_string(const Modular<P>& m) { return to_string(m.value); }
using Mint = Modular<1000000007>;
// using Mint = Modular<998244353>;
// using Mint = long double;
vector<Mint> f, fi;
void init_C(int n) {
f.assign(n, 1); fi.assign(n, 1);
for (int i = 2; i < n; ++i) f[i] = f[i - 1] * i;
fi.back() = Mint(1) / f.back();
for (int i = n - 2; i >= 0; --i) fi[i] = fi[i + 1] * (i + 1);
}
Mint C(int n, int k) {
if (k < 0 || k > n) return 0;
else return f[n] * fi[k] * fi[n - k];
}
}
using namespace mint_ns;
template<typename T, int N>
struct Matrix {
array<array<T, N>, N> m;
Matrix() {
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
m[i][j] = 0;
}
}
}
Matrix(std::initializer_list<std::initializer_list<T>> s) {
int i = 0;
for (auto it = s.begin(); it != s.end(); ++it) {
int j = 0;
for (auto it2 = it->begin(); it2 != it->end(); ++it2) {
m[i][j] = *it2;
++j;
}
++i;
}
}
static Matrix E() {
Matrix e;
for (int i = 0; i < N; ++i) {
e[i][i] = 1;
}
return e;
}
array<T, N> &operator[](int i) {
return m[i];
}
const array<T, N> &operator[](int i) const {
return m[i];
}
Matrix operator * (const Matrix &b) const {
Matrix c;
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
for (int k = 0; k < N; ++k) {
c[i][k] += m[i][j] * b[j][k];
}
}
}
return c;
}
Matrix &operator *= (const Matrix &other) {
*this = (*this) * other;
return *this;
}
Matrix &operator *= (const T &x) {
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
m[i][j] *= x;
}
}
return *this;
}
Matrix operator * (const T &x) const {
Matrix a = *this;
a *= x;
return a;
}
Matrix &operator /= (const T &x) {
T inv = T(1) / x;
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
m[i][j] *= inv;
}
}
return *this;
}
Matrix operator / (const T &x) const {
Matrix a = *this;
a /= x;
return a;
}
Matrix &operator += (const Matrix &other) {
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
m[i][j] += other[i][j];
}
}
return *this;
}
Matrix operator + (const Matrix &other) const {
Matrix a = *this;
a += other;
return a;
}
Matrix &operator -= (const Matrix &other) {
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
m[i][j] -= other[i][j];
}
}
return *this;
}
Matrix operator - (const Matrix &other) const {
Matrix a = *this;
a -= other;
return a;
}
};
template<typename T, int N>
Matrix<T, N> pow(Matrix<T, N> m, ll p) {
Matrix<T, N> res = Matrix<T, N>::E();
while (p) {
if (p & 1) res *= m;
m *= m;
p >>= 1;
}
return res;
}
using M = Matrix<Mint, 4>;
int get_ind(int num, int b) {
return (num == 1) + (b) * 2;
}
struct item {
M m;
template<typename T>
void init(const T &t, int l, int r) {
m = M();
for (int prev = 0; prev < 2; ++prev) {
for (int next = 0; next < 10; ++next) {
if (prev == 1 && next == 3) continue;
if (next <= t) {
m[get_ind(next, next == t)][get_ind(prev, 1)]++;
}
m[get_ind(next, 0)][get_ind(prev, 0)]++;
}
}
}
void update(const item &first, const item &second, int l, int r) {
m = second.m * first.m;
}
static item merge(const item &first, const item &second, int l, int r) {
item res;
res.update(first, second, l, r); // careful with different lengths
return res;
}
};
string to_string(const item &i) {
stringstream ss;
ss << "[" << "]";
return ss.str();
}
ostream& operator << (ostream &o, const item &i) {
return o << to_string(i);
}
struct segtree {
vector<item> tree;
int n = 1;
segtree(int n = 1) : n(n) {
tree.resize(1 << (__lg(max(1, n - 1)) + 2));
}
template<typename T>
void build(const vector<T> &v, int i, int l, int r) {
if (l == r) {
tree[i].init(v[l], l, r);
return;
}
int m = (l + r) >> 1;
build(v, i * 2 + 1, l, m);
build(v, i * 2 + 2, m + 1, r);
tree[i].update(tree[i * 2 + 1], tree[i * 2 + 2], l, r);
}
template<typename T>
void build(const vector<T> &v) {
n = v.size();
tree.resize(1 << (__lg(max(1, n - 1)) + 2));
build(v, 0, 0, n - 1);
}
item ask(int l, int r, int i, int vl, int vr) {
if (l == vl && r == vr) {
return tree[i];
}
int m = (vl + vr) >> 1;
if (r <= m) {
return ask(l, r, i * 2 + 1, vl, m);
} else if (m < l) {
return ask(l, r, i * 2 + 2, m + 1, vr);
} else {
return item::merge(ask(l, m, i * 2 + 1, vl, m), ask(m + 1, r, i * 2 + 2, m + 1, vr), l, r);
}
}
item ask(int l, int r) {
l = max(l, 0); r = min(r, n - 1);
if (l > r) return item();
return ask(l, r, 0, 0, n - 1);
}
template<typename T>
void set(int ind, const T &t) {
static array<pair<int, int>, 30> st;
int l = 0, r = n - 1, i = 0;
int ptr = -1;
while (l != r) {
st[++ptr] = {l, r};
int m = (l + r) >> 1;
if (ind <= m) {
i = i * 2 + 1;
r = m;
} else {
i = i * 2 + 2;
l = m + 1;
}
}
tree[i].init(t, l, r);
while (i != 0) {
i = (i - 1) / 2;
tree[i].update(tree[i * 2 + 1], tree[i * 2 + 2], st[ptr].first, st[ptr].second);
--ptr;
}
}
};
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
int n, q;
cin >> n >> q;
string s;
cin >> s;
vector<int> v;
for (char c : s)
v.pb(c - '0');
segtree tree(n);
tree.build(v);
auto que = [&](int l, int r) {
M m = tree.ask(l, r).m;
Mint ans = 0;
for (int i = 0; i < 4; ++i)
ans += m[i][2];
cout << ans << '\n';
};
que(0, n - 1);
while (q--) {
int t;
cin >> t;
if (t == 1) {
int l, r;
cin >> l >> r;
--l; --r;
que(l, r);
} else {
int ind, c;
cin >> ind >> c;
--ind;
tree.set(ind, c);
}
}
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
0 ms |
204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
0 ms |
204 KB |
Output is correct |
| 4 |
Correct |
0 ms |
204 KB |
Output is correct |
| 5 |
Correct |
1 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
24 ms |
1484 KB |
Output is correct |
| 2 |
Correct |
40 ms |
2560 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
24 ms |
1484 KB |
Output is correct |
| 2 |
Correct |
40 ms |
2560 KB |
Output is correct |
| 3 |
Correct |
65 ms |
17372 KB |
Output is correct |
| 4 |
Correct |
66 ms |
17364 KB |
Output is correct |
| 5 |
Correct |
68 ms |
17492 KB |
Output is correct |
| 6 |
Correct |
81 ms |
17564 KB |
Output is correct |
| 7 |
Correct |
79 ms |
17468 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
0 ms |
204 KB |
Output is correct |
| 4 |
Correct |
0 ms |
204 KB |
Output is correct |
| 5 |
Correct |
1 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
24 ms |
1484 KB |
Output is correct |
| 8 |
Correct |
40 ms |
2560 KB |
Output is correct |
| 9 |
Correct |
27 ms |
1452 KB |
Output is correct |
| 10 |
Correct |
39 ms |
2624 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
0 ms |
204 KB |
Output is correct |
| 4 |
Correct |
0 ms |
204 KB |
Output is correct |
| 5 |
Correct |
1 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
24 ms |
1484 KB |
Output is correct |
| 8 |
Correct |
40 ms |
2560 KB |
Output is correct |
| 9 |
Correct |
65 ms |
17372 KB |
Output is correct |
| 10 |
Correct |
66 ms |
17364 KB |
Output is correct |
| 11 |
Correct |
68 ms |
17492 KB |
Output is correct |
| 12 |
Correct |
81 ms |
17564 KB |
Output is correct |
| 13 |
Correct |
79 ms |
17468 KB |
Output is correct |
| 14 |
Correct |
27 ms |
1452 KB |
Output is correct |
| 15 |
Correct |
39 ms |
2624 KB |
Output is correct |
| 16 |
Correct |
64 ms |
17544 KB |
Output is correct |
| 17 |
Correct |
70 ms |
17560 KB |
Output is correct |
| 18 |
Correct |
78 ms |
17628 KB |
Output is correct |
| 19 |
Correct |
79 ms |
17716 KB |
Output is correct |
| 20 |
Correct |
79 ms |
17688 KB |
Output is correct |
