oj.uz

Submission #258148

# Submission time Handle Problem Language Result Execution time Memory
258148 2020-08-05T12:38:18 Z lyc Lucky Numbers (RMI19_lucky) C++14
100 / 100
 58 ms 18036 KB 
#include <bits/stdc++.h>
using namespace std;

#define TRACE(x) cerr << #x << " :: " << x << endl
#define _ << " " <<
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(),(x).end()
#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define RFOR(i,a,b) for (int i=(a);i>=(b);--i)
using ll=long long;

const int mxN = 1e5+5;
const int mod = 1e9+7;

int N, Q;
string X;

int f[mxN][2][2];

using Data = array<array<array<int,2>,2>,2>; // bound, start 3, end 1;
struct node {
	int s, e, m;
	Data v;
	node *l, *r;
	
	void setLeaf(char c) {
		X[s] = c;
		v[1][0][0] = (c != '3' && c != '1');
		v[1][0][1] = (c == '1');
		v[1][1][0] = (c == '3');
		v[1][1][1] = 0;
		int u = c-'0';
		v[0][0][0] = u - (c > '3') - (c > '1');
		v[0][0][1] = (c > '1');
		v[0][1][0] = (c > '3');
		v[0][1][1] = 0;
		
		//~ cout << "SET" _ s _ c << " :: ";
		//~ FOR(x,0,1) FOR(y,0,1) FOR(z,0,1) cout << v[x][y][z] << ' ';
		//~ cout << endl;
	}
	
	inline Data merge(int L, int R, Data a, Data b) {
		Data u;
		int lenb = R-m;
		FOR(i,0,1){
			FOR(j,0,1){				
				u[1][i][j]  = (ll) a[1][i][0] * b[1][0][j] % mod;
				u[1][i][j] += (ll) a[1][i][0] * b[1][1][j] % mod;
				u[1][i][j] %= mod;
				u[1][i][j] += (ll) a[1][i][1] * b[1][0][j] % mod;
				u[1][i][j] %= mod;
			}
		}
		FOR(i,0,1){
			FOR(j,0,1){				
				u[0][i][j]  = (ll) a[0][i][0] * f[lenb][0][j] % mod;
				u[0][i][j] += (ll) a[0][i][0] * f[lenb][1][j] % mod;
				u[0][i][j] %= mod;
				u[0][i][j] += (ll) a[0][i][1] * f[lenb][0][j] % mod;
				u[0][i][j] %= mod;
				
				u[0][i][j] += (ll) a[1][i][0] * b[0][0][j] % mod;
				u[0][i][j] %= mod;
				u[0][i][j] += (ll) a[1][i][0] * b[0][1][j] % mod;
				u[0][i][j] %= mod;
				u[0][i][j] += (ll) a[1][i][1] * b[0][0][j] % mod;
				u[0][i][j] %= mod;
			}
		}
		
		//~ cout << "MERGE" _ L _ R << " :: ";
		//~ FOR(x,0,1) FOR(y,0,1) FOR(z,0,1) cout << u[x][y][z] << ' ';
		//~ cout << endl;
		return u;
	}
		
	node(int s, int e): s(s), e(e), m((s+e)/2) {
		if (s == e) setLeaf(X[s]);
		else {
			l = new node(s,m), r = new node(m+1,e);
			v = merge(s,e,l->v,r->v);
		}
		
		//~ cout << s _ e << " :: ";
		//~ FOR(x,0,1) FOR(y,0,1) FOR(z,0,1) cout << v[x][y][z] << ' ';
		//~ cout << endl;
	}
	
	void update(int a, char b) {
		if (s == e) { setLeaf(b); return; }
		else if (a <= m) l->update(a,b);
		else r->update(a,b);
		v = merge(s,e,l->v,r->v);
	}
	
	Data query(int a, int b) {
		if (s == a && e == b) return v;
		if (b <= m) return l->query(a,b);
		if (a > m) return r->query(a,b);
		return merge(a, b, l->query(a,m), r->query(m+1,b));
	}
} *root;

void answer(int L, int R) {
	Data res = root->query(L,R);
	int ans = 0;
	//~ FOR(x,0,1) FOR(y,0,1) FOR(z,0,1) cout << res[x][y][z] << ' ';
	//~ cout << " :: ";
	FOR(a,0,1) FOR(b,0,1) FOR(c,0,1) ans = (ans+res[a][b][c])%mod;
	cout << ans << '\n';
}

int main() {
	ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	
	cin >> N >> Q >> X;
	X = '^' + X;
	
	f[0][0][0] = 1;
	f[0][0][1] = f[0][1][0] = f[0][1][1] = 0;
	f[1][0][0] = 8;
	f[1][0][1] = f[1][1][0] = 1;
	f[1][1][1] = 0;
	FOR(i,2,N){
		f[i][0][0]  = (ll) f[i-1][0][0] * 9 % mod;
		f[i][0][0] += (ll) f[i-1][0][1] * 8 % mod;
		f[i][0][0] %= mod;
		f[i][0][1]  = (f[i-1][0][0] + f[i-1][0][1]) % mod;
		
		f[i][1][0]  = (ll) f[i-1][1][0] * 9 % mod;
		f[i][1][0] += (ll) f[i-1][1][1] * 8 % mod;
		f[i][1][0] %= mod;
		f[i][1][1]  = (f[i-1][1][0] + f[i-1][1][1]) % mod;
	}
	root = new node(1,N);
	
	//~ int ans = 0;
	//~ FOR(x,0,1) FOR(y,0,1) {
		//~ ans += f[N][x][y];
		//~ cout << f[N][x][y] << ' ';
	//~ }
	//~ cout << " :: " << ans << endl;
	
	answer(1,N);
	FOR(i,1,Q){
		int T; cin >> T;
		if (T == 1) {
			int L, R; cin >> L >> R;
			//~ TRACE(T _ L _ R);
			answer(L,R);
		} else {
			int P; char D; cin >> P >> D;
			root->update(P,D);
		}
	}
}

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 0 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 0 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 304 KB Output is correct
6 Correct 0 ms 384 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 1792 KB Output is correct
2 Correct 21 ms 2176 KB Output is correct

Subtask #4
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 1792 KB Output is correct
2 Correct 21 ms 2176 KB Output is correct
3 Correct 47 ms 14452 KB Output is correct
4 Correct 45 ms 14452 KB Output is correct
5 Correct 51 ms 16244 KB Output is correct
6 Correct 55 ms 18036 KB Output is correct
7 Correct 56 ms 18036 KB Output is correct

Subtask #5
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 0 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 304 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 17 ms 1792 KB Output is correct
8 Correct 21 ms 2176 KB Output is correct
9 Correct 19 ms 1792 KB Output is correct
10 Correct 25 ms 2176 KB Output is correct

Subtask #6
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 0 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 304 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 17 ms 1792 KB Output is correct
8 Correct 21 ms 2176 KB Output is correct
9 Correct 47 ms 14452 KB Output is correct
10 Correct 45 ms 14452 KB Output is correct
11 Correct 51 ms 16244 KB Output is correct
12 Correct 55 ms 18036 KB Output is correct
13 Correct 56 ms 18036 KB Output is correct
14 Correct 19 ms 1792 KB Output is correct
15 Correct 25 ms 2176 KB Output is correct
16 Correct 46 ms 14452 KB Output is correct
17 Correct 48 ms 14460 KB Output is correct
18 Correct 51 ms 16124 KB Output is correct
19 Correct 58 ms 18036 KB Output is correct
20 Correct 57 ms 17908 KB Output is correct