oj.uz

Submission #272732

# Submission time Handle Problem Language Result Execution time Memory
272732 2020-08-18T14:28:22 Z Atill83 Lucky Numbers (RMI19_lucky) C++14
100 / 100
 51 ms 27900 KB 
#include <bits/stdc++.h>
#define ff first
#define ss second
#define endl '\n'
using namespace std;
const long long INF = (long long) 1e18;
const int mod = (int) 1e9+7;
const int MAXN = (int) 2e5+5;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll n, q;
ll pw[MAXN][3], dp[3][MAXN][3];

string s;

struct node{
    ll ans = 0, bit1 = 0, bas3 = 0;
    bool ok = 0;
} t[2*MAXN];
void g(ll &a){
    while(a < 0) a += mod;
    a %= mod;
}


void build(int v, int l, int r){
    if(l == r){
        t[v].ans = s[l] - '0';
        if(t[v].ans >= 4){
            t[v].bit1 = 1;
            t[v].bas3 = 1;
        }else if(t[v].ans > 1){
            t[v].bit1 = 1;
        }
        t[v].ok = 1;
    }else{
        int m = (l + r) / 2;
        build(2*v, l, m);
        build(2*v + 1, m + 1, r);

        int l2 = r - m;
        t[v].ans = 0;
        t[v].ans = (t[v].ans + t[2*v].ans*pw[l2][0]%mod)%mod;
        t[v].ans = (t[v].ans - (t[2*v].bit1*pw[l2][2]%mod) + mod)%mod;
        g(t[v].ans);
        t[v].ans = (t[v].ans + t[2*v].ok*t[2*v + 1].ans%mod)%mod;
        t[v].ans = (t[v].ans - (t[2*v].ok*(s[m] == '1')*t[2*v + 1].bas3%mod) + mod)%mod;
        g(t[v].ans);

        if(s[l] == '3'){
            t[v].bas3 = (t[v].ans - 2*pw[r - l][0]%mod - pw[r - l + 1][1] + 2*mod)%mod;
            g(t[v].bas3);
            t[v].bas3 %= mod;
        }else if(s[l] >= '4'){
            t[v].bas3 = pw[r - l][0];
        }else{
            t[v].bas3 = 0;
        }

        t[v].bit1 = 0;
        t[v].bit1 = (t[v].bit1 + t[2*v].ans*dp[0][l2][1]%mod)%mod;
        t[v].bit1 = (t[v].bit1 - t[2*v].bit1*dp[2][l2][1]%mod + mod)%mod;
        g(t[v].bit1);
        
        t[v].bit1 += t[2*v].ok*t[2*v + 1].bit1%mod;
        t[v].bit1 %= mod;

        if(s[m] == '1'){
            if(s[m + 1] > '3'){
                t[v].bit1 = (t[v].bit1 - t[2*v].ok*dp[2][r - m][1]%mod + mod)%mod;
                g(t[v].bit1);
            }else if(s[m + 1] == '3'){
                t[v].bit1 = (t[v].bit1 - t[2*v].ok*(t[2*v + 1].bit1 - 2*dp[0][r - m - 1][1]%mod - dp[1][r - m][1] + 2*mod)%mod + mod)%mod;
                g(t[v].bit1);
            }
        }


        if(s[m] == '1' && s[m + 1] == '3'){
            t[v].ok = 0;
        }else{
            t[v].ok = (t[2*v].ok && t[2*v + 1].ok);
        }
    }

}


void upd(int v, int l, int r, int pos){
    if(l == r){
        t[v].ans = s[l] - '0';
        if(t[v].ans >= 4){
            t[v].bit1 = 1;
            t[v].bas3 = 1;
        }else if(t[v].ans > 1){
            t[v].bit1 = 1;
            t[v].bas3 = 0;
        }else{
            t[v].bit1 = 0;
            t[v].bas3 = 0;
        }
        t[v].ok = 1;
    }else{
        int m = (l + r) / 2;
        if(m < pos){
            upd(2*v + 1, m + 1, r, pos);
        }else{
            upd(2*v, l, m, pos);
        }
        t[v].ans = t[v].bit1 = t[v].bas3 = t[v].ok = 0;
        int l2 = r - m;
        t[v].ans = 0;
        t[v].ans = (t[v].ans + t[2*v].ans*pw[l2][0]%mod)%mod;
        t[v].ans = (t[v].ans - (t[2*v].bit1*pw[l2][2]%mod) + mod)%mod;
        g(t[v].ans);
        t[v].ans = (t[v].ans + t[2*v].ok*t[2*v + 1].ans%mod)%mod;
        t[v].ans = (t[v].ans - (t[2*v].ok*(s[m] == '1')*t[2*v + 1].bas3%mod) + mod)%mod;
        g(t[v].ans);

        if(s[l] == '3'){
            t[v].bas3 = (t[v].ans - 2*pw[r - l][0]%mod - pw[r - l + 1][1] + 2*mod)%mod;
            g(t[v].bas3);
            t[v].bas3 %= mod;
        }else if(s[l] >= '4'){
            t[v].bas3 = pw[r - l][0];
        }else{
            t[v].bas3 = 0;
        }

        t[v].bit1 = 0;
        t[v].bit1 = (t[v].bit1 + t[2*v].ans*dp[0][l2][1]%mod)%mod;
        t[v].bit1 = (t[v].bit1 - t[2*v].bit1*dp[2][l2][1]%mod + mod)%mod;
        g(t[v].bit1);
        
        t[v].bit1 += t[2*v].ok*t[2*v + 1].bit1%mod;
        t[v].bit1 %= mod;

        if(s[m] == '1'){
            if(s[m + 1] > '3'){
                t[v].bit1 = (t[v].bit1 - t[2*v].ok*dp[2][r - m][1]%mod + mod)%mod;
                g(t[v].bit1);
            }else if(s[m + 1] == '3'){
                t[v].bit1 = (t[v].bit1 - t[2*v].ok*(t[2*v + 1].bit1 - 2*dp[0][r - m - 1][1]%mod - dp[1][r - m][1] + 2*mod)%mod + mod)%mod;
                g(t[v].bit1);
            }
        }
        t[v].ok = 0;

        if(s[m] == '1' && s[m + 1] == '3'){
            t[v].ok = 0;
        }else{
            t[v].ok = (t[2*v].ok && t[2*v + 1].ok);
        }
    }
}

node que(int v, int tl, int tr, int l, int r){
    if(l > r){
        node a = {-1, -1, -1, 0};
        return a;
    }else if(l == tl && r == tr){
        return t[v];
    }else{
        int tm = (tl + tr) / 2;
        node left = que(2*v, tl, tm, l, min(tm, r)),
             right = que(2*v + 1, tm + 1, tr, max(tm + 1, l), r);
        if(r <= tm){
            return left;
        }else if(l >= tm + 1){
            return right;
        }else{
            node res;
            int l2 = r - tm;
            res.ans = 0;
            res.ans = (res.ans + left.ans*pw[l2][0]%mod)%mod;
            res.ans = (res.ans - (left.bit1*pw[l2][2]%mod) + mod)%mod;
            g(res.ans);

            res.ans = (res.ans + left.ok*right.ans%mod)%mod;
            res.ans = (res.ans - (left.ok*(s[tm] == '1')*right.bas3%mod) + mod)%mod;
            g(res.ans);

            if(s[l] == '3'){
                res.bas3 = (res.ans - 2*pw[r - l][0]%mod - pw[r - l + 1][1] + 2*mod)%mod;
                g(res.bas3);
                res.bas3 %= mod;
            }else if(s[l] >= '4'){
                res.bas3 = pw[r - l][0];
            }else{
                res.bas3 = 0;
            }

            res.bit1 = 0;
            res.bit1 = (res.bit1 + left.ans*dp[0][l2][1]%mod)%mod;
            res.bit1 = (res.bit1 - left.bit1*dp[2][l2][1]%mod + mod)%mod;
            g(res.bit1);
            res.bit1 += left.ok*right.bit1%mod;
            res.bit1 %= mod;

            if(s[tm] == '1'){
                if(s[tm + 1] > '3'){
                    res.bit1 = (res.bit1 - left.ok*dp[2][r - tm][1]%mod + mod)%mod;
                }else if(s[tm + 1] == '3'){
                    res.bit1 = (res.bit1 - left.ok*(right.bit1 - 2*dp[0][r - tm - 1][1]%mod - dp[1][r - tm][1] + 2*mod)%mod + mod)%mod;
                }
                g(res.bit1);
            }


            if(s[tm] == '1' && s[tm + 1] == '3'){
                res.ok = 0;
            }else{
                res.ok = (left.ok && right.ok);
            }
            return res;
        }
    }



}






int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);cout.tie(nullptr);

    #ifdef Local
        freopen("C:/Users/Admin/Desktop/Yazilim/C/IO/int.txt","r",stdin);
        freopen("C:/Users/Admin/Desktop/Yazilim/C/IO/out.txt","w",stdout);
    #endif

    cin>>n>>q;
    pw[0][0] = 0;
    dp[0][1][0] = 8;
    dp[0][1][1] = 1;
    dp[0][1][2] = 1;
    pw[1][0] = 10;
    for(int i = 2; i < MAXN ; i++){
        dp[0][i][0] = (dp[0][i - 1][0] + dp[0][i - 1][1] + dp[0][i - 1][2])%mod*8%mod;
        dp[0][i][1] = (dp[0][i - 1][0] + dp[0][i - 1][1] + dp[0][i - 1][2])%mod;
        dp[0][i][2] = (dp[0][i - 1][0] + dp[0][i - 1][2])%mod;
        pw[i][0] = (dp[0][i][0] + dp[0][i][1] + dp[0][i][2])%mod;
    }
    pw[0][1] = 0;
    dp[1][1][1] = 1;
    pw[1][1] = 1;
    for(int i = 2; i < MAXN ; i++){
        dp[1][i][0] = (dp[1][i - 1][0] + dp[1][i - 1][1] + dp[1][i - 1][2])%mod*8 % mod;
        dp[1][i][1] = (dp[1][i - 1][0] + dp[1][i - 1][1] + dp[1][i - 1][2])%mod;
        dp[1][i][2] = (dp[1][i - 1][0] + dp[1][i - 1][2])%mod;
        pw[i][1] = (dp[1][i][0] + dp[1][i][1] + dp[1][i][2])%mod;
    }

    pw[0][2] = 0;
    dp[2][1][2] = 1;
    pw[1][2] = 1;
    for(int i = 2; i < MAXN ; i++){
        dp[2][i][0] = (dp[2][i - 1][0] + dp[2][i - 1][1] + dp[2][i - 1][2])%mod*8% mod;
        dp[2][i][1] = (dp[2][i - 1][0] + dp[2][i - 1][1] + dp[2][i - 1][2])%mod;
        dp[2][i][2] = (dp[2][i - 1][0] + dp[2][i - 1][2])%mod;
        pw[i][2] = (dp[2][i][0] + dp[2][i][1] + dp[2][i][2])%mod;
    }
    cin>>s;

    build(1, 0, n - 1);
    node cr = que(1, 0, n - 1, 0, n - 1);

    cout<<(cr.ans + cr.ok)%mod<<endl;

    while(q--){
        int type;
        cin>>type;
        if(type == 1){
            int l, r;
            cin>>l>>r;
            
            node cr = que(1, 0, n - 1, l - 1, r - 1);
            cout<<(cr.ans + cr.ok)%mod<<endl;
        }else{
            int idx;
            char val;
            cin>>idx>>val;
            idx--;

            s[idx] = val;
            upd(1, 0, n - 1, idx);
        }
    }



    #ifdef Local
        cout<<endl<<fixed<<setprecision(2)<<1000.0 * clock() / CLOCKS_PER_SEC<< " milliseconds ";
    #endif
}

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 19072 KB Output is correct
2 Correct 18 ms 19076 KB Output is correct
3 Correct 21 ms 18944 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 19072 KB Output is correct
2 Correct 18 ms 19076 KB Output is correct
3 Correct 21 ms 18944 KB Output is correct
4 Correct 18 ms 19072 KB Output is correct
5 Correct 18 ms 19200 KB Output is correct
6 Correct 18 ms 19200 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 19712 KB Output is correct
2 Correct 31 ms 20224 KB Output is correct

Subtask #4
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 19712 KB Output is correct
2 Correct 31 ms 20224 KB Output is correct
3 Correct 43 ms 27624 KB Output is correct
4 Correct 44 ms 27636 KB Output is correct
5 Correct 48 ms 27768 KB Output is correct
6 Correct 48 ms 27640 KB Output is correct
7 Correct 47 ms 27640 KB Output is correct

Subtask #5
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 19072 KB Output is correct
2 Correct 18 ms 19076 KB Output is correct
3 Correct 21 ms 18944 KB Output is correct
4 Correct 18 ms 19072 KB Output is correct
5 Correct 18 ms 19200 KB Output is correct
6 Correct 18 ms 19200 KB Output is correct
7 Correct 28 ms 19712 KB Output is correct
8 Correct 31 ms 20224 KB Output is correct
9 Correct 26 ms 19712 KB Output is correct
10 Correct 32 ms 20472 KB Output is correct

Subtask #6
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 19072 KB Output is correct
2 Correct 18 ms 19076 KB Output is correct
3 Correct 21 ms 18944 KB Output is correct
4 Correct 18 ms 19072 KB Output is correct
5 Correct 18 ms 19200 KB Output is correct
6 Correct 18 ms 19200 KB Output is correct
7 Correct 28 ms 19712 KB Output is correct
8 Correct 31 ms 20224 KB Output is correct
9 Correct 43 ms 27624 KB Output is correct
10 Correct 44 ms 27636 KB Output is correct
11 Correct 48 ms 27768 KB Output is correct
12 Correct 48 ms 27640 KB Output is correct
13 Correct 47 ms 27640 KB Output is correct
14 Correct 26 ms 19712 KB Output is correct
15 Correct 32 ms 20472 KB Output is correct
16 Correct 40 ms 27768 KB Output is correct
17 Correct 41 ms 27776 KB Output is correct
18 Correct 45 ms 27896 KB Output is correct
19 Correct 51 ms 27768 KB Output is correct
20 Correct 46 ms 27900 KB Output is correct