Submission #199686

#	Time	Username	Problem	Language	Result	Execution time	Memory
199686		rqi	Lucky Numbers (RMI19_lucky)	C++14	100 / 100	79 ms	8824 KiB

lucky

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
 
#include <bits/stdc++.h>
 
using namespace std;
 
typedef double db;
typedef long long ll;
typedef long double ld;
typedef string str;
 
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef complex<ld> cd;
 
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
 
#define FOR(i,a,b) for (int i = (a); i < (b); i++)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a : x)
 
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
 
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rsz resize
#define ins insert
 
const int MOD = 1e9+7; // 998244353 = (119<<23)+1
const ll INF = 1e18;
const int MX = 2e5+5;
const ld PI = 4*atan((ld)1);
 
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
 
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
 
using namespace __gnu_pbds;
using namespace __gnu_cxx;
 
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
 
#define ook order_of_key
#define fbo find_by_order
 
namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);
 
    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class T, class... Ts> void re(T& t, Ts&... ts) { 
        re(t); re(ts...); 
    }
 
    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
 
using namespace input;
 
namespace output {
    void pr(int x) { cout << x; }
    void pr(long x) { cout << x; }
    void pr(ll x) { cout << x; }
    void pr(unsigned x) { cout << x; }
    void pr(unsigned long x) { cout << x; }
    void pr(unsigned long long x) { cout << x; }
    void pr(float x) { cout << x; }
    void pr(double x) { cout << x; }
    void pr(ld x) { cout << x; }
    void pr(char x) { cout << x; }
    void pr(const char* x) { cout << x; }
    void pr(const string& x) { cout << x; }
    void pr(bool x) { pr(x ? "true" : "false"); }
    template<class T> void pr(const complex<T>& x) { cout << x; }
    
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T> void pr(const T& x);
    
    template<class T, class... Ts> void pr(const T& t, const Ts&... ts) { 
        pr(t); pr(ts...); 
    }
    template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
        pr("{",x.f,", ",x.s,"}"); 
    }
    template<class T> void pr(const T& x) { 
        pr("{"); // const iterator needed for vector<bool>
        bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; 
        pr("}");
    }
    
    void ps() { pr("\n"); } // print w/ spaces
    template<class T, class... Ts> void ps(const T& t, const Ts&... ts) { 
        pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); 
    }
    
    void pc() { pr("]\n"); } // debug w/ commas
    template<class T, class... Ts> void pc(const T& t, const Ts&... ts) { 
        pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); 
    }
    #define dbg(x...) pr("[",#x,"] = ["), pc(x);
}
 
using namespace output;
 
namespace io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        cin.sync_with_stdio(0); cin.tie(0); // fast I/O
        cin.exceptions(cin.failbit); // ex. throws exception when you try to read letter into int
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
    }
}
 
using namespace io;
 
template<class T> T invGeneral(T a, T b) {
	a %= b; if (a == 0) return b == 1 ? 0 : -1;
	T x = invGeneral(b,a); 
	return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}
 
template<class T> struct modular {
	T val; 
	explicit operator T() const { return val; }
	modular() { val = 0; }
	modular(const ll& v) { 
		val = (-MOD <= v && v <= MOD) ? v : v % MOD;
		if (val < 0) val += MOD;
	}
	
	// friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
	friend void pr(const modular& a) { pr(a.val); }
	friend void re(modular& a) { ll x; re(x); a = modular(x); }
   
	friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
	friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }
	friend bool operator<(const modular& a, const modular& b) { return a.val < b.val; }
 
	modular operator-() const { return modular(-val); }
	modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
	modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
	modular& operator*=(const modular& m) { val = (ll)val*m.val%MOD; return *this; }
	friend modular pow(modular a, ll p) {
		modular ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans;
	}
	friend modular inv(const modular& a) { 
		auto i = invGeneral(a.val,MOD); assert(i != -1);
		return i;
	} // equivalent to return exp(b,MOD-2) if MOD is prime
	modular& operator/=(const modular& m) { return (*this) *= inv(m); }
	
	friend modular operator+(modular a, const modular& b) { return a += b; }
	friend modular operator-(modular a, const modular& b) { return a -= b; }
	friend modular operator*(modular a, const modular& b) { return a *= b; }
	
	friend modular operator/(modular a, const modular& b) { return a /= b; }
};
 
typedef modular<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

mi tpows[100005][4]; //non3non1, non3 1, 3non1, 31

/**
 * Description: 1D point update, range query. \texttt{comb} 
 	* can be any associative operation. $N$ doesn't have to be a power of 2
 	* (but then \texttt{seg[1]} might not equal \texttt{query(0,N-1)}).
 * Time: O(\log N)
 * Source: 
	* http://codeforces.com/blog/entry/18051
	* KACTL
 * Verification: SPOJ Fenwick
 */

typedef pair<array<mi, 4>, array<int, 4>> T;
//non3non1, non3 1, 3non1, 31
//contain 13? end with 1? Start with 3? size
struct Seg { 
	const T ID = {{0, 0, 0, 0}, {-1, -1, -1, -1}}; // comb(ID,b) must equal b
	T comb(T a, T b) { 
		if(a.s[0] == -1){
			return b;
		}
		if(b.s[0] == -1) return a;
		
		T c = ID;
		
		c.s[3] = a.s[3]+b.s[3];
		
		if(a.s[0] == 1 || b.s[0] == 1 || (a.s[1] == 1 && b.s[2] == 1)){
			c.s[0] = 1;
		}
		else c.s[0] = 0;
		
		if(b.s[1] == 1){
			c.s[1] = 1;
		}
		else c.s[1] = 0;
		
		if(a.s[2] == 1){
			c.s[2] = 1;
		}
		else c.s[2] = 0;
		
		//now update the first parts
		if(a.s[0] == 0){
			if(a.s[1] == 0 && a.s[2] == 0){
				//22
				//take care of equality cases
				c.f[0]+=b.f[0]+b.f[2];
				c.f[1]+=b.f[1]+b.f[3];
				a.f[0]-=1;
			}
			else if(a.s[1] == 1 && a.s[2] == 0){
				//21
				c.f[0]+=b.f[0];
				c.f[1]+=b.f[1];
				a.f[1]-=1;
			}
			else if(a.s[1] == 0 && a.s[2] == 1){
				//32
				c.f[2]+=b.f[0]+b.f[2];
				c.f[3]+=b.f[1]+b.f[3];
				a.f[2]-=1;
			}
			else if(a.s[1] == 1 && a.s[2] == 1){
				//31
				c.f[2]+=b.f[0];
				c.f[3]+=b.f[1];
				a.f[3]-=1;
			}
		}
		int bsz = b.s[3];
		c.f[0]+=a.f[0]*(tpows[bsz][0]+tpows[bsz][2])+a.f[1]*(tpows[bsz][0]);
		c.f[1]+=a.f[0]*(tpows[bsz][1]+tpows[bsz][3])+a.f[1]*(tpows[bsz][1]);
		c.f[2]+=a.f[2]*(tpows[bsz][0]+tpows[bsz][2])+a.f[3]*(tpows[bsz][0]);
		c.f[3]+=a.f[2]*(tpows[bsz][1]+tpows[bsz][3])+a.f[3]*(tpows[bsz][1]);
		return c;
	} 
	int n; vector<T> seg;
	void init(int _n) { n = _n; seg.assign(2*n,ID); }
	void pull(int p) { seg[p] = comb(seg[2*p],seg[2*p+1]); }
	void upd(int p, int value) {	// set value at position p
		p+=n;
		seg[p].f = {mi(value+1), 0, 0, 0};
		if(value >= 1){
			seg[p].f[0]-=1;
			seg[p].f[1]+=1;
		}
		if(value >= 3){
			seg[p].f[0]-=1;
			seg[p].f[2]+=1;
		}
		if(value == 1){
			seg[p].s = {0, 1, 0, 1};
		}
		else if(value == 3){
			seg[p].s = {0, 0, 1, 1};
		}
		else{
			seg[p].s = {0, 0, 0, 1};
		}
		
		for (p /= 2; p; p /= 2) pull(p);
	}
	T query(int l, int r) {	 // sum on interval [l, r]
		T ra = ID, rb = ID; 
		for (l += n, r += n+1; l < r; l /= 2, r /= 2) {
			if (l&1) ra = comb(ra,seg[l++]);
			if (r&1) rb = comb(seg[--r],rb);
		}
		return comb(ra,rb);
	}
};
Seg tre;
int main() {
	setIO();
    // you should actually read the stuff at the bottom
    tpows[1][0] = 8;
    tpows[1][1] = 1;
    tpows[1][2] = 1;
    tpows[1][3] = 0;
    for(int i = 2; i < 100005; i++){
    	//make first thing non1, non3
    	tpows[i][0]+=8*(tpows[i-1][0]+tpows[i-1][2]);
    	tpows[i][1]+=8*(tpows[i-1][1]+tpows[i-1][3]);
    	//make first thing 1
    	tpows[i][0]+=tpows[i-1][0];
    	tpows[i][1]+=tpows[i-1][1];
    	//make first thing 3
    	tpows[i][2]+=tpows[i-1][0]+tpows[i-1][2];
    	tpows[i][3]+=tpows[i-1][1]+tpows[i-1][3];
    }
    int N, Q;
    cin >> N >> Q;
    tre.init(N+5);
    string X;
    cin >> X;
    
    for(int i = 1; i <= sz(X); i++){
    	tre.upd(i, X[i-1]-'0');
    }
    T c;
    mi ans;
    c = tre.query(1, N);
    ans = c.f[0]+c.f[1]+c.f[2]+c.f[3];
    ps(int(ans));
    for(int i = 0; i < Q; i++){
    	int t;
    	cin >> t;
    	if(t == 1){
    		int radixL, radixR;
    		cin >> radixL >> radixR;
    		c = tre.query(radixL, radixR);
    		ans = c.f[0]+c.f[1]+c.f[2]+c.f[3];
    		ps(int(ans));
    	}
    	else{
    		int radix, newDigit;
    		cin >> radix >> newDigit;
    		tre.upd(radix, newDigit);
    	}
    }
}
 
/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?), set tle
	* do smth instead of nothing and stay organized
*/

Compilation message (stderr)

lucky.cpp: In function 'void io::setIn(std::__cxx11::string)':
lucky.cpp:135:35: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     void setIn(string s) { freopen(s.c_str(),"r",stdin); }
                            ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
lucky.cpp: In function 'void io::setOut(std::__cxx11::string)':
lucky.cpp:136:36: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     void setOut(string s) { freopen(s.c_str(),"w",stdout); }
                             ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 14 / 14
• Subtask 2: 14 / 14
• Subtask 3: 9 / 9
• Subtask 4: 27 / 27
• Subtask 5: 9 / 9
• Subtask 6: 27 / 27