oj.uz

Submission #226190

# Submission time Handle Problem Language Result Execution time Memory
226190 2020-04-22T19:00:03 Z rqi Boat (APIO16_boat) C++14
100 / 100
 1527 ms 6524 KB 
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair 
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#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)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
    return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
    return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) { 
    bool fst = 1; str res = "{";
    F0R(i,sz(v)) {
        if (!fst) res += ", ";
        fst = 0; res += ts(v[i]);
    }
    res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
    str res = ""; F0R(i,SZ) res += char('0'+b[i]);
    return res; }
template<class T> str ts(T v) {
    bool fst = 1; str res = "{";
    for (const auto& x: v) {
        if (!fst) res += ", ";
        fst = 0; res += ts(x);
    }
    res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
    return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
    pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
    pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
    cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
    DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
    unsyncIO();
    // cin.exceptions(cin.failbit); 
    // throws exception when do smth illegal
    // ex. try to read letter into int
    if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

/**
 * Description: modular arithmetic operations 
 * Source: 
    * KACTL
    * https://codeforces.com/blog/entry/63903
    * https://codeforces.com/contest/1261/submission/65632855 (tourist)
    * https://codeforces.com/contest/1264/submission/66344993 (ksun)
 * Verification: 
    * https://open.kattis.com/problems/modulararithmetic
 */

struct mi {
    typedef decay<decltype(MOD)>::type T; 
     /// don't silently convert to T
    T v; explicit operator T() const { return v; }
    mi() { v = 0; }
    mi(ll _v) { 
        v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
        if (v < 0) v += MOD;
    }
    friend bool operator==(const mi& a, const mi& b) { 
        return a.v == b.v; }
    friend bool operator!=(const mi& a, const mi& b) { 
        return !(a == b); }
    friend bool operator<(const mi& a, const mi& b) { 
        return a.v < b.v; }
    friend void re(mi& a) { ll x; re(x); a = mi(x); }
    friend str ts(mi a) { return ts(a.v); }
   
    mi& operator+=(const mi& m) { 
        if ((v += m.v) >= MOD) v -= MOD; 
        return *this; }
    mi& operator-=(const mi& m) { 
        if ((v -= m.v) < 0) v += MOD; 
        return *this; }
    mi& operator*=(const mi& m) { 
        v = (ll)v*m.v%MOD; return *this; }
    mi& operator/=(const mi& m) { return (*this) *= inv(m); }
    friend mi pow(mi a, ll p) {
        mi ans = 1; assert(p >= 0);
        for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend mi inv(const mi& a) { assert(a.v != 0); 
        return pow(a,MOD-2); }
        
    mi operator-() const { return mi(-v); }
    mi& operator++() { return *this += 1; }
    mi& operator--() { return *this -= 1; }
    friend mi operator+(mi a, const mi& b) { return a += b; }
    friend mi operator-(mi a, const mi& b) { return a -= b; }
    friend mi operator*(mi a, const mi& b) { return a *= b; }
    friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;

int N, M;
int a[505];
int b[505];
set<int> m;
map<int, int> ma;
int vals[1005];
mi dp1[1005];
mi dp2[1005][505];
mi ndp1[1005];
mi ndp2[1005][505];
mi comb[1005][505];

int main() {
    setIO();
    cin >> N;
    for(int i = 1; i <= N; i++){
        cin >> a[i] >> b[i];
        m.insert(a[i]);
        m.insert(b[i]);
    }

    M = sz(m);
    int cnt = 0;
    for(auto u: m){
        cnt++;
        vals[cnt] = u;
        ma[u] = cnt;
    }

    for(int i = 1; i <= N; i++){
        a[i] = ma[a[i]];
        b[i] = ma[b[i]];
    }

    for(int i = 1; i <= M-1; i++){
        ll val = vals[i+1]-vals[i]-1;
        comb[i][0] = 1;
        for(int j = 1; j <= N; j++){
            comb[i][j] = comb[i][j-1]*mi(val-j+1)/mi(j);
        }
    }

    for(int i = 1; i <= N; i++){
        int l = a[i];
        int r = b[i];
        //calculate cdp values
        mi cdp[1005];
        cdp[1] = 1;
        for(int i = 2; i <= M; i++){
            cdp[i] = cdp[i-1]+dp1[i-1];
            for(int j = 1; j <= N; j++){
                cdp[i]+=dp2[i-1][j]*comb[i-1][j];
            }
        } 
        //calculate ndp1
        //calculate ndp2[1]
        for(int i = l; i <= r; i++){
            ndp1[i]+=cdp[i];
            if(i != r) ndp2[i][1]+=ndp1[i]+dp1[i];
        }
       
        //calculate ndp2[non1]
        for(int i = l; i <= r-1; i++){
            for(int j = 2; j <= N; j++){
                ndp2[i][j]+=dp2[i][j-1];
            }
        }

        //add old dp values
        for(int i = 1; i <= M; i++){
            ndp1[i]+=dp1[i];
        }

        for(int i = 1; i <= M-1; i++){
             for(int j = 1; j <= N; j++){
                ndp2[i][j]+=dp2[i][j];
            }
        }


        //swap ndp, dp
        for(int i = 1; i <= M; i++){
            dp1[i] = ndp1[i];
            ndp1[i] = 0;
        }
        for(int i = 1; i <= M-1; i++){
            for(int j = 1; j <= N; j++){
                dp2[i][j] = ndp2[i][j];
                ndp2[i][j] = 0;
            }
        }
    }
    mi ans = 1;
    for(int i = 1; i <= M; i++){
        ans+=dp1[i];
    }
    for(int i = 1; i <= M-1; i++){
        for(int j = 1; j <= N; j++){
            ans+=dp2[i][j]*comb[i][j];
        }
    }
    //subtract empty case
    ps(ans-1);
    // you should actually read the stuff at the bottom
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?)
    * do smth instead of nothing and stay organized
    * WRITE STUFF DOWN
*/

Compilation message

boat.cpp: In function 'void setIn(std::__cxx11::string)':
boat.cpp:123:31: 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); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
boat.cpp: In function 'void setOut(std::__cxx11::string)':
boat.cpp:124:32: 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
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 736 ms 6524 KB Output is correct
2 Correct 690 ms 6520 KB Output is correct
3 Correct 689 ms 6412 KB Output is correct
4 Correct 677 ms 6520 KB Output is correct
5 Correct 674 ms 6520 KB Output is correct
6 Correct 680 ms 6520 KB Output is correct
7 Correct 691 ms 6520 KB Output is correct
8 Correct 676 ms 6520 KB Output is correct
9 Correct 675 ms 6400 KB Output is correct
10 Correct 677 ms 6408 KB Output is correct
11 Correct 687 ms 6400 KB Output is correct
12 Correct 710 ms 6520 KB Output is correct
13 Correct 683 ms 6520 KB Output is correct
14 Correct 709 ms 6520 KB Output is correct
15 Correct 704 ms 6520 KB Output is correct
16 Correct 133 ms 6272 KB Output is correct
17 Correct 136 ms 6272 KB Output is correct
18 Correct 135 ms 6400 KB Output is correct
19 Correct 144 ms 6496 KB Output is correct
20 Correct 133 ms 6272 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 736 ms 6524 KB Output is correct
2 Correct 690 ms 6520 KB Output is correct
3 Correct 689 ms 6412 KB Output is correct
4 Correct 677 ms 6520 KB Output is correct
5 Correct 674 ms 6520 KB Output is correct
6 Correct 680 ms 6520 KB Output is correct
7 Correct 691 ms 6520 KB Output is correct
8 Correct 676 ms 6520 KB Output is correct
9 Correct 675 ms 6400 KB Output is correct
10 Correct 677 ms 6408 KB Output is correct
11 Correct 687 ms 6400 KB Output is correct
12 Correct 710 ms 6520 KB Output is correct
13 Correct 683 ms 6520 KB Output is correct
14 Correct 709 ms 6520 KB Output is correct
15 Correct 704 ms 6520 KB Output is correct
16 Correct 133 ms 6272 KB Output is correct
17 Correct 136 ms 6272 KB Output is correct
18 Correct 135 ms 6400 KB Output is correct
19 Correct 144 ms 6496 KB Output is correct
20 Correct 133 ms 6272 KB Output is correct
21 Correct 1365 ms 6456 KB Output is correct
22 Correct 1371 ms 6520 KB Output is correct
23 Correct 1355 ms 6400 KB Output is correct
24 Correct 1331 ms 6520 KB Output is correct
25 Correct 1309 ms 6496 KB Output is correct
26 Correct 1330 ms 6452 KB Output is correct
27 Correct 1345 ms 6520 KB Output is correct
28 Correct 1305 ms 6400 KB Output is correct
29 Correct 1327 ms 6448 KB Output is correct
30 Correct 1309 ms 6520 KB Output is correct
31 Correct 1279 ms 6468 KB Output is correct
32 Correct 1280 ms 6460 KB Output is correct
33 Correct 1300 ms 6520 KB Output is correct
34 Correct 1285 ms 6520 KB Output is correct
35 Correct 680 ms 6520 KB Output is correct
36 Correct 683 ms 6424 KB Output is correct
37 Correct 680 ms 6520 KB Output is correct
38 Correct 673 ms 6496 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 23 ms 6400 KB Output is correct
2 Correct 23 ms 6400 KB Output is correct
3 Correct 23 ms 6272 KB Output is correct
4 Correct 23 ms 6272 KB Output is correct
5 Correct 24 ms 6272 KB Output is correct
6 Correct 23 ms 6272 KB Output is correct
7 Correct 23 ms 6272 KB Output is correct
8 Correct 24 ms 6272 KB Output is correct
9 Correct 24 ms 6272 KB Output is correct
10 Correct 23 ms 6380 KB Output is correct
11 Correct 23 ms 6400 KB Output is correct
12 Correct 23 ms 6272 KB Output is correct
13 Correct 23 ms 6272 KB Output is correct
14 Correct 23 ms 6272 KB Output is correct
15 Correct 24 ms 6400 KB Output is correct
16 Correct 15 ms 6272 KB Output is correct
17 Correct 14 ms 6400 KB Output is correct
18 Correct 14 ms 6400 KB Output is correct
19 Correct 15 ms 6400 KB Output is correct
20 Correct 15 ms 6272 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 736 ms 6524 KB Output is correct
2 Correct 690 ms 6520 KB Output is correct
3 Correct 689 ms 6412 KB Output is correct
4 Correct 677 ms 6520 KB Output is correct
5 Correct 674 ms 6520 KB Output is correct
6 Correct 680 ms 6520 KB Output is correct
7 Correct 691 ms 6520 KB Output is correct
8 Correct 676 ms 6520 KB Output is correct
9 Correct 675 ms 6400 KB Output is correct
10 Correct 677 ms 6408 KB Output is correct
11 Correct 687 ms 6400 KB Output is correct
12 Correct 710 ms 6520 KB Output is correct
13 Correct 683 ms 6520 KB Output is correct
14 Correct 709 ms 6520 KB Output is correct
15 Correct 704 ms 6520 KB Output is correct
16 Correct 133 ms 6272 KB Output is correct
17 Correct 136 ms 6272 KB Output is correct
18 Correct 135 ms 6400 KB Output is correct
19 Correct 144 ms 6496 KB Output is correct
20 Correct 133 ms 6272 KB Output is correct
21 Correct 1365 ms 6456 KB Output is correct
22 Correct 1371 ms 6520 KB Output is correct
23 Correct 1355 ms 6400 KB Output is correct
24 Correct 1331 ms 6520 KB Output is correct
25 Correct 1309 ms 6496 KB Output is correct
26 Correct 1330 ms 6452 KB Output is correct
27 Correct 1345 ms 6520 KB Output is correct
28 Correct 1305 ms 6400 KB Output is correct
29 Correct 1327 ms 6448 KB Output is correct
30 Correct 1309 ms 6520 KB Output is correct
31 Correct 1279 ms 6468 KB Output is correct
32 Correct 1280 ms 6460 KB Output is correct
33 Correct 1300 ms 6520 KB Output is correct
34 Correct 1285 ms 6520 KB Output is correct
35 Correct 680 ms 6520 KB Output is correct
36 Correct 683 ms 6424 KB Output is correct
37 Correct 680 ms 6520 KB Output is correct
38 Correct 673 ms 6496 KB Output is correct
39 Correct 23 ms 6400 KB Output is correct
40 Correct 23 ms 6400 KB Output is correct
41 Correct 23 ms 6272 KB Output is correct
42 Correct 23 ms 6272 KB Output is correct
43 Correct 24 ms 6272 KB Output is correct
44 Correct 23 ms 6272 KB Output is correct
45 Correct 23 ms 6272 KB Output is correct
46 Correct 24 ms 6272 KB Output is correct
47 Correct 24 ms 6272 KB Output is correct
48 Correct 23 ms 6380 KB Output is correct
49 Correct 23 ms 6400 KB Output is correct
50 Correct 23 ms 6272 KB Output is correct
51 Correct 23 ms 6272 KB Output is correct
52 Correct 23 ms 6272 KB Output is correct
53 Correct 24 ms 6400 KB Output is correct
54 Correct 15 ms 6272 KB Output is correct
55 Correct 14 ms 6400 KB Output is correct
56 Correct 14 ms 6400 KB Output is correct
57 Correct 15 ms 6400 KB Output is correct
58 Correct 15 ms 6272 KB Output is correct
59 Correct 1472 ms 6524 KB Output is correct
60 Correct 1447 ms 6496 KB Output is correct
61 Correct 1435 ms 6480 KB Output is correct
62 Correct 1453 ms 6464 KB Output is correct
63 Correct 1455 ms 6496 KB Output is correct
64 Correct 1489 ms 6472 KB Output is correct
65 Correct 1516 ms 6520 KB Output is correct
66 Correct 1527 ms 6400 KB Output is correct
67 Correct 1504 ms 6496 KB Output is correct
68 Correct 1508 ms 6464 KB Output is correct
69 Correct 1448 ms 6468 KB Output is correct
70 Correct 1451 ms 6468 KB Output is correct
71 Correct 1440 ms 6520 KB Output is correct
72 Correct 1460 ms 6520 KB Output is correct
73 Correct 1453 ms 6520 KB Output is correct
74 Correct 156 ms 6272 KB Output is correct
75 Correct 151 ms 6272 KB Output is correct
76 Correct 150 ms 6272 KB Output is correct
77 Correct 152 ms 6272 KB Output is correct
78 Correct 163 ms 6272 KB Output is correct