#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using ordered_map = tree<T, U, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<str> vstr;
#define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
#define FORD(i,j,k,in) for(int i=(j); i >=(k);i-=in)
#define REP(i,b) FOR(i,0,b,1)
#define REPD(i,b) FORD(i,b,0,1)
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define all(x) begin(x), end(x)
#define rsz resize
const double EPS = 1e-9;
const int MOD = 1e9+7; // 998244353;
const ll INFF = 1e18;
const int INF = 1e9;
const ld PI = acos((ld)-1);
const vi dy = {1, 0, -1, 0, -1, 1, 1, -1};
const vi dx = {0, 1, 0, -1, -1, 1, -1, 1};
#ifdef DEBUG
#define DBG if(1)
#else
#define DBG if(0)
#endif
#define dbg(x) cout << "(" << #x << " : " << x << ")" << endl;
// ostreams
template <class T, class U>
ostream& operator<<(ostream& out, const pair<T, U> &par) {out << "[" << par.first << ";" << par.second << "]"; return out;}
template <class T>
ostream& operator<<(ostream& out, const set<T> &cont) { out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template <class T, class U>
ostream& operator<<(ostream& out, const map<T, U> &cont) {out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template<class T>
ostream& operator<<(ostream& out, const vector<T> &v){ out << "["; REP(i, v.size()) out << v[i] << ", "; out << "]"; return out;}
// istreams
template<class T>
istream& operator>>(istream& in, vector<T> &v){ for(auto &x : v) in >> x; return in; }
template<class T, class U>
istream& operator>>(istream& in, pair<T, U> &p){ in >> p.ff >> p.ss; return in; }
//searches
template<typename T, typename U>
T bsl(T lo, T hi, U f){ hi++; T mid; while(lo < hi){ mid = (lo + hi)/2; f(mid) ? hi = mid : lo = mid+1; } return lo; }
template<typename U>
double bsld(double lo, double hi, U f, double p = 1e-9){ int r = 3 + (int)log2((hi - lo)/p); double mid; while(r--){ mid = (lo + hi)/2; f(mid) ? hi = mid : lo = mid; } return (lo + hi)/2; }
template<typename T, typename U>
T bsh(T lo, T hi, U f){ lo--; T mid; while(lo < hi){ mid = (lo + hi + 1)/2; f(mid) ? lo = mid : hi = mid-1; } return lo; }
template<typename U>
double bshd(double lo, double hi, U f, double p = 1e-9){ int r = 3+(int)log2((hi - lo)/p); double mid; while(r--){ mid = (lo + hi)/2; f(mid) ? lo = mid : hi = mid; } return (lo + hi)/2; }
// some more utility functions
template<typename T>
pair<T, int> get_min(vector<T> &v){ typename vector<T> :: iterator it = min_element(v.begin(), v.end()); return mp(*it, it - v.begin());}
template<typename T>
pair<T, int> get_max(vector<T> &v){ typename vector<T> :: iterator it = max_element(v.begin(), v.end()); return mp(*it, it - v.begin());}
template<typename T> bool ckmin(T& a, const T& b){return b < a ? a = b , true : false;}
template<typename T> bool ckmax(T& a, const T& b){return b > a ? a = b, true : false;}
const int mod = (int)1e9+7;
struct Mint{
int val;
Mint(){ val = 0; }
Mint(long long v){
val = (-mod <= v && v < mod) ? v : v%mod;
if(val < 0) val+= mod;
}
// operators
Mint operator-(){return Mint(-val);}
Mint& operator+=(const Mint& other){ val+=other.val; if(val> mod) val-=mod; return *this;}
Mint& operator-=(const Mint& other){ val-=other.val; if(val < 0) val+=mod; return *this;}
Mint& operator*=(const Mint& other){ val=((long long)val*other.val)%mod; return *this;}
friend Mint binpow(Mint a, long long p){
Mint res(1);
while(p > 0){
if(p&1) res*=a; a*=a; p>>=1;
}
return res;
}
friend Mint inv(Mint a){ return binpow(a, mod-2); }
Mint& operator/=(const Mint &other){ return (*this)*=inv(other);}
friend Mint operator+(Mint a, const Mint& b){ return a+=b; }
friend Mint operator-(Mint a, const Mint& b){ return a-=b; }
friend Mint operator*(Mint a, const Mint& b){ return a*=b; }
friend Mint operator/(Mint a, const Mint& b){ return a/=b; }
bool operator==(const Mint &other){return val == other.val;}
bool operator!=(const Mint &other){return val != other.val;}
bool operator<(const Mint &other){return val < other.val;}
// io
friend ostream& operator<<(ostream &out, Mint &a){ return out << a.val; }
};
struct bruteforce{
vi a;
int n;
map<vi, int> seq;
vector<vi> all_seq;
void generate(int id, vi &arr){ // generates all sequence with len n
if(id == n){
all_seq.pb(arr);
if(arr == a){
cout << all_seq.size() << endl;
exit(0);
}
return;
}
if(id == 0) {
arr.pb(1);
generate(id+1, arr);
arr.pop_back();
}
else{
int maxi = 0;
REP(i, arr.size()){
maxi = max(arr[i], maxi);
}
FOR(i, 1, maxi+2, 1){
arr.pb(i);
generate(id+1, arr);
arr.pop_back();
}
}
}
void print_all(){
vi arr;
generate(0, arr);
sort(all(all_seq));
dbg(all_seq.size());
REP(i, all_seq.size()) cout << all_seq[i] << endl;
}
int get_ans(){
vi arr;
generate(0, arr);
sort(all(all_seq));
REP(i, all_seq.size()) if(all_seq[i] == a) return i+1;
}
/* void find_wa(){ */
/* n = 12; */
/* AcAutomaton solver; */
/* vi arr; */
/* generate(0, arr); */
/* sort(all(all_seq)); */
/* REP(i, all_seq.size()){ */
/* solver.n = all_seq[i].size(); */
/* solver.a = all_seq[i]; */
/* if(solver.solve() != i+1){ */
/* cout << all_seq[i] << " " << i+1 << " " << solver.solve() << endl; */
/* } */
/* } */
/* } */
};
struct AcAutomaton{
int n;
vi a;
void read_in(){
cin >> n;
a.rsz(n);
cin >> a;
}
int solve(){
bruteforce brute; brute.n = n; brute.a = a;
vi arr;
brute.generate(0, arr);
vector<vector<Mint>> dp(2*n+1, vector<Mint>(2*n+1, Mint(0)));
REP(i, n+1){
dp[1][i] = Mint(i+1);
}
FOR(i,2, n+1, 1){
FOR(j,0, n+1, 1){
Mint res(0);
res += Mint(j) * dp[i-1][j];
res += dp[i-1][j+1];
dp[i][j] = res;
}
}
vector<int> maxiprev(n);
int maxi = 0;
REP(i, a.size()){
maxiprev[i] = maxi;
maxi = max(maxi, a[i]);
}
reverse(all(a));
reverse(all(maxiprev));
Mint ans(0);
REP(i, a.size()){
if(a[i] == 1) continue;
if(i == 0){
ans += Mint(a[i]-1);
continue;
}
/* dbg(dp[i+1][a[i]-2]); */
/* dbg(mp(i+1, a[i]-2)); */
ans += Mint(a[i] - 1) * dp[i][maxiprev[i]];
/* dbg(dp[i][maxiprev[i]]); */
/* dbg(mp(i, maxiprev[i])); */
// ans += dp[i+1][a[i]-2];
}
ans += Mint(1);
return ans.val;
cout << ans << endl;
/* REP(i, n+1){ */
/* cout << "["; */
/* REP(j, n+1) cout << dp[i][j] << " "; */
/* cout << "]" << endl; */
/* } */
}
};
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
int tcase = 1; //cin >> tcase;
while(tcase--){
AcAutomaton solver;
solver.read_in();
solver.solve();
//bruteforce brute;
//brute.find_wa();
}
return 0;
}
Compilation message
teams.cpp: In function 'Mint binpow(Mint, long long int)':
teams.cpp:100:13: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
100 | if(p&1) res*=a; a*=a; p>>=1;
| ^~
teams.cpp:100:29: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
100 | if(p&1) res*=a; a*=a; p>>=1;
| ^
teams.cpp: In member function 'void bruteforce::generate(int, vi&)':
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
| ^
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:141:13: note: in expansion of macro 'REP'
141 | REP(i, arr.size()){
| ^~~
teams.cpp: In member function 'void bruteforce::print_all()':
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
| ^
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:156:9: note: in expansion of macro 'REP'
156 | REP(i, all_seq.size()) cout << all_seq[i] << endl;
| ^~~
teams.cpp: In member function 'int bruteforce::get_ans()':
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
| ^
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:162:9: note: in expansion of macro 'REP'
162 | REP(i, all_seq.size()) if(all_seq[i] == a) return i+1;
| ^~~
teams.cpp: In member function 'int AcAutomaton::solve()':
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
| ^
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:205:9: note: in expansion of macro 'REP'
205 | REP(i, a.size()){
| ^~~
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
| ^
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:212:9: note: in expansion of macro 'REP'
212 | REP(i, a.size()){
| ^~~
teams.cpp: In instantiation of 'std::ostream& operator<<(std::ostream&, const std::vector<_Tp>&) [with T = int; std::ostream = std::basic_ostream<char>]':
teams.cpp:156:49: required from here
teams.cpp:26:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
26 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
teams.cpp:28:18: note: in expansion of macro 'FOR'
28 | #define REP(i,b) FOR(i,0,b,1)
| ^~~
teams.cpp:60:69: note: in expansion of macro 'REP'
60 | ostream& operator<<(ostream& out, const vector<T> &v){ out << "["; REP(i, v.size()) out << v[i] << ", "; out << "]"; return out;}
| ^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 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 |
1 ms |
384 KB |
Output is correct |
| 6 |
Correct |
0 ms |
384 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
384 KB |
Output is correct |
| 2 |
Correct |
1 ms |
384 KB |
Output is correct |
| 3 |
Correct |
1 ms |
768 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
96 ms |
65540 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
62 ms |
65540 KB |
Execution killed with signal 9 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
56 ms |
65536 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
50 ms |
65540 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
48 ms |
65536 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
104 ms |
65540 KB |
Execution killed with signal 9 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
62 ms |
65540 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
106 ms |
65540 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
