[AtCoder] E - Rotate and Flip

E - Rotate and Flip

  • Time : O(m + q)
  • Space : O(m)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

using namespace std;

struct PairHash {inline std::size_t operator()(const std::pair<int, int> &v) const { return v.first * 31 + v.second; }};

// speed
#define Code ios_base::sync_with_stdio(false);
#define By ios::sync_with_stdio(0);
#define Sumfi cout.tie(NULL);

// alias
using ll = long long;
using ld = long double;

// constants
const ld PI = 3.14159265358979323846; /* pi */
const ll INF = 1e18;
const ld EPS = 1e-9;
const ll MAX_N = 202020;
const ll mod = 998244353;

// typedef
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef array<ll,3> all3;
typedef array<ll,5> all5;
typedef vector<all3> vall3;
typedef vector<all5> vall5;
typedef vector<ld> vld;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<vs> vvs;
typedef unordered_set<ll> usll;
typedef unordered_set<pll, PairHash> uspll;
typedef unordered_map<ll, ll> umll;
typedef unordered_map<pll, ll, PairHash> umpll;

// macros
#define rep(i,m,n) for(ll i=m;i<n;i++)
#define rrep(i,m,n) for(ll i=n;i>=m;i--)
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define SIZE(x) ll((x).size())
#define pyes cout<<"Yes\n";
#define pno cout<<"No\n";
#define pneg1 cout<<"-1\n";

// utility functions
template <typename T>
void print(T &&t) { cout << t << "\n"; }
template<typename T>
void printv(vector<T>v){ll n=v.size();rep(i,0,n)cout<<v[i]<<" ";cout<<"\n";}
//void readf() {freopen("", "rt", stdin);}

ll __gcd(ll x, ll y) { return !y ? x : __gcd(y, x % y); }
ll __lcm(ll x, ll y) { return x * y / __gcd(x,y); }
ll modpow(ll n, ll x, ll MOD = mod) { if(!x) return 1; ll res = modpow(n,x>>1,MOD); res = (res * res) % MOD; if(x&1) res = (res * n) % MOD; return res; }

using namespace std;

template<typename T>
struct matrix {
int N, M;
std::vector<T> data;

matrix(int _N, int _M, T value = T{}) : N(_N), M(_M), data(N * M, value) {}

typename std::vector<T>::iterator operator[](int i) {
return data.begin() + i * M;
}
typename std::vector<T>::const_iterator operator[](int i) const {
return data.begin() + i * M;
}

friend matrix<T> operator * (const matrix<T>& a, const matrix<T>& b) {
assert(a.M == b.N);
matrix<T> res(a.N, b.M);
for (int i = 0; i < a.N; i++)
for (int k = 0; k < a.M; k++)
for (int j = 0; j < b.M; j++)
res[i][j] += a[i][k] * b[k][j];
return res;
}

friend std::vector<T> operator * (const std::vector<T>& v, const matrix<T>& m) {
assert(sz(v) == m.N);
std::vector<T> res(m.M);
for (int i = 0; i < m.N; i++)
for (int j = 0; j < m.M; j++)
res[j] += v[i] * m[i][j];
return res;
}

friend std::vector<T> operator * (const matrix<T>& m, const std::vector<T>& v) {
assert(m.M == SIZE(v));
std::vector<T> res(m.N);
for (int i = 0; i < m.N; i++)
for (int j = 0; j < m.M; j++)
res[i] += m[i][j] * v[j];
return res;
}

matrix pow(int64_t e) const {
assert(N == M);
if (e == 0) return matrix<T>(N, N, 0, 1);
if (e&1) return *this * pow(e - 1);
return (*this * *this).pow(e / 2);
}

friend void row_reduce(matrix<T> &m) {
int rank = 0;
for (int j = 0; j < m.M && rank < m.N; j++) {
for (int i = rank; i < m.N; i++) {
if (m[i][j] != 0) {
swap_ranges(m[rank], m[rank] + m.M, m[i]);
break;
}
}
if (m[rank][j] == 0)
continue;

T inv = 1 / m[rank][j];
for (int k = j; k < m.M; k++)
m[rank][k] *= inv;

for (int i = 0; i < m.N; i++) {
if (i != rank) {
T c = m[i][j];
for (int k = j; k < m.M; k++)
m[i][k] -= c * m[rank][k];
}
}
rank++;
}

m.N = rank;
m.data.resize(m.N * m.M);
}

friend std::ostream& operator << (std::ostream& os, const matrix<T>& m) {
for (int i = 0; i < m.N; i++) {
os << (i ? i < m.N - 1 ? "\u2503" : "\u2517" : "\n\u250F");
for (int j = 0; j < m.M; j++)
os << std::setw(12) << m[i][j];
os << " " << (i ? i < m.N - 1 ? "\u2503" : "\u251B" : "\u2512") << "\n";
}
return os;
}
};

matrix<ll> op(ll type, ll p) {
matrix<ll> res(3,3);
switch (type) {
case 1:
res[0][1] = 1;
res[1][0] = -1;
break;
case 2:
res[0][1] = -1;
res[1][0] = 1;
break;
case 3:
res[0][0] = -1;
res[0][2] = 2 * p;
res[1][1] = 1;
break;
case 4:
res[0][0] = 1;
res[1][1] = -1;
res[1][2] = 2 * p;
break;
}
res[2][2] = 1;
return res;
}

vpll solve(vvll& A, vpll& B, vpll& Q) {
vpll res;
vector<matrix<ll>> ops(1,matrix<ll>(3,3));
ops[0][0][0] = ops[0][1][1] = ops[0][2][2] = 1;

rep(i,0,B.size()) {
matrix<ll> now = op(B[i].first, B[i].second);
ops.push_back(now * ops.back());
}

rep(i,0,Q.size()) {
auto [op, po] = Q[i];
auto ans = ops[op] * A[po-1];
res.push_back({ans[0], ans[1]});
}

return res;
}

int main() {
Code By Sumfi

cout.precision(12);

ll tc = 1;
//cin>>tc;
for (ll i = 1; i <= tc; i++) {
ll n,m,q;
cin>>n;
vvll A(n,{1,1,1});
rep(i,0,n) cin>>A[i][0]>>A[i][1];
cin>>m;
vpll B(m);
rep(i,0,m) {
cin>>B[i].first;
if(B[i].first >= 3) cin>>B[i].second;
}
cin>>q;
vpll Q(q);
rep(i,0,q) cin>>Q[i].first>>Q[i].second;
for(auto& [x,y] : solve(A,B,Q)) cout<<x<<' '<<y<<endl;
}
return 0;
}
Author: Song Hayoung
Link: https://songhayoung.github.io/2022/07/09/PS/AtCoder/abc189-e/
Copyright Notice: All articles in this blog are licensed under CC BY-NC-SA 4.0 unless stating additionally.