// Arti1990, II UWr
#include <bits/stdc++.h>
#define forr(i, n) for(int i=0; i<n; i++)
#define FOREACH(iter, coll) for(auto iter = coll.begin(); iter != coll.end(); ++iter)
#define FOREACHR(iter, coll) for(auto iter = coll.rbegin(); iter != coll.rend(); ++iter)
#define lbound(P,K,FUN) ({auto SSS=P, PPP = P-1, KKK=(K)+1; while(PPP+1!=KKK) {SSS = (PPP+(KKK-PPP)/2); if(FUN(SSS)) KKK = SSS; else PPP = SSS;} PPP;})
#define testy() int _tests; cin>>_tests; FOR(_test, 1, _tests)
#define CLEAR(tab) memset(tab, 0, sizeof(tab))
#define CONTAIN(el, coll) (coll.find(el) != coll.end())
#define FOR(i, a, b) for(int i=a; i<=b; i++)
#define FORD(i, a, b) for(int i=a; i>=b; i--)
#define MP make_pair
#define PB push_back
#define ff first
#define ss second
#define deb(X) X;
#define M 998244353
#define INF 1000000007LL
#define SIZE 9
using namespace std;
typedef vector <vector<long long>> matrix;
typedef vector<long long> vect;
int n, m, a, S = 1;
long long ile[100007][26][2], suma[100007][2];
long long nowe[100007], dwa[100007];
vector <int> v({177});
set <int> pozycje[26];
matrix ma, mb, id, d[250007];
int byl[7];
void init()
{
forr(i, SIZE)
{
id.PB(vect(9, 0));
id[i][i] = 1;
}
ma.PB(vect({0, 0, 1, 0,-1, 0, 0, 0, 0}));
ma.PB(vect({0, 1, 0, 0, 0, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 1, 0, 0, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 1, 1, 0, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 0, 0, 1, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 0, 0, 1, 1, 1, 0, 0}));
ma.PB(vect({0, 0, 1, 0,-1, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 0, 0, 0, 0, 0, 0, 0}));
ma.PB(vect({0, 0, 1, 0, 0, 0, 0, 0, 1}));
/*
r[0] = (rr[2] - rr[4] + M) % M; // lasta - last2a
r[1] = rr[1]; // lastb - last2b
r[2] = rr[2]; // suma
r[3] = (rr[3] + rr[2]) % M; // sumb
r[4] = rr[4]; // sum2a
r[5] = (rr[5] + rr[4] + rr[6]) % M; // sum2b
r[6] = (rr[2] - rr[4] + M) % M; // roznicaa
r[7] = 0; //rr[3] - rr[5]; // roznicab
r[8] = (rr[8] + rr[2]) % M; // suma
*/
mb.PB(vect({1, 0, 0, 0, 0, 0, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 1, 0,-1, 0, 0, 0}));
mb.PB(vect({0, 0, 1, 1, 0, 0, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 1, 0, 0, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 0, 1, 1, 0, 1, 0}));
mb.PB(vect({0, 0, 0, 0, 0, 1, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 0, 0, 0, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 1, 0,-1, 0, 0, 0}));
mb.PB(vect({0, 0, 0, 1, 0, 0, 0, 0, 1}));
/*
r[0] = rr[0];
r[1] = (rr[3] - rr[5] + M) % M;
r[2] = (rr[2] + rr[3]) % M;
r[3] = rr[3];
r[4] = (rr[4] + rr[5] + rr[7]) % M;
r[5] = rr[5];
r[6] = 0; // rr[2] - rr[4];
r[7] = (rr[3] + M - rr[5]) % M;
r[8] = (rr[8] + rr[3]) % M;
*/
}
void copy(matrix &a, matrix &b)
{
b.clear();
for(auto el : a)
b.PB(el);
}
void mult(matrix &a, matrix &b, matrix &c)
{
forr(i, SIZE)
forr(j, SIZE)
{
c[i][j] = 0;
forr(k, SIZE)
c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % M;
}
}
vect mult_v(matrix &a, vect &b)
{
vect res(SIZE, 0);
forr(i, SIZE)
forr(j, SIZE)
res[i] = (res[i] + a[i][j] * b[j]) % M;
return res;
}
/*
int znajdz_poprzednia(int poz)
{
auto it = pozycje[v[poz]].lower_bound(poz);
it--;
return *it;
}
int policz_old()
{
long long res = 0;
FOR(i, 1, n)
{
forr(c, 6)
ile[i][c][0] = ile[i][c][1] = 0;
suma[i][0] = suma[i][1] = 0;
}
FOR(i, 1, n)
{
int poprz = znajdz_poprzednia(i);
cout << "poprz dla pozycji " << i << " to " << poprz << '\n';
cout << " i: " << i << ", litera " << (char)(v[i]+'a') << '\n';
FORD(dl, i, 1)
{
long long diff = suma[dl-1][0] - ile[dl][v[i]][0];
ile[dl][v[i]][0] += diff;
suma[dl][0] += diff;
cout << " na dlugosci " << dl << " i b 0 ustawil " << ile[dl][v[i]][0] << '\n';
diff = suma[dl-1][1] - ile[dl][v[i]][1];
ile[dl][v[i]][1] += diff;
suma[dl][1] += diff;
res += diff;
cout << " na dlugosci " << dl << " i b 1 ustawil " << ile[dl][v[i]][1] << '\n';
}
}
return res;
}
*/
long long policz_brut()
{
nowe[0] = 1;
FOR(i, 1, n)
{
nowe[i] = 0;
dwa[i] = 0;
int poz = i-1;
while(poz >= 0)
{
nowe[i] += nowe[poz];
dwa[i] += dwa[poz];
if(v[poz] == v[i])
break;
poz--;
}
if(poz > 0)
dwa[poz] = nowe[poz];
nowe[i] %= M;
dwa[i] %= M;
}
//FOR(i, 1, n)
// cout << i << " - nowe: " << nowe[i] << ", dwa: " << dwa[i] << '\n';
long long res = 0;
FOR(i, 1, n)
{
res += dwa[i];
}
return res % M;
}
long long policz()
{
//cout << "liczy "<< endl;
matrix res, pom;
copy(id, res);
copy(id, pom);
//cout << "przed" << endl;
FOR(i, 1, n)
{
if(v[i] == 0)
mult(res, ma, pom);
else
mult(res, mb, pom);
copy(pom, res);
}
//cout << "po" << endl;
vect vv({0, 0, 1, 1, 0, 0, 0, 0, 0});
auto rv = mult_v(res, vv);
return (rv[8] - rv[0] - rv[1] + 2*M) % M;
}
long long policz3()
{
long long last_a = 0;
long long last_b = 0;
long long sum_a = 1;
long long sum_b = 1;
long long last2a = 0;
long long last2b = 0;
long long sum2a = 0;
long long sum2b = 0;
long long roznica_a = 0;
long long roznica_b = 0;
long long suma = 0;
vector <long long> r({0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0});
FOR(i, 1, n)
{
auto rr = r;
if(v[i] == 0)
{
// - r[0] + r[4] - r[1] + r[5]
r[0] = (rr[2] - rr[4] + M) % M; // lasta - last2a
r[1] = rr[1]; // lastb - last2b
r[2] = rr[2]; // suma
r[3] = (rr[3] + rr[2]) % M; // sumb
//r[4] = rr[4]; // last2a
//r[5] = rr[5]; // last2b
r[4] = rr[4]; // sum2a
r[5] = (rr[5] + rr[4] + rr[6]) % M; // sum2b
r[6] = (rr[2] - rr[4] + M) % M; // roznicaa
r[7] = 0; //rr[3] - rr[5]; // roznicab
r[8] = (rr[8] + rr[2]) % M; // suma
//cout << i << " - nowe: " << r[2] << ", podwojne: " << r[4] << '\n';
}
else
{
r[0] = rr[0];
r[1] = (rr[3] - rr[5] + M) % M;
r[2] = (rr[2] + rr[3]) % M;
r[3] = rr[3];
//r[4] = rr[4];
//r[5] = rr[5];
r[4] = (rr[4] + rr[5] + rr[7]) % M;
r[5] = rr[5];
r[6] = 0; // rr[2] - rr[4];
r[7] = (rr[3] + M - rr[5]) % M;
r[8] = (rr[8] + rr[3]) % M;
//cout << i << " - nowe: " << r[3] << ", podwojne: " << r[5] << '\n';
}
//for(auto j : vector<int>({2, 3, 6, 7, 8, 9, 10}))
// cout << j << ": " << r[j] << ", ";
//cout << '\n';
}
/*
long long res = r[8];
if(v[n] == 0)
res = (r[8] + r[2]) - r[2] + r[6] - r[1] + r[5];
else
res += r[3];
return (res - r[2] + r[6] - r[3] + r[7] + 2*M) % M;
*/
return (r[8] - r[0] - r[1] + 2*M) % M;
}
long long policz_ab(int poz, int val)
{
if(val == 0)
copy(ma, d[S + poz]);
else
copy(mb, d[S + poz]);
int nr = (S + poz)/2;
while(nr >= 1)
{
mult(d[nr*2], d[nr*2+1], d[nr]);
nr /= 2;
}
vect vv({0, 0, 1, 1, 0, 0, 0, 0, 0});
auto rv = mult_v(d[1], vv);
return (rv[8] - rv[0] - rv[1] + 2*M) % M;
}
int solve()
{
init();
string str;
char c;
cin >> n >> m;
cin >> str;
FOR(i, 1, n)
{
v.PB(str[i-1]-'a');
byl[str[i-1]-'a'] = 1;
}
suma[0][0] = 1;
cout << policz_brut() << '\n';
//FOR(i, 1, n)
// forr(c, 2)
// forr(b, 2)
// cout << i << ", " << c << ", " << b << ": " << ile[i][c][b] << '\n';
vector <pair<int, int>> q;
forr(i, m)
{
cin >> a >> c;
q.PB({a, c - 'a'});
byl[a, c-'a']++;
}
if(byl[2] == 0 && byl[3] == 0 && byl[4] == 0 && byl[5] == 0)
{
//cout << "case ab" << '\n';
S = 1;
while(S < n+2)
S *= 2;
forr(i, 2*S)
copy(id, d[i]);
FOR(i, 1, n)
if(v[i] == 0)
copy(ma, d[i+S]);
else
copy(mb, d[i+S]);
FORD(i, S-1, 1)
{
mult(d[i*2], d[i*2+1], d[i]);
}
for(auto p : q)
{
cout << policz_ab(p.ff, p.ss) << '\n';
}
}
else
{
//cout << "case a-f" << '\n';
for(auto p : q)
{
v[p.ff] = p.ss;
cout << policz_brut() << '\n';
}
}
return 0;
}
int main()
{
std::ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
solve();
return 0;
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 | // Arti1990, II UWr #include <bits/stdc++.h> #define forr(i, n) for(int i=0; i<n; i++) #define FOREACH(iter, coll) for(auto iter = coll.begin(); iter != coll.end(); ++iter) #define FOREACHR(iter, coll) for(auto iter = coll.rbegin(); iter != coll.rend(); ++iter) #define lbound(P,K,FUN) ({auto SSS=P, PPP = P-1, KKK=(K)+1; while(PPP+1!=KKK) {SSS = (PPP+(KKK-PPP)/2); if(FUN(SSS)) KKK = SSS; else PPP = SSS;} PPP;}) #define testy() int _tests; cin>>_tests; FOR(_test, 1, _tests) #define CLEAR(tab) memset(tab, 0, sizeof(tab)) #define CONTAIN(el, coll) (coll.find(el) != coll.end()) #define FOR(i, a, b) for(int i=a; i<=b; i++) #define FORD(i, a, b) for(int i=a; i>=b; i--) #define MP make_pair #define PB push_back #define ff first #define ss second #define deb(X) X; #define M 998244353 #define INF 1000000007LL #define SIZE 9 using namespace std; typedef vector <vector<long long>> matrix; typedef vector<long long> vect; int n, m, a, S = 1; long long ile[100007][26][2], suma[100007][2]; long long nowe[100007], dwa[100007]; vector <int> v({177}); set <int> pozycje[26]; matrix ma, mb, id, d[250007]; int byl[7]; void init() { forr(i, SIZE) { id.PB(vect(9, 0)); id[i][i] = 1; } ma.PB(vect({0, 0, 1, 0,-1, 0, 0, 0, 0})); ma.PB(vect({0, 1, 0, 0, 0, 0, 0, 0, 0})); ma.PB(vect({0, 0, 1, 0, 0, 0, 0, 0, 0})); ma.PB(vect({0, 0, 1, 1, 0, 0, 0, 0, 0})); ma.PB(vect({0, 0, 0, 0, 1, 0, 0, 0, 0})); ma.PB(vect({0, 0, 0, 0, 1, 1, 1, 0, 0})); ma.PB(vect({0, 0, 1, 0,-1, 0, 0, 0, 0})); ma.PB(vect({0, 0, 0, 0, 0, 0, 0, 0, 0})); ma.PB(vect({0, 0, 1, 0, 0, 0, 0, 0, 1})); /* r[0] = (rr[2] - rr[4] + M) % M; // lasta - last2a r[1] = rr[1]; // lastb - last2b r[2] = rr[2]; // suma r[3] = (rr[3] + rr[2]) % M; // sumb r[4] = rr[4]; // sum2a r[5] = (rr[5] + rr[4] + rr[6]) % M; // sum2b r[6] = (rr[2] - rr[4] + M) % M; // roznicaa r[7] = 0; //rr[3] - rr[5]; // roznicab r[8] = (rr[8] + rr[2]) % M; // suma */ mb.PB(vect({1, 0, 0, 0, 0, 0, 0, 0, 0})); mb.PB(vect({0, 0, 0, 1, 0,-1, 0, 0, 0})); mb.PB(vect({0, 0, 1, 1, 0, 0, 0, 0, 0})); mb.PB(vect({0, 0, 0, 1, 0, 0, 0, 0, 0})); mb.PB(vect({0, 0, 0, 0, 1, 1, 0, 1, 0})); mb.PB(vect({0, 0, 0, 0, 0, 1, 0, 0, 0})); mb.PB(vect({0, 0, 0, 0, 0, 0, 0, 0, 0})); mb.PB(vect({0, 0, 0, 1, 0,-1, 0, 0, 0})); mb.PB(vect({0, 0, 0, 1, 0, 0, 0, 0, 1})); /* r[0] = rr[0]; r[1] = (rr[3] - rr[5] + M) % M; r[2] = (rr[2] + rr[3]) % M; r[3] = rr[3]; r[4] = (rr[4] + rr[5] + rr[7]) % M; r[5] = rr[5]; r[6] = 0; // rr[2] - rr[4]; r[7] = (rr[3] + M - rr[5]) % M; r[8] = (rr[8] + rr[3]) % M; */ } void copy(matrix &a, matrix &b) { b.clear(); for(auto el : a) b.PB(el); } void mult(matrix &a, matrix &b, matrix &c) { forr(i, SIZE) forr(j, SIZE) { c[i][j] = 0; forr(k, SIZE) c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % M; } } vect mult_v(matrix &a, vect &b) { vect res(SIZE, 0); forr(i, SIZE) forr(j, SIZE) res[i] = (res[i] + a[i][j] * b[j]) % M; return res; } /* int znajdz_poprzednia(int poz) { auto it = pozycje[v[poz]].lower_bound(poz); it--; return *it; } int policz_old() { long long res = 0; FOR(i, 1, n) { forr(c, 6) ile[i][c][0] = ile[i][c][1] = 0; suma[i][0] = suma[i][1] = 0; } FOR(i, 1, n) { int poprz = znajdz_poprzednia(i); cout << "poprz dla pozycji " << i << " to " << poprz << '\n'; cout << " i: " << i << ", litera " << (char)(v[i]+'a') << '\n'; FORD(dl, i, 1) { long long diff = suma[dl-1][0] - ile[dl][v[i]][0]; ile[dl][v[i]][0] += diff; suma[dl][0] += diff; cout << " na dlugosci " << dl << " i b 0 ustawil " << ile[dl][v[i]][0] << '\n'; diff = suma[dl-1][1] - ile[dl][v[i]][1]; ile[dl][v[i]][1] += diff; suma[dl][1] += diff; res += diff; cout << " na dlugosci " << dl << " i b 1 ustawil " << ile[dl][v[i]][1] << '\n'; } } return res; } */ long long policz_brut() { nowe[0] = 1; FOR(i, 1, n) { nowe[i] = 0; dwa[i] = 0; int poz = i-1; while(poz >= 0) { nowe[i] += nowe[poz]; dwa[i] += dwa[poz]; if(v[poz] == v[i]) break; poz--; } if(poz > 0) dwa[poz] = nowe[poz]; nowe[i] %= M; dwa[i] %= M; } //FOR(i, 1, n) // cout << i << " - nowe: " << nowe[i] << ", dwa: " << dwa[i] << '\n'; long long res = 0; FOR(i, 1, n) { res += dwa[i]; } return res % M; } long long policz() { //cout << "liczy "<< endl; matrix res, pom; copy(id, res); copy(id, pom); //cout << "przed" << endl; FOR(i, 1, n) { if(v[i] == 0) mult(res, ma, pom); else mult(res, mb, pom); copy(pom, res); } //cout << "po" << endl; vect vv({0, 0, 1, 1, 0, 0, 0, 0, 0}); auto rv = mult_v(res, vv); return (rv[8] - rv[0] - rv[1] + 2*M) % M; } long long policz3() { long long last_a = 0; long long last_b = 0; long long sum_a = 1; long long sum_b = 1; long long last2a = 0; long long last2b = 0; long long sum2a = 0; long long sum2b = 0; long long roznica_a = 0; long long roznica_b = 0; long long suma = 0; vector <long long> r({0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}); FOR(i, 1, n) { auto rr = r; if(v[i] == 0) { // - r[0] + r[4] - r[1] + r[5] r[0] = (rr[2] - rr[4] + M) % M; // lasta - last2a r[1] = rr[1]; // lastb - last2b r[2] = rr[2]; // suma r[3] = (rr[3] + rr[2]) % M; // sumb //r[4] = rr[4]; // last2a //r[5] = rr[5]; // last2b r[4] = rr[4]; // sum2a r[5] = (rr[5] + rr[4] + rr[6]) % M; // sum2b r[6] = (rr[2] - rr[4] + M) % M; // roznicaa r[7] = 0; //rr[3] - rr[5]; // roznicab r[8] = (rr[8] + rr[2]) % M; // suma //cout << i << " - nowe: " << r[2] << ", podwojne: " << r[4] << '\n'; } else { r[0] = rr[0]; r[1] = (rr[3] - rr[5] + M) % M; r[2] = (rr[2] + rr[3]) % M; r[3] = rr[3]; //r[4] = rr[4]; //r[5] = rr[5]; r[4] = (rr[4] + rr[5] + rr[7]) % M; r[5] = rr[5]; r[6] = 0; // rr[2] - rr[4]; r[7] = (rr[3] + M - rr[5]) % M; r[8] = (rr[8] + rr[3]) % M; //cout << i << " - nowe: " << r[3] << ", podwojne: " << r[5] << '\n'; } //for(auto j : vector<int>({2, 3, 6, 7, 8, 9, 10})) // cout << j << ": " << r[j] << ", "; //cout << '\n'; } /* long long res = r[8]; if(v[n] == 0) res = (r[8] + r[2]) - r[2] + r[6] - r[1] + r[5]; else res += r[3]; return (res - r[2] + r[6] - r[3] + r[7] + 2*M) % M; */ return (r[8] - r[0] - r[1] + 2*M) % M; } long long policz_ab(int poz, int val) { if(val == 0) copy(ma, d[S + poz]); else copy(mb, d[S + poz]); int nr = (S + poz)/2; while(nr >= 1) { mult(d[nr*2], d[nr*2+1], d[nr]); nr /= 2; } vect vv({0, 0, 1, 1, 0, 0, 0, 0, 0}); auto rv = mult_v(d[1], vv); return (rv[8] - rv[0] - rv[1] + 2*M) % M; } int solve() { init(); string str; char c; cin >> n >> m; cin >> str; FOR(i, 1, n) { v.PB(str[i-1]-'a'); byl[str[i-1]-'a'] = 1; } suma[0][0] = 1; cout << policz_brut() << '\n'; //FOR(i, 1, n) // forr(c, 2) // forr(b, 2) // cout << i << ", " << c << ", " << b << ": " << ile[i][c][b] << '\n'; vector <pair<int, int>> q; forr(i, m) { cin >> a >> c; q.PB({a, c - 'a'}); byl[a, c-'a']++; } if(byl[2] == 0 && byl[3] == 0 && byl[4] == 0 && byl[5] == 0) { //cout << "case ab" << '\n'; S = 1; while(S < n+2) S *= 2; forr(i, 2*S) copy(id, d[i]); FOR(i, 1, n) if(v[i] == 0) copy(ma, d[i+S]); else copy(mb, d[i+S]); FORD(i, S-1, 1) { mult(d[i*2], d[i*2+1], d[i]); } for(auto p : q) { cout << policz_ab(p.ff, p.ss) << '\n'; } } else { //cout << "case a-f" << '\n'; for(auto p : q) { v[p.ff] = p.ss; cout << policz_brut() << '\n'; } } return 0; } int main() { std::ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); solve(); return 0; } |
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