QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#673654 | #9489. 0100 Insertion | hos_lyric | AC ✓ | 90ms | 200896kb | C++14 | 7.6kb | 2024-10-25 05:46:23 | 2024-10-25 05:46:24 |
Judging History
answer
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
/*
0^a[0] 1 0^a[1] 1 ... 1 0^a[n]
a,b -> a+b-3 (a >= 1, b >= 2)
a[i] -= 3
a,b -> a+b (a >= -2, b >= -1)
-3: failed (if n >= 1)
-2: cannot merge with its left
cannot merge with its right -1 (if n >= 2)
merge with 0 ==> still -2
need +1 to the right
*/
void exper() {
constexpr int N = 7;
set<int> dp[N + 1];
dp[0].insert(0);
for (int n = 0; n < N; ++n) {
for (const int p : dp[n]) {
for (int i = 0; i <= 4*n; ++i) {
dp[n + 1].insert((p & ((1<<i)-1)) | (2 << i) | (p >> i << (i+4)));
}
}
}
for (int n = 0; n <= N; ++n) {
cerr << "|dp[n]| = " << dp[n].size() << endl;
}
for (int n = 0; n <= N; ++n) {
for (const int p : dp[n]) {
vector<int> is{-1};
for (int i = 0; i < 4*n; ++i) if (p >> i & 1) is.push_back(i);
is.push_back(4*n);
vector<int> as(n + 1);
for (int j = 0; j <= n; ++j) as[j] = (is[j + 1] - is[j] - 1) - 3;
for (int i = 0; i < 4*n; ++i) putchar("01"[p >> i & 1]);
cout << " " << as << endl;
}
}
for (int n = 0; n <= N; ++n) {
for (int p = 0; p < 1 << (4*n); ++p) if (__builtin_popcount(p) == n) {
vector<int> is{-1};
for (int i = 0; i < 4*n; ++i) if (p >> i & 1) is.push_back(i);
is.push_back(4*n);
vector<int> as(n + 1);
for (int j = 0; j <= n; ++j) as[j] = (is[j + 1] - is[j] - 1) - 3;
const bool brt = dp[n].count(p);
const bool grd = [&]() -> bool {
for (auto bs = as; ; ) {
const int bsLen = bs.size();
if (bsLen == 1) return true;
if (bs[0] >= -2 && *min_element(bs.begin() + 1, bs.end()) >= -1) return true;
for (int j = bsLen; --j >= 0; ) if (bs[j] <= -3) {
return false;
}
for (int j = bsLen; --j >= 0; ) if (bs[j] == -2) {
if (j + 1 == bsLen) return false;
if (bs[j + 1] <= 0) {
if (j + 2 == bsLen) return false;
// merge bs[j+1, j+2]
bs[j + 1] += bs[j + 2];
bs.erase(bs.begin() + (j + 2));
goto found;
} else {
// merge bs[j, j+1]
bs[j] += bs[j + 1];
bs.erase(bs.begin() + (j + 1));
goto found;
}
}
assert(false);
found:{}
}
}();
const bool slv = [&]() -> bool {
if (n == 0) return true;
for (int j = 0; j <= n; ++j) if (as[j] <= -3) return false;
int now = 0;
int mn = 0;
for (int j = n; j >= 1; --j) {
now += as[j];
if (mn - 2 >= now) return false;
chmin(mn, now);
}
return true;
}();
if (!(brt == grd && brt == slv)) {
cerr << "FAIL ";
for (int i = 0; i < 4*n; ++i) cerr << (p >> i & 1);
cerr << " " << as << ": " << brt << " " << grd << " " << slv << endl;
assert(false);
}
}
cerr << "PASSED n = " << n << endl;
}
}
int N;
char S[510];
// pos, # 1, now - mn, last
Mint dp[510][130][380][2];
int main() {
// exper();
for (; ~scanf("%d", &N); ) {
N /= 4;
scanf("%s", S);
memset(dp, 0, sizeof(dp));
dp[4*N][0][0][1] = 1;
for (int i = 4*N; --i >= 0; ) {
for (int k = 0; k <= N; ++k) for (int d = 0; d <= 3*N; ++d) for (int l = 0; l < 2; ++l) {
if (S[i] == '?' || S[i] == '0') {
dp[i][k][d + 1][0] += dp[i + 1][k][d][l];
}
if (S[i] == '?' || S[i] == '1') {
if (d >= 2 && l == 0) {
dp[i][k + 1][max(d - 3, 0)][1] += dp[i + 1][k][d][l];
}
}
}
}
Mint ans = 0;
for (int d = 0; d <= 3*N; ++d) {
ans += dp[0][N][d][0];
}
printf("%u\n", ans.x);
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 11ms
memory: 200628kb
input:
8 0??0?100
output:
2
result:
ok "2"
Test #2:
score: 0
Accepted
time: 4ms
memory: 200700kb
input:
4 ?10?
output:
1
result:
ok "1"
Test #3:
score: 0
Accepted
time: 0ms
memory: 200692kb
input:
28 ???????????0???0??????1???0?
output:
2023
result:
ok "2023"
Test #4:
score: 0
Accepted
time: 7ms
memory: 200684kb
input:
4 ????
output:
1
result:
ok "1"
Test #5:
score: 0
Accepted
time: 0ms
memory: 200604kb
input:
8 11111111
output:
0
result:
ok "0"
Test #6:
score: 0
Accepted
time: 89ms
memory: 200888kb
input:
500 ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????...
output:
870731023
result:
ok "870731023"
Test #7:
score: 0
Accepted
time: 87ms
memory: 200888kb
input:
500 ???????????????????0???????????????????????????????????????0??????????????????????1???????????????????????????????????????00????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????1???????????????????????????????????...
output:
763641704
result:
ok "763641704"
Test #8:
score: 0
Accepted
time: 28ms
memory: 200896kb
input:
344 ?0???????????1???????0?0?????0?????????????0?0????0?0??1??0?????0??0???1?????0????00?????1?????1????????1?????10????0??????????1????0???1????????0???10?????1?0?0???1??????????0??0???1?0??00??0???????001????????1????1??????1?0????1??????????????????1????1????????????0???????????01?1??????0?0?????...
output:
273835616
result:
ok "273835616"
Test #9:
score: 0
Accepted
time: 8ms
memory: 200604kb
input:
152 ?1???1??????????????????00??????????0?????0????????0??1?????0????0????????0????010???????????????1??1??????0?10??1????0???????????????1?????0???1???????
output:
539361138
result:
ok "539361138"
Test #10:
score: 0
Accepted
time: 14ms
memory: 200628kb
input:
216 ???????1?????1??1????1???1?????????????0?1???????????????????????????????????????????????1?????????????????10???0???1???????????????????????1????????????0???????0??????0?????????1???????????????????????1?????????0???
output:
336079328
result:
ok "336079328"
Test #11:
score: 0
Accepted
time: 25ms
memory: 200608kb
input:
316 ??????00?????????????????????1??????????????????0?????????????????0??0??????0???1??1?????????0??????????????????????0?????????0?0?1??0?????1?1??????1?1?????????????????????????????????0??????????????????????10???????1???????????1?????????????1????1????????????0????????????????1????1???0??0??1???...
output:
919261244
result:
ok "919261244"
Test #12:
score: 0
Accepted
time: 31ms
memory: 200600kb
input:
340 ?0?001??1?0????1?????1???01?????????1??01??0???1???1?????????????0?1??????1??1?10??0????????10?????1????1?010???1?????????????1???????1????01???????1???????00???1?0?00??0????????00???0??????1??1?1?????10??1????0??1????1????0????????0????0??????00?0??00???1??001????????0?1?????????????????0???1??...
output:
743485908
result:
ok "743485908"
Test #13:
score: 0
Accepted
time: 50ms
memory: 200560kb
input:
392 ??????0??????????10???????????????????????1????????1???????0???????????0??????????????101???????????????????????0??????????0??0??????????1?????1???????????????????1?0?????????????1???????????????????????1????????0???0?????1????????????????0??????1?????????????0????????????????0?????????????????1...
output:
213859453
result:
ok "213859453"
Test #14:
score: 0
Accepted
time: 7ms
memory: 200628kb
input:
96 ????????0??1??1??????????????????????????1?0?????0??????1?????????1?0?????00??????????1???1?????
output:
860127276
result:
ok "860127276"
Test #15:
score: 0
Accepted
time: 0ms
memory: 200556kb
input:
116 ???????????????????????????????01?1???????????????0?00????0?????????????????1?0?????????????????1???????????????00??
output:
717954632
result:
ok "717954632"
Test #16:
score: 0
Accepted
time: 24ms
memory: 200600kb
input:
280 ?????1????0??0??????1????????0????0?1?0????????00???0???????0????0???????????1?0?1???????????1?????10????1??????100??????????1?1?????01?1??????0????01??1???1?????0????????0?1?0???????????01??00??????1?????????????????1?1?????????1????????????????0????????????????????????0????????
output:
553679844
result:
ok "553679844"
Test #17:
score: 0
Accepted
time: 24ms
memory: 200604kb
input:
260 ????????0????0???????????????1???????0?00??0???????????????0??????0?????1?????????????????????????????????????0???????1????????0??????????????????????1???????????????????1?0????1???????00?0????10???????????0?1?10??????????????????0??0???????1???????1??1???????
output:
121486637
result:
ok "121486637"
Test #18:
score: 0
Accepted
time: 85ms
memory: 200612kb
input:
500 ??0????1???1??????1?1??????????????????????????????????0??0??????????????????????1???????01????????0???0???????????????????????1????????1??????????????1????????0?1???0?????0???????????????????0??????????????1????????0???????0?0??????????????0???????1???????1??????????????????????????0????0??????...
output:
397451125
result:
ok "397451125"
Test #19:
score: 0
Accepted
time: 90ms
memory: 200624kb
input:
500 ??????1???????????????????0????????????????????????0??????0???????????1??????????10???0???0?????????????1??1????????0??????1???????????00????????????0???????????????????1??0???0????0?????????????0?????????????????????????????????????0????0??????????1??????????????????????????????????????????????...
output:
248838567
result:
ok "248838567"
Test #20:
score: 0
Accepted
time: 81ms
memory: 200592kb
input:
500 ?0??0????1???????????????????????????1????????????????????0????????1????????????????1????0?????????????1???????????1?0????????????????????0?????????????0????0????????????1????????1????????????????0???0?1???1???1???????????1?????1???0??????????1????????1?????1???0?1???????????1???????????????????...
output:
53824210
result:
ok "53824210"
Test #21:
score: 0
Accepted
time: 12ms
memory: 200604kb
input:
76 ????0????????0??0???1??0??????00?0????0???1??????1?0????0?1?????????????1???
output:
205686585
result:
ok "205686585"
Test #22:
score: 0
Accepted
time: 4ms
memory: 200600kb
input:
24 ?0?0?????0??????????????
output:
587
result:
ok "587"
Test #23:
score: 0
Accepted
time: 7ms
memory: 200604kb
input:
76 ?????0?????????????????0????????????????????????????1???0???????????????????
output:
83575746
result:
ok "83575746"
Test #24:
score: 0
Accepted
time: 7ms
memory: 200896kb
input:
28 00???0???0?0??0???0???0?????
output:
859
result:
ok "859"
Test #25:
score: 0
Accepted
time: 12ms
memory: 200604kb
input:
44 ?00??1???00??1???0??1?100??1?0???0??1???0???
output:
63
result:
ok "63"
Test #26:
score: 0
Accepted
time: 57ms
memory: 200604kb
input:
444 ???0???0???????????????1?????1??????0?????1??????1??????????10?1???????????????????????????????1?1??00?0??0????0??????????1???????101?0????10??????????????0?0???????1???????????????1????????0?????????1????????????1???0??????????????????????????0??????1??????????0???10??1???????????01????????????...
output:
847293915
result:
ok "847293915"
Test #27:
score: 0
Accepted
time: 74ms
memory: 200556kb
input:
484 ?????1?1???????????1?????1??????????0?1???????????1?????0?1???0000?1?1?0?00????1????0?0?00?????????????????????1????????1?01??????01??1?????0??????0???000?????????1????????0?1??01?????0???1???0?????1???0???????0?????1?1?0??0???????01????????0???1???0??0???0?????????????????1??????1???10??1010???...
output:
679474848
result:
ok "679474848"
Test #28:
score: 0
Accepted
time: 70ms
memory: 200692kb
input:
456 ?????0???????????????0?????1???????0???1??????????????????1??????1?????????????1??????1??????????0??????????????1????????????????????1??????????1???0???0??1???1????????00??0?????1???0?????????????1?0??1??1?1???0???1????????????0???????????????0?0??0?????0????????01?????????????????????????????10...
output:
920943116
result:
ok "920943116"
Test #29:
score: 0
Accepted
time: 83ms
memory: 200620kb
input:
484 ????????????????????????????????0????1???1???????1????????1?????????0?????1??1??????????????????????1???????01???????????????????1??1???????????????1?1?0?0??1????????1??1???????????????????????????0?????????????0?????????????1????0??????1?????????0?0??????????1????????????1??????????????????????...
output:
453361220
result:
ok "453361220"
Test #30:
score: 0
Accepted
time: 66ms
memory: 200600kb
input:
448 ?1?01??1????01?10????1???0????????????10????0??????1????1??????1?????1?0??1????101?1????1??????????????0?????1???0???????01?0?1?1????1???1?01?????????????0?1???1???01????0???????????????1??????01?1??????1?1?1??0???0?????????1????????1??1?0?1?0???????????????1?????1???0?0?????0????0??0???????????...
output:
84175678
result:
ok "84175678"
Test #31:
score: 0
Accepted
time: 82ms
memory: 200604kb
input:
480 ?0?????????????????????0???00???1???0?????1?????????1??????????1?????1????????0??????????1????0???10?????????1????1????0?????0???01??????????0?????0???0?????????0???????01??????????????0????????0?????1????1?0??0?0????????????????1???1??01????????????1????0??????0??????1??1???????????????????????...
output:
247404334
result:
ok "247404334"
Test #32:
score: 0
Accepted
time: 89ms
memory: 200560kb
input:
492 ??????00??????0??0??????????1???1?1?010????????????????????00???1???0?????0???????1?????????0???????1?????????????1???10???0?????????????????0??????????????0??????1???0????0?0???0??100?0?????????1??1????1???????????1????1??0?????????00??????1??1??????1????01?1?0??????0???????1????????????1??0???...
output:
487405442
result:
ok "487405442"
Test #33:
score: 0
Accepted
time: 71ms
memory: 200604kb
input:
456 ????1???????????1???1????0????????????????????????????????????1???????0?????1???1?1??????????????????????????1?????????1?00??????????10?0????????????1??????????1?0????????1?1?????????????????0??????0???????1???????????????????????????0????????0??????1??????????0??1???????????????????????????????...
output:
884555628
result:
ok "884555628"
Test #34:
score: 0
Accepted
time: 72ms
memory: 200604kb
input:
460 ??????1????1??????????0??0?????????????????0?????0???????????1?????????????1???????????01???????0????????????0???0???????????????????????????1???0????0??????????0??0??????1????0???????????????01?????????????0???????????????????????????????1????0????0????1??????1???????1???0??????????????????????...
output:
244536851
result:
ok "244536851"
Test #35:
score: 0
Accepted
time: 78ms
memory: 200696kb
input:
456 ???????1?1????????????????00??????????1??1?0???????0??????0??????????0??1?????0??1???0?1??1?1?1???00?10?0???01??????????????0???01?0??000?1????1????????0????1?1????1???01???0?????1?0??????????1???0???1?1??????????01???1?????0???????0?1????1???1?0??0????1????0?0??1????????????0???0?????0??????01?...
output:
890392505
result:
ok "890392505"
Extra Test:
score: 0
Extra Test Passed