QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#717805 | #7509. 01tree | hcywoi | AC ✓ | 38ms | 27608kb | C++23 | 6.0kb | 2024-11-06 18:59:33 | 2024-11-06 18:59:36 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
template<class T>
T qmi(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
i64 mul(i64 a, i64 b, i64 p) {
i64 res = a * b - i64(1.L * a * b / p) * p;
res %= p;
if (res < 0) {
res += p;
}
return res;
}
template<int P>
struct modint {
int x;
constexpr modint() : x{} {}
constexpr modint(i64 x) : x{norm(x % getmod())} {}
static int mod;
constexpr static int getmod() {
if (P > 0) {
return P;
} else {
return mod;
}
}
constexpr static void setmod(int m) {
mod = m;
}
constexpr int norm(int x) const {
if (x < 0) {
x += getmod();
}
if (x >= getmod()) {
x -= getmod();
}
return x;
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr modint operator-() const {
modint res;
res.x = norm(getmod() - x);
return res;
}
constexpr modint inv() const {
assert(x != 0);
return qmi(*this, getmod() - 2);
}
constexpr modint &operator*= (modint v) & {
x = 1LL * x * v.x % getmod();
return *this;
}
constexpr modint &operator+= (modint v) & {
x = norm(x + v.x);
return *this;
}
constexpr modint &operator-= (modint v) & {
x = norm(x - v.x);
return *this;
}
constexpr modint &operator/= (modint v) & {
return *this *= v.inv();
}
friend constexpr modint operator- (modint a, modint b) {
modint res = a;
res -= b;
return res;
}
friend constexpr modint operator+ (modint a, modint b) {
modint res = a;
res += b;
return res;
}
friend constexpr modint operator* (modint a, modint b) {
modint res = a;
res *= b;
return res;
}
friend constexpr modint operator/ (modint a, modint b) {
modint res = a;
res /= b;
return res;
}
friend constexpr std::istream &operator>> (std::istream& is, modint& a) {
i64 v;
is >> v;
a = modint(v);
return is;
}
friend constexpr std::ostream &operator<< (std::ostream& os, const modint& a) {
return os << a.val();
}
friend constexpr bool operator== (modint a, modint b) {
return a.val() == b.val();
}
friend constexpr bool operator!= (modint a, modint b) {
return a.val() != b.val();
}
};
constexpr int P = 1E9 + 7;
using mint = modint<P>;
struct Comb {
int n;
std::vector<mint> fact;
std::vector<mint> invefact;
std::vector<mint> inve;
Comb() : n{0}, fact{1}, invefact{1}, inve{0} {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
if (m <= n) return;
fact.resize(m + 1);
invefact.resize(m + 1);
inve.resize(m + 1);
for (int i = n + 1; i <= m; i++) {
fact[i] = fact[i - 1] * i;
}
invefact[m] = fact[m].inv();
for (int i = m; i > n; i--) {
invefact[i - 1] = invefact[i] * i;
inve[i] = invefact[i] * fact[i - 1];
}
n = m;
}
mint fac(int m) {
if (m > n) init(2 * m);
return fact[m];
}
mint invfac(int m) {
if (m > n) init(2 * m);
return invefact[m];
}
mint inv(int m) {
if (m > n) init(2 * m);
return inve[m];
}
mint binom(int n, int m) {
if (n < m || m < 0) return 0;
return fac(n) * invfac(m) * invfac(n - m);
}
} comb;
struct Mo {
int X, Y;
int ix, iy;
mint ans;
Mo(int A, int B) {
X = A, Y = B;
ix = 0, iy = 0;
ans = comb.binom(X, Y);
}
void move(int x, int y) {
while (iy < y) {
iy++;
ans += comb.binom(ix, iy) * comb.binom(X - ix, Y - iy);
}
while (iy > y) {
ans -= comb.binom(ix, iy) * comb.binom(X - ix, Y - iy);
iy--;
}
while (ix < x) {
ans -= comb.binom(ix, iy) * comb.binom(X - 1 - ix, Y - 1 - iy);
ix++;
if (ix == 0) {
ans = iy >= 0 ? comb.binom(X, Y) : 0;
}
}
while (ix > x) {
ix--;
if (ix < 0) {
ans = 0;
} else {
ans += comb.binom(ix, iy) * comb.binom(X - 1 - ix, Y - 1 - iy);
}
}
}
};
void solve() {
int n;
std::cin >> n;
std::vector<std::vector<int>> adj(n);
for (int i = 0; i < n - 1; i++) {
int u, v;
std::cin >> u >> v;
u--;
v--;
adj[u].push_back(v);
adj[v].push_back(u);
}
std::string a, b;
std::cin >> a >> b;
std::vector<int> s1(n), t1(n), sq(n), tq(n);
auto dfs = [&](auto self, int x, int p, int d) -> void {
if (a[x] == '?') {
sq[x]++;
} else if (a[x] == d + '0') {
s1[x]++;
}
if (b[x] == '?') {
tq[x]++;
} else if (b[x] == d + '0') {
t1[x]++;
}
for (auto y : adj[x]) {
if (y == p) {
continue;
}
self(self, y, x, d ^ 1);
sq[x] += sq[y];
s1[x] += s1[y];
tq[x] += tq[y];
t1[x] += t1[y];
}
};
dfs(dfs, 0, -1, 0);
int X = sq[0] + tq[0];
int Y = sq[0] + s1[0] - t1[0];
std::vector<std::array<int, 2>> ask;
for (int i = 0; i < n; i++) {
int x = sq[i] + tq[i];
int y = sq[i] + s1[i] - t1[i];
ask.push_back({x, y});
}
constexpr int B = 710;
std::sort(ask.begin(), ask.end(),
[&](std::array<int, 2> i, std::array<int, 2> j) {
if (i[0] / B != j[0] / B) {
return i[0] < j[0];
}
return i[1] < j[1];
});
mint ans = 0;
int ix = 0, iy = 0;
Mo m1(X, Y), m2(X - 1, Y - 1);
for (auto [x, y] : ask) {
m1.move(x, y);
m2.move(x - 1, y - 1);
mint G = m1.ans, H = m2.ans;
ans += 2 * (y * G - x * H) + x * comb.binom(X - 1, Y - 1) - y * comb.binom(X, Y);
}
std::cout << ans << "\n";
}
int main() {
// freopen("opt.in", "r", stdin);
// freopen("opt.out", "w", stdout);
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int t;
std::cin >> t;
while (t--) {
solve();
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3476kb
input:
3 2 1 2 00 11 3 1 2 2 3 ??? ??? 3 1 2 2 3 ??1 0?0
output:
1 16 1
result:
ok 3 number(s): "1 16 1"
Test #2:
score: 0
Accepted
time: 4ms
memory: 3556kb
input:
1000 23 1 2 1 3 1 4 2 5 5 6 4 7 3 8 4 9 8 10 8 11 8 12 1 13 7 14 10 15 7 16 7 17 5 18 18 19 12 20 9 21 21 22 6 23 00?10?0000??1?00111?010 011??1?10?01?110?0??101 6 1 2 1 3 1 4 4 5 3 6 000?10 1???01 25 1 2 2 3 2 4 4 5 5 6 2 7 4 8 5 9 7 10 8 11 11 12 5 13 11 14 3 15 6 16 14 17 1 18 4 19 6 20 4 21 5 22...
output:
53545 24 11724 2228 162 14 711 28 550 1680 52 2 13 988 9480 2342 626416 0 71780 1 88 39207 19448 4 37395 9602 3253496 38057200 1066 3 303732 1608 281022 11718 170 78 15 1219376 29364 9092 7 0 2 7014 1942448 170371 75845 167217 16554 64 904 564290 14822 1127090 1758504 1227646 14833316 14954550 36055...
result:
ok 1000 numbers
Test #3:
score: 0
Accepted
time: 1ms
memory: 3904kb
input:
1 3000 1 2 2 3 2 4 1 5 3 6 2 7 5 8 8 9 9 10 10 11 2 12 11 13 7 14 11 15 7 16 13 17 8 18 1 19 11 20 10 21 18 22 7 23 7 24 15 25 23 26 24 27 14 28 15 29 25 30 16 31 6 32 10 33 3 34 30 35 16 36 9 37 36 38 28 39 26 40 33 41 1 42 11 43 20 44 23 45 14 46 31 47 41 48 11 49 48 50 45 51 6 52 10 53 32 54 38 5...
output:
924036898
result:
ok 1 number(s): "924036898"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3908kb
input:
1 3000 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4 9 5 10 5 11 6 12 6 13 7 14 7 15 8 16 8 17 9 18 9 19 10 20 10 21 11 22 11 23 12 24 12 25 13 26 13 27 14 28 14 29 15 30 15 31 16 32 16 33 17 34 17 35 18 36 18 37 19 38 19 39 20 40 20 41 21 42 21 43 22 44 22 45 23 46 23 47 24 48 24 49 25 50 25 51 26 52 26 53 27 54 2...
output:
429465738
result:
ok 1 number(s): "429465738"
Test #5:
score: 0
Accepted
time: 1ms
memory: 4488kb
input:
1 3000 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 5...
output:
650625747
result:
ok 1 number(s): "650625747"
Test #6:
score: 0
Accepted
time: 38ms
memory: 12040kb
input:
1 100000 1 2 1 3 3 4 1 5 2 6 6 7 2 8 1 9 6 10 1 11 3 12 11 13 5 14 9 15 12 16 6 17 13 18 13 19 14 20 7 21 14 22 21 23 12 24 17 25 14 26 3 27 4 28 8 29 22 30 12 31 6 32 30 33 4 34 15 35 12 36 3 37 20 38 7 39 37 40 5 41 13 42 34 43 9 44 27 45 39 46 43 47 3 48 17 49 36 50 12 51 1 52 45 53 35 54 15 55 2...
output:
143309878
result:
ok 1 number(s): "143309878"
Test #7:
score: 0
Accepted
time: 24ms
memory: 13520kb
input:
1 100000 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4 9 5 10 5 11 6 12 6 13 7 14 7 15 8 16 8 17 9 18 9 19 10 20 10 21 11 22 11 23 12 24 12 25 13 26 13 27 14 28 14 29 15 30 15 31 16 32 16 33 17 34 17 35 18 36 18 37 19 38 19 39 20 40 20 41 21 42 21 43 22 44 22 45 23 46 23 47 24 48 24 49 25 50 25 51 26 52 26 53 27 54...
output:
724432513
result:
ok 1 number(s): "724432513"
Test #8:
score: 0
Accepted
time: 35ms
memory: 26020kb
input:
1 100000 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52...
output:
164448583
result:
ok 1 number(s): "164448583"
Test #9:
score: 0
Accepted
time: 26ms
memory: 13656kb
input:
1 100000 1 2 1 3 1 4 4 5 2 6 5 7 3 8 5 9 9 10 6 11 4 12 6 13 11 14 1 15 6 16 15 17 6 18 6 19 8 20 11 21 1 22 11 23 20 24 9 25 2 26 5 27 14 28 7 29 28 30 10 31 7 32 17 33 2 34 24 35 14 36 10 37 2 38 5 39 39 40 14 41 35 42 25 43 33 44 11 45 41 46 1 47 33 48 36 49 25 50 20 51 13 52 4 53 46 54 45 55 21 ...
output:
159386883
result:
ok 1 number(s): "159386883"
Test #10:
score: 0
Accepted
time: 19ms
memory: 13648kb
input:
1 100000 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4 9 5 10 5 11 6 12 6 13 7 14 7 15 8 16 8 17 9 18 9 19 10 20 10 21 11 22 11 23 12 24 12 25 13 26 13 27 14 28 14 29 15 30 15 31 16 32 16 33 17 34 17 35 18 36 18 37 19 38 19 39 20 40 20 41 21 42 21 43 22 44 22 45 23 46 23 47 24 48 24 49 25 50 25 51 26 52 26 53 27 54...
output:
752214506
result:
ok 1 number(s): "752214506"
Test #11:
score: 0
Accepted
time: 23ms
memory: 27608kb
input:
1 100000 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52...
output:
419022702
result:
ok 1 number(s): "419022702"