整理的一些模板
graph
struct graph {
int n, cnt;
vector<vector<pair<int, int>>> G2;
vector<vector<int>> G;
vector<int> in, fa, dep, siz, btm, son, top, id, rk;
vector<int> f;
graph() {}
graph(int n) { init(n); }
void init(int n) {
this->n = n;
cnt = 0;
G.resize(n + 1);
G2.resize(n + 1);
in.resize(n + 1);
fa.resize(n + 1);
btm.resize(n + 1);
dep.resize(n + 1);
siz.resize(n + 1);
son.resize(n + 1);
top.resize(n + 1);
id.resize(n + 1);
rk.resize(n + 1);
f.resize(n + 1);
}
void work(int rt = 1) {
dfs1(rt, 0, 1);
dfs2(rt, rt);
}
void add(int a, int b) {
G[a].emplace_back(b);
in[b]++;
}
void add2(int a, int b, int v) {
G2[a].emplace_back(b, v);
in[b]++;
}
void dfs1(int u, int fath, int depth) {
fa[u] = fath, dep[u] = depth, siz[u] = 1;
for (auto it : G[u]) {
if (it == fath)
continue;
else {
dfs1(it, u, depth + 1);
siz[u] += siz[it];
if (siz[it] > siz[son[u]]) son[u] = it;
}
}
}
void dfs2(int u, int t) {
top[u] = t;
id[u] = ++cnt;
rk[cnt] = u;
btm[u] = cnt;
if (!son[u])
return;
else
dfs2(son[u], t), btm[u] = cnt;
for (auto it : G[u]) {
if (it != son[u] and it != fa[u]) dfs2(it, it);
btm[u] = cnt;
}
}
int lca(int u, int v) {
while (top[u] != top[v]) {
if (dep[u] < dep[v]) swap(u, v);
u = fa[top[u]];
}
if (dep[u] > dep[v]) swap(u, v);
return u;
}
int dist(int u, int v) { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }
int jump(int u, int k) {
if (dep[u] < k) return -1;
int d = dep[u] - k;
while (dep[top[u]] > d) u = fa[top[u]];
return rk[id[u] - dep[u] + k];
}
};
math
struct math {
int n, cnt, tot, mod;
using pii = pair<int, int>;
math(int _n) : n(_n) { init(); }
vector<int> primes, st, p, phi, sum, flg, jie, invjie, inv;
void init() {
cnt = tot = 0;
primes.resize(n + 1);
st.resize(n + 1);
p.resize(n + 1);
phi.resize(n + 1);
sum.resize(n + 1);
flg.resize(n + 1);
jie.resize(n + 1);
inv.resize(n + 1);
invjie.resize(n + 1);
get_primes(n);
sieve(n);
}
void set_mod(int mod) { this->mod = mod; }
int get_inv(int x) {
if (inv[x])
return inv[x];
else {
main_init();
return inv[x];
}
}
void main_init() {
jie[0] = inv[1] = 1;
for (int i = 1; i <= n; i++) jie[i] = jie[i - 1] * i % mod;
invjie[n] = qmi(jie[n], mod - 2, mod);
for (int i = n - 1; ~i; i--) invjie[i] = invjie[i + 1] * (i + 1) % mod;
for (int i = 2; i <= n; i++) inv[i] = (mod - mod / i) * inv[mod % i] % mod;
}
int C(int n, int m) {
return n >= m && m >= 0ll ? jie[n] * invjie[m] % mod * invjie[n - m] % mod
: 0ll;
}
void get_primes(int n) {
for (int i = 2; i <= n; i++) {
if (!st[i]) {
primes[cnt++] = i;
}
for (int j = 0; primes[j] <= n / i; j++) {
st[primes[j] * i] = true;
if (i % primes[j] == 0) break;
}
}
}
int qmi(int a, int b, int p) {
int res = 1 % p;
while (b) {
if (b & 1) res = res * a % p;
a = a * a % p;
b >>= 1;
}
return res;
}
int exgcd(int a, int b, int &x, int &y) {
if (b == 0) {
x = 1;
y = 0;
return a;
}
int x1, y1, gcd;
gcd = exgcd(b, a % b, x1, y1);
x = y1, y = x1 - a / b * y1;
return gcd;
}
vector<pii> divide1(int x) {
vector<pii> ans;
for (int i = 2; i <= x / i; i++)
if (x % i == 0) {
int s = 0;
while (x % i == 0) x /= i, s++;
ans.emplace_back(i, s);
}
if (x > 1) ans.emplace_back(x, 1);
return ans;
}
vector<int> divide2(int x) {
vector<int> ans;
for (int i = 2; i <= x / i; i++)
if (x % i == 0) {
ans.push_back(i);
if (i * i != x) ans.push_back(x / i);
}
if (x > 1) ans.push_back(x);
return ans;
}
int sushu(int num) {
if (num == 1) return 0;
if (num == 2 || num == 3) return 1;
if (num % 6 != 1 && num % 6 != 5) return 0;
int tmp = sqrtl(num);
for (int i = 5; i <= tmp; i += 6)
if (num % i == 0 || num % (i + 2) == 0) return 0;
return 1;
}
void sieve(int n) {
phi[1] = 1;
for (int i = 2; i <= n; ++i) {
if (!flg[i]) p[++tot] = i, phi[i] = i - 1;
for (int j = 1; j <= tot && i * p[j] <= n; ++j) {
flg[i * p[j]] = 1;
if (i % p[j] == 0) {
phi[i * p[j]] = phi[i] * p[j];
break;
} else {
phi[i * p[j]] = phi[i] * phi[p[j]];
}
}
}
for (int i = 1; i <= n; ++i) sum[i] = sum[i - 1] + phi[i];
}
};
MInt
using i64 = long long;
template <class T>
constexpr T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
constexpr 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 MInt {
int x;
constexpr MInt() : x{} {}
constexpr MInt(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 Mod_) { Mod = Mod_; }
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 MInt operator-() const {
MInt res;
res.x = norm(getMod() - x);
return res;
}
constexpr MInt inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MInt &operator*=(MInt rhs) & {
x = 1LL * x * rhs.x % getMod();
return *this;
}
constexpr MInt &operator+=(MInt rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr MInt &operator-=(MInt rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr MInt &operator/=(MInt rhs) & { return *this *= rhs.inv(); }
friend constexpr MInt operator*(MInt lhs, MInt rhs) {
MInt res = lhs;
res *= rhs;
return res;
}
friend constexpr MInt operator+(MInt lhs, MInt rhs) {
MInt res = lhs;
res += rhs;
return res;
}
friend constexpr MInt operator-(MInt lhs, MInt rhs) {
MInt res = lhs;
res -= rhs;
return res;
}
friend constexpr MInt operator/(MInt lhs, MInt rhs) {
MInt res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
i64 v;
is >> v;
a = MInt(v);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
return os << a.val();
}
friend constexpr bool operator==(MInt lhs, MInt rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MInt lhs, MInt rhs) {
return lhs.val() != rhs.val();
}
};
template <>
int MInt<0>::Mod = 998244353;
template <int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
MLong
using i64 = long long;
template <class T>
constexpr T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
constexpr 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 <i64 P>
struct MLong {
i64 x;
constexpr MLong() : x{} {}
constexpr MLong(i64 x) : x{norm(x % getMod())} {}
static i64 Mod;
constexpr static i64 getMod() {
if (P > 0) {
return P;
} else {
return Mod;
}
}
constexpr static void setMod(i64 Mod_) { Mod = Mod_; }
constexpr i64 norm(i64 x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr i64 val() const { return x; }
explicit constexpr operator i64() const { return x; }
constexpr MLong operator-() const {
MLong res;
res.x = norm(getMod() - x);
return res;
}
constexpr MLong inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MLong &operator*=(MLong rhs) & {
x = mul(x, rhs.x, getMod());
return *this;
}
constexpr MLong &operator+=(MLong rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr MLong &operator-=(MLong rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr MLong &operator/=(MLong rhs) & { return *this *= rhs.inv(); }
friend constexpr MLong operator*(MLong lhs, MLong rhs) {
MLong res = lhs;
res *= rhs;
return res;
}
friend constexpr MLong operator+(MLong lhs, MLong rhs) {
MLong res = lhs;
res += rhs;
return res;
}
friend constexpr MLong operator-(MLong lhs, MLong rhs) {
MLong res = lhs;
res -= rhs;
return res;
}
friend constexpr MLong operator/(MLong lhs, MLong rhs) {
MLong res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream &operator>>(std::istream &is, MLong &a) {
i64 v;
is >> v;
a = MLong(v);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MLong &a) {
return os << a.val();
}
friend constexpr bool operator==(MLong lhs, MLong rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MLong lhs, MLong rhs) {
return lhs.val() != rhs.val();
}
};
template <>
i64 MLong<0LL>::Mod = i64(1E18) + 9;
LazySegmentTree
template <class Info, class Tag>
struct LazySegmentTree {
int n;
std::vector<Info> info;
std::vector<Tag> tag;
LazySegmentTree() : n(0) {}
LazySegmentTree(int n_, Info v_ = Info()) { init(n_, v_); }
template <class T>
LazySegmentTree(std::vector<T> init_) {
init(init_);
}
void init(int n_, Info v_ = Info()) { init(std::vector<Info>(n_, v_)); }
template <class T>
void init(std::vector<T> init_) {
n = init_.size();
info.assign(4 << std::__lg(n), Info());
tag.assign(4 << std::__lg(n), Tag());
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
info[p] = init_[l];
return;
}
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
pull(p);
};
build(1, 0, n);
}
void pull(int p) { info[p] = info[2 * p] + info[2 * p + 1]; }
void apply(int p, const Tag &v) {
info[p].apply(v);
tag[p].apply(v);
}
void push(int p) {
apply(2 * p, tag[p]);
apply(2 * p + 1, tag[p]);
tag[p] = Tag();
}
void modify(int p, int l, int r, int x, const Info &v) {
if (r - l == 1) {
info[p] = v;
return;
}
int m = (l + r) / 2;
push(p);
if (x < m) {
modify(2 * p, l, m, x, v);
} else {
modify(2 * p + 1, m, r, x, v);
}
pull(p);
}
void modify(int p, const Info &v) { modify(1, 0, n, p, v); }
Info rangeQuery(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return Info();
}
if (l >= x && r <= y) {
return info[p];
}
int m = (l + r) / 2;
push(p);
return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
}
Info rangeQuery(int l, int r) { return rangeQuery(1, 0, n, l, r); }
void rangeApply(int p, int l, int r, int x, int y, const Tag &v) {
if (l >= y || r <= x) {
return;
}
if (l >= x && r <= y) {
apply(p, v);
return;
}
int m = (l + r) / 2;
push(p);
rangeApply(2 * p, l, m, x, y, v);
rangeApply(2 * p + 1, m, r, x, y, v);
pull(p);
}
void rangeApply(int l, int r, const Tag &v) {
return rangeApply(1, 0, n, l, r, v);
}
template <class F>
int findFirst(int p, int l, int r, int x, int y, F pred) {
if (l >= y || r <= x || !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
push(p);
int res = findFirst(2 * p, l, m, x, y, pred);
if (res == -1) {
res = findFirst(2 * p + 1, m, r, x, y, pred);
}
return res;
}
template <class F>
int findFirst(int l, int r, F pred) {
return findFirst(1, 0, n, l, r, pred);
}
template <class F>
int findLast(int p, int l, int r, int x, int y, F pred) {
if (l >= y || r <= x || !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
push(p);
int res = findLast(2 * p + 1, m, r, x, y, pred);
if (res == -1) {
res = findLast(2 * p, l, m, x, y, pred);
}
return res;
}
template <class F>
int findLast(int l, int r, F pred) {
return findLast(1, 0, n, l, r, pred);
}
}; // 懒标记线段树
struct Tag {
void apply(Tag t) {}
};
struct Info {
void apply(Tag t) {}
};
Info operator+(const Info &a, const Info &b) {
// 合并两个信息节点
Info c;
return c;
}
UnionFindSet
struct UnionFindSet {
vector<int> F;
vector<int> rank;
int n;
UnionFindSet(int _n = 2e6 + 10) {
n = _n;
F.resize(n + 1);
rank.resize(n + 1, 1);
for (int i = 1; i <= n; i++) {
F[i] = i;
}
}
int find(int x) { return x == F[x] ? x : F[x] = find(F[x]); }
bool merge(int x, int y) {
int fx = find(x), fy = find(y);
if (fx == fy) return false;
if (rank[fx] < rank[fy]) swap(fx, fy);
F[fy] = fx;
rank[fx] += rank[fy];
return true;
}
};
树状数组
struct szsz {
int N;
szsz(int u) : N(u) { val.resize(u + 1); }
vector<int> val;
int lowbit(int u) { return (u) & (-u); };
void update(int idx, int x) {
for (int i = idx; i < N; i += lowbit(i)) {
val[i] += x;
}
};
int ask(int u) {
int res = 0;
for (int i = u; i; i -= lowbit(i)) {
res += val[i];
}
return res;
};
};
ST表最值
struct ST {
int N = 2e5 + 10, M = 21;
vector<vector<int>> MAX;
vector<int> a;
int query(int l, int r) {
int k = __lg(r - l + 1);
return max(MAX[l][k], MAX[r - (1 << k) + 1][k]);
}
ST(vector<int> a = vector<int>(), int n = 0, int m = 0) : N(n), M(m) {
MAX.resize(N);
for (auto &i : MAX) i.resize(M);
for (int i = 0; i < n; i++) {
MAX[i][0] = a[i];
}
for (int i = 1; i < M; i++) {
for (int j = 1; j + (1 << i) - 1 < n; j++) {
MAX[j][i] = max(MAX[j][i - 1], MAX[j + (1 << (i - 1))][i - 1]);
}
}
}
};