結果
| 問題 | No.3720 Balanced Reduction |
| コンテスト | |
| ユーザー |
👑  Forested
|
| 提出日時 | 2026-09-18 22:17:14 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
WA
不安定
|
| 実行時間 | - |
| コード長 | 15,242 bytes |
| 記録 | |
| コンパイル時間 | 3,322 ms |
| コンパイル使用メモリ | 365,584 KB |
| 実行使用メモリ | 61,360 KB |
| 最終ジャッジ日時 | 2026-09-18 22:17:21 |
| 合計ジャッジ時間 | 6,561 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 15 WA * 1 |
ソースコード
#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
// ============
#ifdef DEBUGF
#else
#define DBG(...) (void)0
#endif
// ============
#include <iostream>
#include <cassert>
#include <vector>
template <typename T>
struct Edge {
using W = T;
int from, to, id;
W weight;
Edge<T> rev() const {
return Edge<T>{to, from, id, weight};
}
};
template <typename T>
void debug(const Edge<T> &e) {
std::cerr << e.from << " -> " << e.to << " id = " << e.id << std::cerr << " weight = ";
debug(e.weight);
}
template <typename T = int, bool DIR = false>
class Graph {
public:
using E = Edge<T>;
using W = T;
static constexpr bool DIRECTED = DIR;
struct Adjacency {
using Iter = typename std::vector<E>::iterator;
Iter be, en;
Iter begin() const { return be; }
Iter end() const { return en; }
int size() const { return (int)std::distance(be, en); }
E &operator[](int idx) const { return be[idx]; }
};
struct ConstAdjacency {
using Iter = typename std::vector<E>::const_iterator;
Iter be, en;
Iter begin() const { return be; }
Iter end() const { return en; }
int size() const { return (int)std::distance(be, en); }
const E &operator[](int idx) const { return be[idx]; }
};
private:
int n, m;
std::vector<E> edges, csr;
std::vector<int> sep;
bool built;
public:
Graph(int n) : n(n), m(0), built(false) {}
int v() const { return n; }
int e() const { return m; }
int add_vertex() {
return n++;
}
void add_edge(int from, int to, W weight = 1) {
assert(0 <= from && from < n && 0 <= to && to < n);
edges.emplace_back(E{from, to, m++, weight});
}
void build() {
sep.assign(n + 1, 0);
csr.resize(DIRECTED ? m : 2 * m);
for (const E &e : edges) {
++sep[e.from + 1];
if (!DIRECTED) {
++sep[e.to + 1];
}
}
for (int i = 0; i < n; ++i) {
sep[i + 1] += sep[i];
}
std::vector<int> c = sep;
for (const E &e : edges) {
csr[c[e.from]++] = e;
if (!DIRECTED) {
csr[c[e.to]++] = e.rev();
}
}
built = true;
}
Adjacency operator[](int v) {
assert(built && 0 <= v && v < n);
return Adjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
}
ConstAdjacency operator[](int v) const {
assert(built && 0 <= v && v < n);
return ConstAdjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
}
};
// ============
// ============
#include <utility>
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned)((unsigned long long)ret * self % mod);
}
self = (unsigned)((unsigned long long)self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok) return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
a = safe_mod(a, b);
T s = b, t = a, m0 = 0, m1 = 1;
while (t) {
T u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) {
m0 += b / s;
}
return std::pair<T, T>(s, m0);
}
// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
T _a = safe_mod(a, b);
T quot = (a - _a) / b;
T x00 = 0, x01 = 1, y0 = b;
T x10 = 1, x11 = -quot, y1 = _a;
while (y1) {
T u = y0 / y1;
x00 -= u * x10;
x01 -= u * x11;
y0 -= u * y1;
std::swap(x00, x10);
std::swap(x01, x11);
std::swap(y0, y1);
}
if (x00 < 0) {
x00 += b / y0;
x01 -= a / y0;
}
return std::tuple<T, T, T>(y0, x00, x01);
}
// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
return extgcd(x, m).second;
}
// ============
i64 loop(i64 k, const V<i64> &a) {
DBG(k, a);
i32 n = LEN(a);
if (n % 2 == 1) {
V<i64> ops(n, 0);
REP(i, 1, n) {
ops[i] = a[i] - ops[i - 1];
}
i64 more = a[0] - (ops[0] + ops[n - 1]);
if (more % 2 != 0) {
return -1;
}
more /= 2;
REP(i, n) {
if (i % 2 == 0) {
ops[i] += more;
} else {
ops[i] -= more;
}
}
DBG(ops);
i64 ans = 0;
REP(i, n) {
if (ops[i] < 0 || (0 < ops[i] && ops[i] < k)) {
return -1;
}
ans += ceil_div(ops[i], 2 * k);
}
return ans;
}
assert(n % 2 == 0);
V<i64> ops(n, 0);
REP(i, 1, n) {
ops[i] = a[i] - ops[i - 1];
}
if (ops[0] + ops[n - 1] != a[0]) {
return -1;
}
DBG(k, n, a, ops);
// +x -x +x -x ... +x -x
i64 low = -INF64, high = INF64;
REP(i, n / 2) {
chmax(low, -ops[2 * i]);
chmin(high, ops[2 * i + 1]);
}
if (low > high) {
return -1;
}
// mendou
i64 ans = 0;
REP(i, n) {
ans += ceil_div(ops[i], 2 * k);
}
// tasukete!!!!
V<tuple<i64, i64, i32>> add;
REP(i, n / 2) {
{
i64 val = ops[2 * i];
i64 md = safe_mod(val, 2 * k);
if (md == 0) {
add.emplace_back(1, 2 * k, 1);
} else if (md >= 2) {
add.emplace_back(2 * k + 1 - md, 2 * k, 1);
}
}
{
i64 val = ops[2 * i + 1];
i64 md = safe_mod(val, 2 * k);
if (md != 0) {
add.emplace_back(md, 2 * k, -1);
}
}
}
DBG(ans, low, high, add);
V<tuple<i64, i64, i32>> ban;
if (k > 1) {
REP(i, n / 2) {
{
i64 val = ops[2 * i];
// 1 <= val + x < k
// 1 - val <= x < k - val
i64 l = 1 - val, r = k - val;
if (floor_div(l, 2 * k) < floor_div(r - 1, 2 * k)) {
ban.emplace_back(safe_mod(l, 2 * k), 2 * k, floor_div(l, 2 * k));
ban.emplace_back(0, safe_mod(r, 2 * k), floor_div(r, 2 * k));
} else {
ban.emplace_back(safe_mod(l, 2 * k), safe_mod(r - 1, 2 * k) + 1, floor_div(l, 2 * k));
}
}
{
i64 val = ops[2 * i];
// 1 <= val - x < k
// val - k < x <= val - 1
i64 l = val - k + 1, r = val; // [l, r)
if (floor_div(l, 2 * k) < floor_div(r - 1, 2 * k)) {
ban.emplace_back(safe_mod(l, 2 * k), 2 * k, floor_div(l, 2 * k));
ban.emplace_back(0, safe_mod(r, 2 * k), floor_div(r, 2 * k));
} else {
ban.emplace_back(safe_mod(l, 2 * k), safe_mod(r - 1, 2 * k) + 1, floor_div(l, 2 * k));
}
}
}
}
DBG(ban);
V<i64> pos;
pos.push_back(0);
pos.push_back(2 * k);
for (auto [l, r, v] : add) {
pos.push_back(l);
pos.push_back(r);
}
for (auto [l, r, v] : ban) {
pos.push_back(l);
pos.push_back(r);
}
pos.push_back(safe_mod(low, 2 * k));
pos.push_back(safe_mod(high + 1, 2 * k));
sort(ALL(pos));
pos.erase(unique(ALL(pos)), end(pos));
i32 m = LEN(pos);
VV<i32> push(m), remov(m);
V<i32> lu(m, 0);
for (auto [l, r, v] : add) {
lu[lob(pos, l)] += v;
lu[lob(pos, r)] -= v;
}
REP(i, m - 1) {
lu[i + 1] += lu[i];
}
for (auto [l, r, v] : ban) {
l = lob(pos, l);
r = lob(pos, r);
push[l].push_back(v);
remov[r].push_back(v);
}
multiset<i64> ms;
i32 diff = INF;
REP(i, m - 1) {
for (i64 v : remov[i]) {
ms.erase(ms.find(v));
}
for (i64 v : push[i]) {
ms.insert(v);
}
i64 md = pos[i];
// md + 2 * k * x >= low
// x >= ceil((low - md) / (2 * k))
i64 x = ceil_div(low - md, 2 * k);
bool ok = false;
while (md + 2 * x * k <= high) {
if (!ms.contains(x)) {
ok = true;
break;
}
++x;
}
if (ok) {
chmin(diff, lu[i]);
}
}
ans += diff;
return ans;
}
void solve() {
I32(n);
I64(k);
VEC(i64, a, n);
Graph<> g(n);
REP(i, n) {
I32(u, v);
--u;
--v;
g.add_edge(u, v);
}
g.build();
V<i32> deg(n);
REP(i, n) {
deg[i] = LEN(g[i]);
}
queue<i32> que;
i64 ans = 0;
REP(i, n) {
if (deg[i] == 1) {
que.push(i);
}
}
while (!que.empty()) {
i32 v = que.front();
que.pop();
i32 u = -1;
for (auto e : g[v]) {
if (deg[e.to] >= 2) {
u = e.to;
}
}
assert(u != -1);
if (a[v] < 0 || (0 < a[v] && a[v] < k)) {
cout << -1 << '\n';
return;
}
a[u] -= a[v];
ans += ceil_div(a[v], 2 * k);
if (--deg[u] == 1) {
que.push(u);
}
}
DBG(deg, a, ans);
REP(v, n) {
if (deg[v] != 2) {
continue;
}
V<i64> arr;
i32 cur = v;
i32 prv = -1;
while (true) {
arr.push_back(a[cur]);
deg[cur] = -1;
i32 to = -1;
for (auto e : g[cur]) {
if (deg[e.to] == 2 && e.to != prv) {
to = e.to;
break;
}
}
if (to == -1) {
break;
}
prv = exchange(cur, to);
}
i64 sub = loop(k, arr);
if (sub == -1) {
cout << -1 << '\n';
return;
}
ans += sub;
}
cout << ans << '\n';
}
int main() {
i32 t = 1;
// cin >> t;
while (t--) {
solve();
}
}