ロリハを衝突させるやつ (tree attack) (String/tree_attack.cpp)
- category: String
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- Last commit date: 2020-07-11 14:53:01+09:00
- see: https://codeforces.com/blog/entry/60442
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#ifndef H_tree_attack
#define H_tree_attack
/**
* @brief ロリハを衝突させるやつ (tree attack)
* @author えびちゃん
* @see https://codeforces.com/blog/entry/60442
*/
#include <cstddef>
#include <cstdint>
#include <algorithm>
#include <queue>
#include <tuple>
#include <vector>
#include "utility/literals.cpp"
std::vector<int> tree_attack(intmax_t p, intmax_t b, size_t k, int sigma = 2) {
struct node {
intmax_t value;
size_t pos, neg;
int coef;
node() = default;
node(intmax_t v, size_t l, size_t r, int c): value(v), pos(l), neg(r), coef(c) {}
bool operator <(node const& that) const { return value < that.value; }
};
std::vector<std::vector<node>> cl(k+1);
size_t n = 1_zu << k;
cl[0].assign(n, node(1, n-1, -1_zu, 1));
intmax_t pow = 1;
for (size_t j = 1; j < n; ++j) {
pow = __int128(pow) * b % p;
cl[0][j].value = pow;
cl[0][j].coef = 1;
intmax_t cur = pow;
for (int s = 2; s < sigma; ++s) {
cur = __int128(cur + pow) % p;
if (cur < cl[0][j].value) {
cl[0][j].value = cur;
cl[0][j].coef = s;
}
}
cl[0][j].pos = n-1-j;
}
std::sort(cl[0].begin(), cl[0].end());
std::vector<int> coef(n);
for (size_t i = 0; i < n; ++i)
coef[cl[0][i].pos] = cl[0][i].coef;
for (size_t i = 1; i <= k; ++i) {
cl[i].resize(n >> i);
for (size_t j = 0; j < cl[i].size(); ++j) {
size_t jl = j << 1 | 0;
size_t jr = j << 1 | 1;
if (cl[i-1][jr] < cl[i-1][jl]) {
cl[i][j].value = cl[i-1][jl].value - cl[i-1][jr].value;
cl[i][j].pos = jl;
cl[i][j].neg = jr;
} else {
cl[i][j].value = cl[i-1][jr].value - cl[i-1][jl].value;
cl[i][j].pos = jr;
cl[i][j].neg = jl;
}
}
std::sort(cl[i].begin(), cl[i].end());
if (cl[i][0].value > 0) continue;
std::vector<int> res(n, 0);
std::queue<std::tuple<size_t, size_t, bool>> q; // i, j, neg?
q.emplace(i-1, cl[i][0].pos, false);
q.emplace(i-1, cl[i][0].neg, true);
while (!q.empty()) {
auto [i, j, neg] = q.front();
q.pop();
if (i == -1_zu) {
if (j != -1_zu) res[j] = (neg? -coef[j]: +coef[j]);
continue;
}
q.emplace(i-1, cl[i][j].pos, neg);
q.emplace(i-1, cl[i][j].neg, !neg);
}
return res;
}
return {};
}
#endif /* !defined(H_tree_attack) */
#line 1 "String/tree_attack.cpp"
/**
* @brief ロリハを衝突させるやつ (tree attack)
* @author えびちゃん
* @see https://codeforces.com/blog/entry/60442
*/
#include <cstddef>
#include <cstdint>
#include <algorithm>
#include <queue>
#include <tuple>
#include <vector>
#line 1 "utility/literals.cpp"
/**
* @brief ユーザ定義リテラル
* @author えびちゃん
*/
#line 11 "utility/literals.cpp"
constexpr intmax_t operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
constexpr int8_t operator ""_i8(unsigned long long n) { return n; }
constexpr int16_t operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t operator ""_u8(unsigned long long n) { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }
#line 18 "String/tree_attack.cpp"
std::vector<int> tree_attack(intmax_t p, intmax_t b, size_t k, int sigma = 2) {
struct node {
intmax_t value;
size_t pos, neg;
int coef;
node() = default;
node(intmax_t v, size_t l, size_t r, int c): value(v), pos(l), neg(r), coef(c) {}
bool operator <(node const& that) const { return value < that.value; }
};
std::vector<std::vector<node>> cl(k+1);
size_t n = 1_zu << k;
cl[0].assign(n, node(1, n-1, -1_zu, 1));
intmax_t pow = 1;
for (size_t j = 1; j < n; ++j) {
pow = __int128(pow) * b % p;
cl[0][j].value = pow;
cl[0][j].coef = 1;
intmax_t cur = pow;
for (int s = 2; s < sigma; ++s) {
cur = __int128(cur + pow) % p;
if (cur < cl[0][j].value) {
cl[0][j].value = cur;
cl[0][j].coef = s;
}
}
cl[0][j].pos = n-1-j;
}
std::sort(cl[0].begin(), cl[0].end());
std::vector<int> coef(n);
for (size_t i = 0; i < n; ++i)
coef[cl[0][i].pos] = cl[0][i].coef;
for (size_t i = 1; i <= k; ++i) {
cl[i].resize(n >> i);
for (size_t j = 0; j < cl[i].size(); ++j) {
size_t jl = j << 1 | 0;
size_t jr = j << 1 | 1;
if (cl[i-1][jr] < cl[i-1][jl]) {
cl[i][j].value = cl[i-1][jl].value - cl[i-1][jr].value;
cl[i][j].pos = jl;
cl[i][j].neg = jr;
} else {
cl[i][j].value = cl[i-1][jr].value - cl[i-1][jl].value;
cl[i][j].pos = jr;
cl[i][j].neg = jl;
}
}
std::sort(cl[i].begin(), cl[i].end());
if (cl[i][0].value > 0) continue;
std::vector<int> res(n, 0);
std::queue<std::tuple<size_t, size_t, bool>> q; // i, j, neg?
q.emplace(i-1, cl[i][0].pos, false);
q.emplace(i-1, cl[i][0].neg, true);
while (!q.empty()) {
auto [i, j, neg] = q.front();
q.pop();
if (i == -1_zu) {
if (j != -1_zu) res[j] = (neg? -coef[j]: +coef[j]);
continue;
}
q.emplace(i-1, cl[i][j].pos, neg);
q.emplace(i-1, cl[i][j].neg, !neg);
}
return res;
}
return {};
}