# competitive-programming-library

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View the Project on GitHub kmyk/competitive-programming-library

# graph/tree_decomposition.aoj_2405.test.cpp

## Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2405"
#include <cstdio>
#include "graph/tree_decomposition.hpp"
#include "modulus/mint.hpp"
#include "utils/macros.hpp"
using namespace std;

constexpr int MOD = 1000003;
mint<MOD> solve(int n, int m, vector<vector<int> > & g) {
// add the implicitly given edges to g
REP (x, n) {
g[x].push_back((x + 1) % n);
g[(x + 1) % n].push_back(x);
}
REP (x, n) {
sort(ALL(g[x]));
g[x].erase(unique(ALL(g[x])), g[x].end());
}

// get a tree decomposition
auto [parent, bags_] = get_tree_decomposition(g);
auto nice = get_nice_tree_decomposition(parent, bags_);

// dp on a nice tree decomposition
vector<set<int> > bags(nice.size());
auto index = [&](int a, int x) {
assert (bags[a].count(x));
return distance(bags[a].begin(), bags[a].find(x));
};
auto translate = [&](int a, int s, int b) {
int t = 0;
for (int x : bags[a]) {
if (bags[b].count(x) and (s & (1 << index(a, x)))) {
t |= 1 << index(b, x);
}
}
return t;
};
vector<vector<mint<MOD> > > dp(nice.size());
REP (a, nice.size()) {
auto [tag, x, b] = nice[a];

if (tag == LEAF) {
bags[a].insert(x);
dp[a].resize(1 << bags[a].size());
dp[a][0] += 1;

} else if (tag == INTRODUCE) {
bags[a] = bags[b];
bags[a].insert(x);
assert (bags[a].size() <= 3);
dp[a].resize(1 << bags[a].size());
REP (t, dp[b].size()) {
int s = translate(b, t, a);
dp[a][s] += dp[b][t];
}

} else if (tag == FORGET) {
assert (bags[b].count(x));
bags[a] = bags[b];
bags[a].erase(x);
dp[a].resize(1 << bags[a].size());
REP (t, dp[b].size()) {
int s = translate(b, t, a);
if (t & (1 << index(b, x))) {
dp[a][s] += dp[b][t];
} else {
for (int y : g[x]) {
if (bags[a].count(y) and not (s & (1 << index(a, y)))) {
int u = s | (1 << index(a, y));
dp[a][u] += dp[b][t];
}
}
}
}

} else if (tag == JOIN) {
assert (bags[x] == bags[b]);
bags[a] = bags[b];
dp[a].resize(1 << bags[a].size());
REP (s, dp[a].size()) {
REP (t, dp[a].size()) if ((s & t) == 0) {
dp[a][s | t] += dp[x][s] * dp[b][t];
}
}

}
}
return dp.back().back();
}

int main() {
while (true) {
int n, m; scanf("%d%d", &n, &m);
if (n == 0 and m == 0) break;
vector<vector<int> > g(n);
REP (i, m) {
int a, b; scanf("%d%d", &a, &b);
-- a;
-- b;
g[a].push_back(b);
g[b].push_back(a);
}
mint<MOD> cnt = solve(n, m, g);
printf("%d\n", cnt.value);
}
return 0;
}



#line 1 "graph/tree_decomposition.aoj_2405.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2405"
#include <cstdio>
#line 2 "graph/tree_decomposition.hpp"
#include <algorithm>
#include <cassert>
#line 5 "graph/tree_decomposition.hpp"
#include <cstdint>
#include <functional>
#include <set>
#include <stack>
#include <tuple>
#include <unordered_set>
#include <utility>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 14 "graph/tree_decomposition.hpp"

/**
* @brief 木分解 (木幅 $t \le 2$)
* @docs graph/tree_decomposition.md
* @note $O(N)$ ?
* @see https://ei1333.hateblo.jp/entry/2020/02/12/150319
* @arg g is a simple connected graph $G = (V, E)$ whose treewidth $t \le 2$
* @return a decomposed tree $T = (I, F)$ as a triple of (the root, the list of children $c : I \to \mathcal{P} \to I$, what vertices are contained $X : I \to \mathcal{P}(V)$)
*/
inline std::pair<std::vector<int>, std::vector<std::vector<int> > > get_tree_decomposition(const std::vector<std::vector<int> > & g) {
int n = g.size();

// prepare the info about g
std::vector<int> used(n, -1);
std::vector<int> degree(n);
std::unordered_set<int64_t> edges;
auto pack = [&](int x, int y) {
if (x > y) std::swap(x, y);
return ((int64_t)x << 32) | y;
};
REP (x, n) {
degree[x] = g[x].size();
for (int y : g[x]) if (x < y) {
edges.insert(pack(x, y));
}
}

// prepare the info about t
std::vector<int> parent;
std::vector<int> antecedent;
std::function<int (int)> find_root = [&](int a) {
// union-find tree with only path-compression
return (antecedent[a] == -1 ? a : antecedent[a] = find_root(antecedent[a]));
};
std::vector<std::vector<int> > bags;

// construct the tree with a stack
std::stack<int> stk;
REP (x, n) {
if (g[x].size() <= 2) {
stk.push(x);
}
}
while (not stk.empty()) {
int x = stk.top();
stk.pop();
if (degree[x] == 0) continue;
used[x] = bags.size();
parent.push_back(-1);
antecedent.push_back(-1);
bags.emplace_back();
auto & bag = bags.back();

// make the new bag
bag.push_back(x);
for (int y : g[x]) {
if (used[y] == -1) {
// add a vertex y into the new bag
bag.push_back(y);

} else if (used[y] >= 0) {
// connect a bag used[y] as a child
int root = find_root(used[y]);
if (root == used[x]) {
// nop

} else if (bags[used[y]].size() == 2) {
// the sub-bag is removing a vertex
if (parent[root] == -1) {
parent[root] = antecedent[root] = used[x];
}
assert (bags[used[y]][1] == x);
bag.push_back(y);

} else if (bags[used[y]].size() == 3) {
// the sub-bag is removing an edge
if (parent[root] == -1) {
parent[root] = antecedent[root] = used[x];
}
assert (bags[root][1] == x or bags[root][2] == x);
bag.push_back(bags[root][1] ^ bags[root][2] ^ x);
used[bags[root][0]] = used[x];
} else {
assert (false);
}

} else {
// nop
}
}
std::sort(bag.begin() + 1, bag.end());
bag.erase(std::unique(bag.begin() + 1, bag.end()), bag.end());
assert (bag.size() == degree[x] + 1);

// remove and add edges
auto decr = [&](int y) {
-- degree[y];
if (degree[y] == 2) {
stk.push(y);
}
};
if (degree[x] == 1) {
decr(bag[1]);
} if (degree[x] == 2) {
if (not edges.insert(pack(bag[1], bag[2])).second) {
decr(bag[1]);
decr(bag[2]);
}
}
degree[x] = 0;
}

if (std::count(ALL(degree), 0) != n) return std::make_pair(std::vector<int>(), std::vector<std::vector<int> >());
assert (std::count(ALL(parent), -1) == 1);
return std::make_pair(parent, bags);
}

enum nice_tree_decomposition_tag {
LEAF,
INTRODUCE,
FORGET,
JOIN,
};

/**
* @note $O(t N)$
*/
inline std::vector<std::tuple<nice_tree_decomposition_tag, int, int> > get_nice_tree_decomposition(const std::vector<int> & parent, const std::vector<std::vector<int> > & bags) {
assert (not parent.empty());
assert (parent.back() == -1);  // assume that vertices are topologically sorted and reversed
int n = parent.size();
std::vector<std::vector<int> > children(n);
std::vector<int> node(n, -1);
std::vector<std::tuple<nice_tree_decomposition_tag, int, int> > nice;
REP (a, n) {
assert (not bags[a].empty());
if (children[a].empty()) {
for (int x : bags[a]) {
if (x == bags[a].front()) {
nice.emplace_back(LEAF, x, -1);
} else {
nice.emplace_back(INTRODUCE, x, nice.size() - 1);
}
}
node[a] = nice.size() - 1;
} else {
for (int b : children[a]) {
for (int y : bags[b]) {
if (not count(ALL(bags[a]), y)) {
nice.emplace_back(FORGET, y, node[b]);
node[b] = nice.size() - 1;
}
}
for (int x : bags[a]) {
if (not count(ALL(bags[b]), x)) {
nice.emplace_back(INTRODUCE, x, node[b]);
node[b] = nice.size() - 1;
}
}
if (b == children[a].front()) {
std::swap(node[a], node[b]);
} else {
nice.emplace_back(JOIN, node[a], node[b]);
node[a] = nice.size() - 1;
}
}
}
if (parent[a] != -1) {
children[parent[a]].push_back(a);
}
};
for (int x : bags.back()) {
nice.emplace_back(FORGET, x, node.back());
node.back() = nice.size() - 1;
}
return nice;
}
#line 3 "modulus/mint.hpp"
#include <iostream>
#line 4 "modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
uint_fast64_t y = 1;
for (; k; k >>= 1) {
if (k & 1) (y *= x) %= MOD;
(x *= x) %= MOD;
}
assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
return y;
}
#line 5 "modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
assert (0 <= value and value < MOD);
if (value == 0) return -1;
int64_t a = value, b = MOD;
int64_t x = 0, y = 1;
for (int64_t u = 1, v = 0; a; ) {
int64_t q = b / a;
x -= q * u; std::swap(x, u);
y -= q * v; std::swap(y, v);
b -= q * a; std::swap(b, a);
}
if (not (value * x + MOD * y == b and b == 1)) return -1;
if (x < 0) x += MOD;
assert (0 <= x and x < MOD);
return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
int32_t y = modinv_nocheck(x, MOD);
assert (y != -1);
return y;
}
#line 6 "modulus/mint.hpp"

/**
* @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
*/
template <int32_t MOD>
struct mint {
int32_t value;
mint() : value() {}
mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
mint(int32_t value_, std::nullptr_t) : value(value_) {}
explicit operator bool() const { return value; }
inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
inline bool operator == (mint<MOD> other) const { return value == other.value; }
inline bool operator != (mint<MOD> other) const { return value != other.value; }
inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 6 "graph/tree_decomposition.aoj_2405.test.cpp"
using namespace std;

constexpr int MOD = 1000003;
mint<MOD> solve(int n, int m, vector<vector<int> > & g) {
// add the implicitly given edges to g
REP (x, n) {
g[x].push_back((x + 1) % n);
g[(x + 1) % n].push_back(x);
}
REP (x, n) {
sort(ALL(g[x]));
g[x].erase(unique(ALL(g[x])), g[x].end());
}

// get a tree decomposition
auto [parent, bags_] = get_tree_decomposition(g);
auto nice = get_nice_tree_decomposition(parent, bags_);

// dp on a nice tree decomposition
vector<set<int> > bags(nice.size());
auto index = [&](int a, int x) {
assert (bags[a].count(x));
return distance(bags[a].begin(), bags[a].find(x));
};
auto translate = [&](int a, int s, int b) {
int t = 0;
for (int x : bags[a]) {
if (bags[b].count(x) and (s & (1 << index(a, x)))) {
t |= 1 << index(b, x);
}
}
return t;
};
vector<vector<mint<MOD> > > dp(nice.size());
REP (a, nice.size()) {
auto [tag, x, b] = nice[a];

if (tag == LEAF) {
bags[a].insert(x);
dp[a].resize(1 << bags[a].size());
dp[a][0] += 1;

} else if (tag == INTRODUCE) {
bags[a] = bags[b];
bags[a].insert(x);
assert (bags[a].size() <= 3);
dp[a].resize(1 << bags[a].size());
REP (t, dp[b].size()) {
int s = translate(b, t, a);
dp[a][s] += dp[b][t];
}

} else if (tag == FORGET) {
assert (bags[b].count(x));
bags[a] = bags[b];
bags[a].erase(x);
dp[a].resize(1 << bags[a].size());
REP (t, dp[b].size()) {
int s = translate(b, t, a);
if (t & (1 << index(b, x))) {
dp[a][s] += dp[b][t];
} else {
for (int y : g[x]) {
if (bags[a].count(y) and not (s & (1 << index(a, y)))) {
int u = s | (1 << index(a, y));
dp[a][u] += dp[b][t];
}
}
}
}

} else if (tag == JOIN) {
assert (bags[x] == bags[b]);
bags[a] = bags[b];
dp[a].resize(1 << bags[a].size());
REP (s, dp[a].size()) {
REP (t, dp[a].size()) if ((s & t) == 0) {
dp[a][s | t] += dp[x][s] * dp[b][t];
}
}

}
}
return dp.back().back();
}

int main() {
while (true) {
int n, m; scanf("%d%d", &n, &m);
if (n == 0 and m == 0) break;
vector<vector<int> > g(n);
REP (i, m) {
int a, b; scanf("%d%d", &a, &b);
-- a;
-- b;
g[a].push_back(b);
g[b].push_back(a);
}
mint<MOD> cnt = solve(n, m, g);
printf("%d\n", cnt.value);
}
return 0;
}