cp-reference-codes/src/2-graph/euler_circ.cpp at main · manoflearning/cp-reference-codes · GitHub

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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};
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#include"../0-common/common.hpp"

// what: build an Eulerian circuit in an undirected multigraph (adjacency matrix).
// time: O(n^2+m); memory: O(n^2)
// constraint: 1-indexed; all nonzero-degree nodes connected.
// usage: euler_cir g; g.init(n); g.add_edge(u,v); if (g.can()) auto path=g.run(1);
structeuler_cir {
int n;
 vector<vector<int>> adj;
 vector<int> nxt, path;

voidinit(int n_) {
// goal: allocate adjacency matrix and reset state.
 n = n_;
 adj.assign(n + 1, vector<int>(n + 1));
 nxt.assign(n + 1, 1);
 path.clear();
 }
voidadd_edge(int u, int v, int c = 1) {
// goal: add c parallel edges between u and v.
if (u == v) adj[u][u] += 2 * c;
else adj[u][v] += c, adj[v][u] += c;
 }
boolcan() {
// result: whether an Euler circuit exists.
 vector<int> deg(n + 1);
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) deg[i] += adj[i][j];
for (int i = 1; i <= n; i++)
if (deg[i] & 1) return0;
int s = 0;
for (int i = 1; i <= n; i++)
if (deg[i]) {
 s = i;
break;
 }
if (!s) return1;
 vector<int> vis(n + 1);
 queue<int> q;
 q.push(s);
 vis[s] = 1;
while (!q.empty()) {
int v = q.front();
 q.pop();
for (int i = 1; i <= n; i++)
if (adj[v][i] && !vis[i]) vis[i] = 1, q.push(i);
 }
for (int i = 1; i <= n; i++)
if (deg[i] && !vis[i]) return0;
return1;
 }
voiddfs(int v) {
// goal: Hierholzer DFS to build circuit.
for (int &i = nxt[v]; i <= n; i++) {
while (i <= n && adj[v][i]) {
 adj[v][i]--;
 adj[i][v]--;
dfs(i);
 }
 }
 path.push_back(v);
 }
 vector<int> run(int s = 1) {
// result: Euler circuit starting from s (if exists).
for (int i = 1; i <= n; i++) nxt[i] = 1;
 path.clear();
dfs(s);
reverse(all(path));
return path;
 }
};