VI dijkstra(VVI& graph, int v) {
std::set<int> visited;
VI rho(graph.size());
VI pred(graph.size()); pred[v] = nil;
for (VI::iterator itr = rho.begin(); itr != rho.end(); ++itr) {
*itr = inf;
}
rho[v] = 0;
int current_min_rho;
while (visited.size() != graph.size()) {
// travers
current_min_rho = inf;
for (int i = 0; i < graph.size(); ++i) {
if (visited.find(i) == visited.end() && current_min_rho > rho[i])
current_min_rho = i;
}
visited.insert(current_min_rho);
// mark
for (int i = 0; i < graph.size(); ++i) {
if (graph[current_min_rho][i] && visited.find(i) == visited.end()) {
if (rho[i] > rho[current_min_rho] + graph[current_min_rho][i]) {
rho[i] = rho[current_min_rho] + graph[current_min_rho][i];
pred[i] = current_min_rho;
}
}
}
}
return rho;
}
bool multi(VVI & x, VVI & y, VVI & z) {
int mx = x.size();
int my = y.size();
if (mx == 0 || my == 0) return false;
int nx = x[0].size();
int ny = y[0].size();
if (nx == 0 || ny == 0) return false;
//cout << "mx: " << mx << endl;
//cout << "my: " << my << endl;
//cout << "nx: " << nx << endl;
//cout << "ny: " << ny << endl;
if (nx != my) return false;
z.clear();
for (int i = 0; i < mx; i++) {
z.push_back(VI(ny, 0));
for (int j = 0; j < ny; j++) {
double sum = 0;
for (int k = 0; k < my; k++) {
sum += (double)x[i][k] * (double)y[k][j];
}
if (sum > INT_MAX || sum < INT_MIN) return false;
z[i][j] = (int)sum;
}
}
return true;
}
void CalcOmegaMatrix(const VVI & RM, const VVI & DM, VVI & OmegaM) {
if (RM.size() == 0 || DM.size() == 0) {
cerr << "Size of relation matrix and decison matrix is 0 !" << endl;
exit(-1);
}
//OmegaM: n * d
OmegaM.clear();
VI viTmp(DM[0].size(), 0);
OmegaM.insert(OmegaM.begin(), RM.size(), viTmp);
// cout << OmegaM.size() << "\t" << OmegaM[0].size() <<endl;
unsigned int i, j, k;
STR2VI_MAP::iterator it;
int sum = 0;
for (i = 0; i < RM.size(); ++i) {
for (j = 0; j < DM[0].size(); ++j) {
sum = 0;
for (k = 0; k < DM.size(); ++k) {
sum += RM[i][k] * DM[k][j];
}
OmegaM[i][j] = sum;
}
}
}
void CalcH(const VVI OmegaM, const VI LM, VVD & H) {
if (OmegaM.size() == 0 || LM.size() == 0) {
cerr << "Size of Omega matrix or Lambda matrix is 0 !" << endl;
exit(-1);
}
H.clear();
VD vdTmp(OmegaM[0].size(), 0);
H.insert(H.begin(), OmegaM.size(), vdTmp);
unsigned int i, j;
for (i = 0; i < H.size(); ++i)
for (j = 0; j < H[0].size(); ++j) {
H[i][j] = 1.0 * OmegaM[i][j] / LM[i];
}
/*
for(it=DMap.begin(), i=0; it!= DMap.end(); ++it, ++i)
{
for(j=0;j<RM.size();++j)
{
sum = 0;
for(k=0;k<(*it).second.size();++k)
{
sum += RM[j][(*it).second[k]];
}
H[i][j] = 1.0 * sum / LM [j];
}
}*/
}
string moreClasses(string a, vector <string> b) {
int i, j, k, x, y, z, n;
string ret = "";
VVI m;
for( i = 0; i < b.size(); i++ ) {
n = atoi(b[i].c_str());
for( j = 0; j < n; j++ ) {
m.push_back(VI());
for( k = 0; k < b[i].size(); k++ ) if( !isdigit(b[i][k]) )
m.back().push_back(b[i][k]);
}
}
if( m.size() > 128 ) return "0";
for( i = 0; i < a.size(); i++ ) taken[a[i]] = 1;
n = m.size()-bipartitematch(m);
x = 33;
while( n ) {
if( x >= 128 ) return "0";
if( taken[x] ) {x++; continue;}
taken[x] = 1;
if (x >= 67)
cout<<x;
z = m.size()-bipartitematch(m);
if( z == n )
taken[x] = 0;
else
ret += x;
n = z;
x++;
}
return ret;
}
int BipartiteMatching(const VVI & w, VI & mr, VI & mc) {
mr = VI(w.size(), -1);
mc = VI(w[0].size(), -1);
int ct = 0;
for (int i = 0; i < w.size(); i++) {
VI seen(w[0].size());
if (FindMatch(i, w, mr, mc, seen)) ct++;
}
return ct;
}
latin_square(const VVI& mat, const VI& rp, const VI& cp) : r(mat.size(), 0),
c(mat.size(), 0),
m(mat.size(), VI(mat.size())) {
int n = mat.size();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
r[i] <<= 3;
r[i] += mat[rp[i]][cp[j]];
c[i] <<= 3;
c[i] += mat[rp[j]][cp[i]];
m[i][j] = mat[rp[i]][cp[j]];
}
}
}
VVI mul(VVI a, VVI b) {
int m = a.size();
int n = a[0].size();
int p = b.size();
VVI c(m, VI(p, 0));
for (int i = 0; i < m; i++) {
for (int j = 0; j < p; j++) {
for (int k = 0; k < n; k++) {
c[i][j] += a[i][k] * b[k][j];
}
if (c[i][j] > 0) c[i][j] = 1;
}
}
return c;
}
void display(VVI v){
for(int i=0;i<v.size();i++){
for(int j=0;j<v[i].size();j++)
printf("%d ", v[i][j]);
printf("\n");
}
}
void initDfs(int u,int level = 0)
{
LVL[u] = level;
SZ[u] = 1;
for(int i = 0; i < adj[u].size(); ++i)
{
int v = adj[u][i];
if(SZ[v])continue;
P[v] = u;
initDfs(v,level + 1);
SZ[u] += SZ[v];
}
for(int i = 0; i < adj[u].size(); ++i)
{
int v = adj[u][i];
if(v == P[u])continue;
if(2*SZ[v] > SZ[u]-1){
PC[u] = v;
}
else
{
groups.push_back(VI());
for(int j = v; j != -1; j = PC[j])
groups.back().push_back(j) ,
groupId[j] = groups.size() - 1 ,
groupPos[j] = groups.back().size()-1;
}
}
}
void d1s1(VVI &inp){
int vald1s1 = 0;
int vald1s2 = 0;
int vald2s1 = 0;
int vald2s2 = 0;
int n=inp.size();
int n1 = n-1;
int ij ;
STACK stid1s1,stjd1s1;
STACK stid1s2,stjd1s2;
STACK stid2s1,stjd2s1;
STACK stid2s2,stjd2s2;
for(int i=0;i<n;i++){
for(int j=0;j<=i;j++){
ij = i-j;
update(inp,stid1s1,stjd1s1,ij,j,vald1s1);
if(i<(n1)){
update(inp,stid1s2,stjd1s2,n1-j,n1-ij,vald1s2);
}
update(inp,stid2s1,stjd2s1,j,n1-ij,vald2s1);
if(i<(n1)){
update(inp,stid2s2,stjd2s2,n1-ij,j,vald2s2);
}
}
emptyStacks(inp,stid1s1,stjd1s1,vald1s1);
emptyStacks(inp,stid1s2,stjd1s2,vald1s2);
emptyStacks(inp,stid2s1,stjd2s1,vald2s1);
emptyStacks(inp,stid2s2,stjd2s2,vald2s2);
}
}
/// Calc diagonal matrix Lambda
void CalcLambda(const VVI RM, VI & LM) {
if (RM.size() == 0) {
cerr << "Size of relation matrix!" << endl;
exit(-1);
}
LM.clear();
unsigned int i, j;
int sum = 0;
for (i = 0; i < RM.size(); ++i) {
sum = 0;
for (j = 0; j < RM[i].size(); ++j) {
sum += RM[i][j];
}
LM.push_back(sum);
}
}
pair<int, VI> GetMinCut(VVI &weights) {
int N = weights.size();
VI used(N), cut, best_cut;
int best_weight = -1;
for (int phase = N-1; phase >= 0; phase--) {
VI w = weights[0];
VI added = used;
int prev, last = 0;
for (int i = 0; i < phase; i++) {
prev = last;
last = -1;
for (int j = 1; j < N; j++)
if (!added[j] && (last == -1 || w[j] > w[last])) last = j;
if (i == phase-1) {
for (int j = 0; j < N; j++) weights[prev][j] += weights[last][j];
for (int j = 0; j < N; j++) weights[j][prev] = weights[prev][j];
used[last] = true;
cut.push_back(last);
if (best_weight == -1 || w[last] < best_weight) {
best_cut = cut;
best_weight = w[last];
}
} else {
for (int j = 0; j < N; j++)
w[j] += weights[last][j];
added[last] = true;
}
}
}
return make_pair(best_weight, best_cut);
}
int solve_impl(VVI &adj_list, int node, int k) {
int N = adj_list.size();
static VB visited(N);
static VI fn(N), gn(N);
// fn[i] contains no of subtrees rooted at i
// gn[i] contains no of subtrees not rooted at i
visited[node] = true;
VI f_values, g_values;
for (int i = 0; i < adj_list[node].size(); i++) {
int child = adj_list[node][i];
if (!visited[child]) {
solve_impl(adj_list, child, k);
f_values.push_back(fn[child]);
g_values.push_back(gn[child]);
}
}
fn[node] = max(subset_sum_count(f_values, k - 1) + 1, 1);
gn[node] = 0;
for (int i = 0; i < f_values.size(); i++) {
gn[node] += f_values[i] + g_values[i];
}
cout << "fn and gn for " << node << " are " << fn[node] << " " << gn[node]
<< endl;
return fn[node] + gn[node];
}
void levelOrder(TreeNode* root, int iDeepth, VVI& result) {
if (!root) return;
if (iDeepth >= result.size())
result.resize(iDeepth + 1);
result[iDeepth].push_back(root->val);
levelOrder(root->left, iDeepth + 1, result);
levelOrder(root->right, iDeepth + 1, result);
}
void print(VVI& v) {
for(int i = 0; i < v.size(); ++i) {
for(int j = 0; j < v[i].size() - 1; ++j) {
cout<<v[i][j]<<" ";
}
cout<<endl;
}
}
void OutputMatrix(const VVI matrix) {
unsigned int i, j;
for (i = 0; i < matrix.size(); ++i) {
for (j = 0; j < matrix[i].size(); ++j) {
cout << matrix[i][j] << " ";
}
cout << endl;
}
}
HLD(VVI adj) {
N = adj.size();
P = PC = VI(N , -1);
LVL = SZ = groupId = groupPos = VI(N , 0);
this->adj = adj;
for(int i = 0; i < N; ++i)
{
if(SZ[i] == 0)
{
initDfs(i);
groups.push_back(VI());
for(int j = i; j != -1; j = PC[j])
groups.back().push_back(j) ,
groupId[j] = groups.size() - 1 ,
groupPos[j] = groups.back().size()-1;
}
}
}
void imprime(VVI& dist){
const int V = dist.size();
for(int i=0;i<V;++i){
for(int j=0;j<V;++j){
if(dist[i][j]==INF) cout<<"- ";
else cout<<dist[i][j]<< " ";
}
cout<<endl;
}
}
bool check(const VVI &g)
{
int n = g.size();
allisok = 1;
for (int i = 0; i < n; ++i)
colors[i] = 0;
for (int i = 0; i < n; ++i)
if (colors[i] == 0)
dfs(g, i, 1);
return allisok;
}
//SUMA DE MATRICES BAJO EL ENFOQUE FILA-COLUMNA
VVI sum_filcol(VVI A, VVI B)
{
int size=A.size();
VVI rslt(size,VI(size));
for(int i=0;i<size;i++)
for(int j=0;j<size;j++)
rslt[i][j]=A[i][j]+B[i][j];
return rslt;
}
int GetMaxFlow(int s, int t) {
N = cap.size();
flow = VVI(N, VI(N));
reached = VI(N);
int totflow = 0;
while (int amt = Augment(s, t, INF)) {
totflow += amt;
fill(reached.begin(), reached.end(), 0);
}
return totflow;
}
//SUMA DE MATRICES BAJO EL ENFOQUE COLUMNA-FILA
VVI sum_colfil(VVI A, VVI B)
{
int size=A.size();
VVI rslt(size,VI(size));
for(int i=0;i<size;i++)
for(int j=0;j<size;j++)
rslt[j][i]=A[j][i]+B[j][i];
return rslt;
}
//lastrow = row for the last column
void getPath(const VVI &parent, int lastrow, VI &path)
{
int nc = parent.size();
path.clear();
path.push_back(lastrow);
if(nc > 1){
for(int c = nc - 2; c >= 0; c--){
//decide row for column c
int r = parent[c+1][path.back()];
path.push_back(r);
}
}
}
bool checkConnected(VVI &g)
{
int n = g.size();
if (n == 0)
return 1;
for (int i = 0; i < n; ++i)
used[i] = 0;
dfs(0, g);
for (int i = 0; i < n; ++i)
if (!used[i])
return 0;
return 1;
}
VVI exactify(const VVI& S, const int N) {
VVI vec;
for(int r = 0; r < N; ++r) {
for(int c = 0; c < N; ++c) {
for(int cand = 0; cand < N; ++cand) {
if(S[r][c] != 0 && S[r][c] != cand + 1) {
continue;
}
row_cand[vec.size()] = r*N*N + c*N + cand;
vector<int> L(4*N*N);
vec.push_back(L);
int reg = region(r,c,N);
vec.back()[r*N + c] = 1;
vec.back()[N*N + r*N + cand] = 1;
vec.back()[2*N*N + N*c + cand] = 1;
vec.back()[3*N*N + N*reg + cand] = 1;
}
}
}
if(!given_solution.empty()) {
map<int,int> rev;
map<int,int>::iterator it;
for(it = row_cand.begin(); it != row_cand.end(); ++it) {
rev[it->second] = it->first;
}
vector<int> check(vec[0].size());
for(int x = 0; x < given_solution.size(); ++x) {
for(int y = 0; y < given_solution[x].size(); ++y) {
int val = x * N * N + y * N + given_solution[x][y] - 1;
for(int i = 0; i < vec[rev[val]].size(); ++i) {
check[i] += vec[rev[val]][i];
}
}
}
for(int i = 0; i < check.size(); ++i) {
assert(check[i] == 1);
}
}
return vec;
}
bool add(VVI & x, VVI & y, VVI & z) {
int mx = x.size();
int my = y.size();
if (mx == 0 || my == 0) return false;
int nx = x[0].size();
int ny = y[0].size();
if (nx == 0 || ny == 0) return false;
//cout << "mx: " << mx << endl;
//cout << "my: " << my << endl;
//cout << "nx: " << nx << endl;
//cout << "ny: " << ny << endl;
if (mx != my || nx != ny) return false;
z.clear();
for (int i = 0; i < mx; i++) {
z.push_back(VI(nx, 0));
for (int j = 0; j < nx; j++) {
double tmp = (double)x[i][j] + (double)y[i][j];
if (tmp > INT_MAX || tmp < INT_MIN) return false;
z[i][j] = (int)tmp;
}
}
return true;
}
/*void hs(VVI &inp){
int valh = 0;
int valv = 0;
int n=inp.size();
STACK stih,stjh;
STACK stiv,stjv;
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
update(inp,stih,stjh,i,j,valh);
update(inp,stiv,stjv,j,i,valv);
}
emptyStacks(inp,stih,stjh,valh);
emptyStacks(inp,stiv,stjv,valv);
}
}*/
void hs(VVI &inp){
int n = inp.size();
STACK stc_h;
STACK stc_v;
int val_h =0;
int val_v=0;
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
if(inp[i][j]>0){
val_h++;
stc_h.push(j);
} else {
while(!stc_h.empty()){
int j_h = stc_h.top(); stc_h.pop();
if(inp[i][j_h]<val_h){
inp[i][j_h]=val_h;
}
}
val_h=0;
}
if(inp[j][i]>0){
val_v++;
stc_v.push(j);
} else {
while(!stc_v.empty()){
int j_v = stc_v.top(); stc_v.pop();
if(inp[j_v][i]<val_v){
inp[j_v][i] = val_v;
}
}
val_v=0;
}
}
while(!stc_h.empty()){
int j_h = stc_h.top(); stc_h.pop();
if(inp[i][j_h]<val_h){
inp[i][j_h]=val_h;
}
}
val_h=0;
while(!stc_v.empty()){
int j_v = stc_v.top(); stc_v.pop();
if(inp[j_v][i]<val_v){
inp[j_v][i] = val_v;
}
}
val_v=0;
}
}
bool checkBipartate(VVI &g, int k)
{
int n = g.size();
if (n == 0)
return 1;
for (int i = 0; i < n; ++i)
used[i] = 0;
for (int i = 0; i < n; ++i)
if (!used[i])
{
k--;
dfs(i, g);
}
return k == 0;
}
VS print(VVI & m) {
VS M;
for (int i = 0; i < (int)m.size(); i++) {
M.push_back("");
for (int j = 0; j < (int)m[i].size(); j++) {
ostringstream os;
os << m[i][j];
if (j == 0) M[i] += os.str();
else M[i] += (" " + os.str());
}
}
//for (int i = 0; i < (int)M.size(); i++)
//cout << M[i] << endl;
return M;
}
