/**
* @param n an integer
* @param m an integer
* @param operators an array of point
* @return an integer array
*/
vector<int> numIslands2(int n, int m, vector<Point> &operators) {
b.clear();
dj.clear();
this->n = n;
this->m = m;
b.resize(n * m, false);
dj.resize(n * m);
int i;
for (i = 0; i < n * m; ++i) {
dj[i] = i;
}
int cc = 0;
int x, y;
int x1, y1;
int r, r1;
vector<int> ans;
vector<int> adj;
int j;
for (i = 0; i < operators.size(); ++i) {
x = operators[i].x;
y = operators[i].y;
if (b[x * m + y]) {
ans.push_back(cc);
continue;
}
b[x * m + y] = true;
adj.clear();
for (j = 0; j < 4; ++j) {
x1 = x + d[j][0];
y1 = y + d[j][1];
if (inbound(x1, y1) && b[x1 * m + y1]) {
adj.push_back(x1 * m + y1);
}
}
if (adj.empty()) {
ans.push_back(++cc);
continue;
}
dj[findRoot(adj[0])] = findRoot(x * m + y);
for (j = 1; j < adj.size(); ++j) {
r = findRoot(x * m + y);
r1 = findRoot(adj[j]);
if (r != r1) {
dj[r1] = r;
--cc;
}
}
ans.push_back(cc);
}
return ans;
}
inline static
LabelT set_union(LabelT *P, LabelT i, LabelT j){
LabelT root = findRoot(P, i);
if(i != j){
LabelT rootj = findRoot(P, j);
if(root > rootj){
root = rootj;
}
setRoot(P, j, root);
}
setRoot(P, i, root);
return root;
}
void C_WeightedQuickUnion::connect(unsigned int inx1, unsigned int inx2) {
unsigned int inx_root_1 = findRoot(inx1);
unsigned int inx_root_2 = findRoot(inx2);
if (inx_root_1 == inx_root_2) return;
if (treeWeights[inx_root_1] > treeWeights[inx_root_2]){
IDs_raw_ptr->at(inx_root_2) = inx_root_1;
treeWeights[inx_root_1] += treeWeights[inx_root_2];
} else {
IDs_raw_ptr->at(inx_root_1) = inx_root_2;
treeWeights[inx_root_2] += treeWeights[inx_root_1];
}
}
int height(std::vector<std::unordered_set<int>> &children,
const std::vector<int> parents)
{
int root = findRoot(parents);
std::vector<int> leaves = findLeaves(children),
subtreeHeight(parents.size(), 1);
while (!leaves.empty()) {
std::vector<int> newLeaves;
for (int nextLeaf: leaves) {
int nextParent = parents.at(nextLeaf);
if (nextParent == -1) {
continue;
}
subtreeHeight[nextParent] = subtreeHeight[nextLeaf] + 1;
children[nextParent].erase(nextLeaf);
if (children[nextParent].empty()) {
newLeaves.push_back(nextParent);
}
}
leaves = newLeaves;
}
return subtreeHeight[root];
}
int findRoot(int tree[], int n) {
if (tree[n] == -1) return n;
else {
tree[n] = findRoot(tree, tree[n]);
return tree[n];
}
}
const Real GreensFunction2DAbs::drawTheta(const Real rnd,
const Real r,
const Real t) const
{
THROW_UNLESS(std::invalid_argument, 0.0<=rnd && rnd <= 1.0);
if(rnd == 1e0)
return 2e0 * M_PI;
if(fabs(r) < CUTOFF)// r == 0e0 ?
{
throw std::invalid_argument(
(boost::format("2DAbs::drawTheta r is too small: r=%f10") % r).str());
}
if(fabs(r-a) < CUTOFF)// r == a ?
{
//when R equal a, p_int_theta is zero at any theta
throw std::invalid_argument(
(boost::format("2DAbs::drawTheta r is nealy a: r=%f10, a=%f10") % r % a).str());
}
if(t == 0e0 || D == 0e0)
return 0e0;
Real int_2pi = p_int_2pi(r, t);
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* When t is too large, int_2pi become zero and drawR returns 2pi *
* at any value of rnd. To avoid this, return rnd * theta / 2pi *
* because when t -> \infty the probability density function of theta*
* become uniform distribution *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
if(int_2pi == 0e0)
{
std::cout << dump();
std::cout << "Warning: t is too large. t = " << t << std::endl;
}
p_theta_params params = {this, t, r, rnd * int_2pi};
gsl_function F =
{
reinterpret_cast<double (*)(double, void*)>(&p_theta_F), ¶ms
};
const Real low(0e0);
const Real high(2e0 * M_PI);
const gsl_root_fsolver_type* solverType(gsl_root_fsolver_brent);
gsl_root_fsolver* solver(gsl_root_fsolver_alloc(solverType));
const Real theta(findRoot(F, solver, low, high, 1e-18, 1e-12,
"GreensFunction2DAbsSym::drawTheta"));
gsl_root_fsolver_free(solver);
return theta;
}
const Real GreensFunction2DAbs::drawTime(const Real rnd) const
{
THROW_UNLESS(std::invalid_argument, 0.0<=rnd && rnd <= 1.0);
if(D == 0e0 || a == std::numeric_limits<Real>::infinity() || rnd == 1e0)
return std::numeric_limits<Real>::infinity();
if(a == r0 || rnd == 0e0)
return 0e0;
p_survival_params params = {this, rnd};
gsl_function F =
{
reinterpret_cast<double (*)(double, void*)>(&p_survival_F), ¶ms
};
// this is not so accurate because
// initial position is not the center of this system.
const Real t_guess(a * a * 0.25 / D);
Real value(GSL_FN_EVAL(&F, t_guess));
Real low(t_guess);
Real high(t_guess);
// to determine high and low border
if(value < 0.0)
{
do
{
high *= 1e1;
value = GSL_FN_EVAL(&F, high);
if(fabs(high) > t_guess * 1e6)
throw std::invalid_argument("could not adjust higher border");
}
while(value <= 0e0);
}
else
{
Real value_prev = value;
do
{
low *= 1e-1;
value = GSL_FN_EVAL(&F, low);
if(fabs(low) <= t_guess * 1e-6 || fabs(value - value_prev) < CUTOFF)
throw std::invalid_argument("could not adjust lower border");
value_prev = value;
}
while(value >= 0e0);
}
//find the root
const gsl_root_fsolver_type* solverType(gsl_root_fsolver_brent);
gsl_root_fsolver* solver(gsl_root_fsolver_alloc(solverType));
const Real t(findRoot(F, solver, low, high, 1e-18, 1e-12,
"GreensFunction2DAbs::drawTime"));
gsl_root_fsolver_free(solver);
return t;
}
void mergeClusters(int e1,int e2)
{
int root1 = findRoot(e1);
int root2 = findRoot(e2);
if(root1 > root2)
{
clusters[root2] = root1;
size[root1]+=size[root2];
}
else
{
clusters[root1] = root2;
size[root2]+=size[root1];
}
nClusters--;
}
void DisjointSet::setUnion(const uint elementA, const uint elementB) {
int rootA, rootB;
rootA = findRoot(elementA);
rootB = findRoot(elementB);
if ( (rootA == -1) || (rootB == -1) || (rootA == rootB) )
return;
if (m_sets[rootA] <= m_sets[rootB]) {
m_sets[rootA] += m_sets[rootB];
m_sets[rootB] = rootA;
}
else {
m_sets[rootB] += m_sets[rootA];
m_sets[rootA] = rootB;
}
}
void unite(int x, int y) {
x = findRoot( x );
y = findRoot( y );
if(x == y) return;
if( depth[ x ] < depth[ y ]) {
root[ x ] = y;
} else {
root[ y ] = x;
}
if(depth[ x ] == depth[ y ]) depth[ y ]++;
};
bool check(vector<vector<int>>& edges, int omitIndex) {
memset(parent, -1, sizeof(parent));
memset(treeParent, -1, sizeof(treeParent));
for (int i = 0; i < edges.size(); ++i) {
if (i == omitIndex) continue;
auto& v = edges[i];
int root1 = findRoot(v[0]);
int root2 = findRoot(v[1]);
if (root1 == root2) {
return false;
}
parent[root1] = root2;
if (treeParent[v[1]] != -1) {
return false;
}
treeParent[v[1]] = v[0];
}
return true;
}
int findRoot(int x){
if (Tree[x]==-1)
{
return x;
}else{
int tmp=findRoot(Tree[x]);
Tree[x]=tmp;
return tmp;
}
}
void Tree::print(ostream& out, string mode) {
try {
int root = findRoot();
printBranch(root, out, mode);
out << ";" << endl;
}
catch(exception& e) {
m->errorOut(e, "Tree", "print");
exit(1);
}
}
void lookForLeafs(MonomialIterator w,MonomialIterator e) {
TrieLocation L;
Variable v;
bool go = true;
while(w!=e&&go) {
v = *w;
if(findRoot(L,v)) {
++w;
} else {
go = lookForLeafs(L,w,e);
};
};
};
int countComponents(int n, vector<pair<int, int>>& edges) {
// start coding at 1:50
// create nodes vec
vector<int> roots;
for (int i = 0; i < n; i++) roots.push_back(i);
// traverse edges
for (auto e : edges) {
int i = findRoot(e.first, roots);
int j = findRoot(e.second, roots);
roots[j] = i;
}
// count roots
int ans = 0;
for (int i = 0; i < n; i++) {
if (roots[i] == i) ans += 1;
}
// return
return ans;
}
int countComponents(int n, vector<pair<int, int> >& edges) {
root = vector<int>(n, -1);
int size = edges.size();
//int count = n;
for(int i = 0; i < size; ++i)
{
int u = edges[i].first;
int v = edges[i].second;
int uroot = findRoot(u);
int vroot = findRoot(v);
if(uroot != vroot)
{
//--count;
unionSet(uroot, u, vroot, v);
}
}
int count = 0;
for (int i = 0; i < n; i++) {
if (findRoot(i) == i)
count++;
}
//return count;
return count;
}
TreeNode *buildBinaryTree(int beginIn, int beginPost, int len){
if(len <= 0){
return NULL;
}
TreeNode *root = new TreeNode(post[beginPost + len - 1]);
int rootPos = findRoot(post[beginPost + len - 1], beginIn, len);
if(rootPos == -1){
return NULL;
}
int newLenLeft = rootPos;
int newLenRight = len - newLenLeft - 1;
root->left = buildBinaryTree(beginIn, beginPost, newLenLeft);
root->right = buildBinaryTree(beginIn + rootPos + 1, beginPost + newLenLeft, newLenRight);
return root;
}
void UniformVector::associate() {
Uniform::associate();
// Doesn't have link
if (!hasLink())
return;
// Find the link
transformable = Scout<Transformable>::search(findRoot(this), getLink());
if (transformable == NULL) {
NodeException e(tag);
e << "[UniformVector] Could not find node '" << getLink() << "'.";
throw e;
}
}
TreeNode *buildBinaryTree(int beginIn, int beginPre, int len){
if(len <= 0){
return NULL;
}
int rootValue = pre[beginPre];
TreeNode *root = new TreeNode(rootValue);
int rootPos = findRoot(rootValue, beginIn, len);
if(rootPos == -1){
return NULL;
}
int newLenLeft = rootPos;
int newLenRight = len - newLenLeft - 1;
root->left = buildBinaryTree(beginIn, beginPre + 1, newLenLeft);
root->right = buildBinaryTree(beginIn + newLenLeft + 1, beginPre + newLenLeft + 1, newLenRight);
return root;
}
Skeleton
Skeletonize::getSkeleton() {
UTIL_TIME_METHOD;
findBoundaryNodes();
initializeEdgeMap();
findRoot();
for (int i = 0; i < _parameters.maxNumSegments; ++i) {
if (!extractLongestSegment()) break;
}
return parseVolumeSkeleton();
}
void unionWith(ptr_tag<CDA_ComputationTarget> b)
{
findRoot();
b->findRoot();
if (parent == b->parent)
return;
if (parent->rank > b->parent->rank)
b->parent->parent = parent;
else if (b->parent->rank > parent->rank)
parent->parent = b->parent;
else
{
b->parent->parent = parent;
parent->rank++;
}
}
int DisjointSet::findRoot(const uint element) {
int max, min;
max = m_sets.size() - 1;
min = 0;
if ( (element > max) || (element < min) ) {
return -1;
}
if (m_sets[element] < 0)
return element;
// Flattens the 'tree'
m_sets[element] = findRoot(m_sets[element]);
return m_sets[element];
}
void drawFunctions()
{
const float STEP = graphWin.findSmartStepX();
glPointSize(2.0f);
//Draw selected (f(x))
for(float x=graphWin.xMin(); x<graphWin.xMax(); x+=STEP)
graphWin.plot(x, f(x), 1.0f,0.5f,0.0f);
//Draw f(x) = x
for(float x=graphWin.xMin(); x<graphWin.xMax(); x+=STEP)
graphWin.plot( x, x, 0.5f,0.5f,0.5f);
//Draw g(x)
for(float x=graphWin.xMin()+STEP; x<graphWin.xMax(); x+=STEP)
graphWin.plot(x, g(x), 1.0f,0.5f,1.0f);
clear();
printHeader();
std::cout << "x est compris dans l'ensemble [" << graphWin.xMin() << ";" << graphWin.xMax() << "[" << std::endl;
std::cout << "y est compris dans l'ensemble [" << graphWin.yMin() << ";" << graphWin.yMax() << "[" << std::endl << std::endl;
std::cout << "Information graphique : " << std::endl
<< "- Fonction choisie (f(x)) en orange" << std::endl
<< "- Fonction h(x) = x, en gris" << std::endl
<< "- Fonction g(x) = x + l*f(x), l = 1, en rose" << std::endl
<< "- Les axes x,y en bleu " << std::endl
<< "- Les vecteurs unitaires en rouge " << std::endl
<< "- Les solutions de la fonction en vert" << std::endl << std::endl;
vector<long double> solutions = findRoot();
std::cout << "Solutions : " << std::endl;
glColor3f(0.0f, 1.0f, 0.0f);
glPointSize(10);
//Draw solutions
for(unsigned int i = 0;i < solutions.size(); ++i)
{
std::cout << "[" << i << "] -> " << static_cast<double>(solutions[i]) << std::endl;
glBegin( GL_POINTS );
glVertex3d(solutions[i], 0, 0.0);
glEnd();
}
}
// Calculates the roots of tan(x*a)=-x/h
Real
GreensFunction1DRadAbs::root_n(int n) const
{
const Real L( this->geta()-this->getsigma() );
const Real h( (this->getk()+this->getv()/2.0) / this->getD() );
// the drift v also comes into this constant, h=(k+v/2)/D
Real upper, lower;
if ( h*L < 1 )
{
// 1E-10 to make sure that he doesn't include the transition
lower = (n-1)*M_PI + 1E-10;
// (asymptotic) from infinity to -infinity
upper = n *M_PI - 1E-10;
}
else
{
lower = (n-1)*M_PI + M_PI_2 + 1E-10;
upper = n *M_PI + M_PI_2 - 1E-10;
}
gsl_function F;
struct tan_f_params params = { L, h };
F.function = &GreensFunction1DRadAbs::tan_f;
F.params = ¶ms;
// define a new solver type brent
const gsl_root_fsolver_type* solverType( gsl_root_fsolver_brent );
// make a new solver instance
// TODO: incl typecast?
gsl_root_fsolver* solver( gsl_root_fsolver_alloc( solverType ) );
// get the root = run the rootsolver
const Real root( findRoot( F, solver, lower, upper, 1.0*EPSILON, EPSILON,
"GreensFunction1DRadAbs::root_tan" ) );
gsl_root_fsolver_free( solver );
return root/L;
// This rescaling is important, because the function tan_f is used to solve for
// tan(x)+x/h/L=0, whereas we actually need tan(x*L)+x/h=0, So if x solves the
// subsidiary equation, x/L solves the original one.
}
// This prints out the tree in Newick form.
void Tree::createNewickFile(string f) {
try {
int root = findRoot();
filename = f;
m->openOutputFile(filename, out);
printBranch(root, out, "branch");
// you are at the end of the tree
out << ";" << endl;
out.close();
}
catch(exception& e) {
m->errorOut(e, "Tree", "createNewickFile");
exit(1);
}
}
/**
* Solves qubic equation ax^3 + bx^2 + cx + d = 0
* @param roots roots found
* @return number of roots (should be 1 or 3)
*/
int solve(FT* roots)
{
double q = (mA < 0) ? -1 : 1;
mA *= q;
mB *= q;
mC *= q;
mD *= q;
FT D = mB * mB - 3. * mA * mC;
FT T = BNBMAX((BNBABS(mB) + BNBABS(mC) + BNBABS(mD)) / BNBABS(mA), 1.);
int nr;
if(D <= 0.) {
nr = 1;
findRoot(-T, T, roots);
} else if(D > 0.) {
FT Q = sqrt(D);
FT x1 = (-mB - Q) / (3. * mA);
FT x2 = (-mB + Q) / (3. * mA);
FT f1 = f(x1);
FT f2 = f(x2);
if(f1 < 0.) {
nr = 1;
findRoot(x2, T, roots);
} else if(f1 == 0.) {
roots[0] = x1;
if(f2 == 0.) {
nr = 1;
} else {
nr = 2;
findRoot(x2, T, roots + 1);
}
} else if(f1 > 0.) {
findRoot(-T, x1, roots);
if(f2 > 0.) {
nr = 1;
} else if(f2 == 0.) {
nr = 2;
roots[1] = x2;
} else if(f2 < 0.) {
nr = 3;
findRoot(x1, x2, roots + 1);
findRoot(x2, T, roots + 2);
}
}
}
mA *= q;
mB *= q;
mC *= q;
mD *= q;
return nr;
}
//根据数组list，生成近似最有查找树T
void createSOSTree(BiTNode **T, node* list, int start, int end)
{
/*
伪代码：
使用递归
结束条件：start>end
root=findRoot(list,start,end)
*T=malloc();
T->value=list[root];
T->number=root;
createSOSTree(T->lchild,list,start,root-1);
createSOSTree(T->rchild,list,root+1,end);
*/
if(start>end) return;
int root = findRoot(list,start,end);
*T = (BiTNode*) malloc(sizeof(BiTNode));
(*T)->value = list[root];
(*T)->number= root;
createSOSTree(&((*T)->lchild),list,start,root-1);
createSOSTree(&((*T)->rchild),list,root+1,end);
}
/*!
** @brief Lookup a DAG in the hosts.xia file
**
** @param name The name of an XIA service or host.
**
** @returns a character point to the dag on success
** @returns NULL on failure
**
*/
char *hostsLookup(const char *name) {
char line[512];
char *linend;
char *dag;
char _dag[NS_MAX_DAG_LENGTH];
// look for an hosts_xia file locally
FILE *hostsfp = fopen(strcat(findRoot(), ETC_HOSTS), "r");
int answer_found = 0;
if (hostsfp != NULL) {
while (fgets(line, 511, hostsfp) != NULL) {
linend = line+strlen(line)-1;
while (*linend == '\r' || *linend == '\n' || *linend == '\0') {
linend--;
}
*(linend+1) = '\0';
if (line[0] == '#') {
continue;
} else if (!strncmp(line, name, strlen(name))
&& line[strlen(name)] == ' ') {
strncpy(_dag, line+strlen(name)+1, strlen(line)-strlen(name)-1);
_dag[strlen(line)-strlen(name)-1] = '\0';
answer_found = 1;
}
}
fclose(hostsfp);
if (answer_found) {
dag = (char*)malloc(sizeof(_dag) + 1);
strcpy(dag, _dag);
return dag;
}
} else {
//printf("XIAResolver file error\n");
}
//printf("Name not found in ./hosts_xia\n");
return NULL;
}
// Calculates the roots of tan(aL)=-ak/h
const Real FirstPassageGreensFunction1DRad::a_n(const int n) const
{
// L=length of domain=2*a
const Real L(this->getL());
// h=k/D
const Real h(this->getk()/this->getD());
Real upper, lower;
if ( h*L < 1 )
{
// 1E-10 to make sure that he doesn't include the transition
lower = (n-1)*M_PI + 1E-10;
// (asymptotic) from infinity to -infinity
upper = n *M_PI - 1E-10;
}
else
{
lower = (n-1)*M_PI + M_PI_2 + 1E-10;
upper = n *M_PI + M_PI_2 - 1E-10;
}
gsl_function F;
struct tan_f_params params = { L, h};
F.function = &FirstPassageGreensFunction1DRad::tan_f;
F.params = ¶ms;
// define a new solver type brent
const gsl_root_fsolver_type* solverType( gsl_root_fsolver_brent );
// make a new solver instance
// incl typecast?
gsl_root_fsolver* solver( gsl_root_fsolver_alloc( solverType ) );
const Real a( findRoot( F, solver, lower, upper, 1.0*EPSILON, EPSILON,
"FirstPassageGreensFunction1DRad::root_tan" ) );
gsl_root_fsolver_free( solver );
return a;
}
bool ChrsGrid::isDeadMap()
{
//遍历每一个汉字元素
for (int x = 0; x < m_col; x++)
{
//遍历列
for (int y = 0; y < m_row; y++)
{
//存放可消除的汉字元素序列，用于系统提示
m_AnswerChrs.clear();
//从汉字元素盒子中选定一个汉字元素
auto chr = m_ChrsBox[x][y];
if (findRoot(chr))
{
return false;//找到路了，则不是死图，否则继续下一个chr
}
}
}
log ("this is a deadmap!");
return true;
}