Hey Guys!↵
========= ↵
↵
I am really so happy to share my custom Order-Statistic Tree using Red Black trees, with the Select(x, i) and Rank(x)...which allow in finding the order statistic and the rank of the key element in log(n) time...↵
↵
Now I do know that PBDS in C++ does exist, but as a challenge I built this..with great hardwork..and also took reference from CLRS which helped me in understanding the working of this data structure...↵
↵
At first I actually encountered this problem in CSES named Josephus Problem, and that could be solved using Circular Doubly Linked Lists (in O(N) time) as well, but even O(NlogN) would suffice so I thought of doing so...A pretty fun experience in building own custom stuff, apart from the STL...↵
↵
Also wanted the opinion of you guys, on how can I improve my work or further make some new functionalities to it in the future, or even build more such data structures allowing iterators like begin() and end() for the same..As far as the debugging part I have submitted the code as well just to be sure of any errors..↵
↵
CSES Josephus Problem 2 (Accepted Code) -> [...](https://pastebin.com/9HuFespD)↵
↵
Thank You So Much! ↵
↵
Have a great day ahead!!!↵
↵
Here is my Code in C++ :↵
↵
↵
~~~~~↵
//MARK:- PRACTICE↵
↵
#define len(a) (ll)a.size()↵
typedef long long ll;↵
typedef long double ld;↵
↵
bool test=false;↵
ll mod1=1e9+7;↵
ll mod2=998244353;↵
ll inf=1e10+5;↵
↵
enum colour {red, black};↵
↵
struct Node {↵
↵
ll data, size;↵
bool colour;↵
Node *parent, *left, *right;↵
};↵
↵
class RBTree {↵
↵
Node *root, *tNil;↵
↵
Node* findNode(Node *z) {↵
↵
Node *x=this->root;↵
↵
while(x!=tNil) {↵
↵
if(x->data==z->data) {↵
↵
return x;↵
} else if(z->data<x->data) {↵
↵
x=x->left;↵
} else {↵
↵
x=x->right;↵
}↵
}↵
↵
return tNil;↵
}↵
↵
Node* findMin(Node *z) {↵
↵
while(z->left!=tNil) {↵
↵
z=z->left;↵
}↵
↵
return z;↵
}↵
↵
void leftRotate(Node *x) {↵
↵
if(x->right==tNil) {↵
↵
return;↵
}↵
↵
Node *y=x->right;↵
x->right=y->left;↵
↵
if(y->left!=tNil) {↵
↵
y->left->parent=x;↵
}↵
↵
y->parent=x->parent;↵
↵
if(x->parent==tNil) {↵
↵
this->root=y;↵
} else if(x==x->parent->left) {↵
↵
x->parent->left=y;↵
} else {↵
↵
x->parent->right=y;↵
}↵
↵
y->left=x;↵
x->parent=y;↵
y->size=x->size;↵
x->size=x->left->size+x->right->size+1;↵
}↵
↵
void rightRotate(Node *y) {↵
↵
if(y->left==tNil) {↵
↵
return;↵
}↵
↵
Node *x=y->left;↵
y->left=x->right;↵
↵
if(x->right!=tNil) {↵
↵
x->right->parent=y;↵
}↵
↵
x->parent=y->parent;↵
↵
if(y->parent==tNil) {↵
↵
this->root=x;↵
} else if(y==y->parent->right) {↵
↵
y->parent->right=x;↵
} else {↵
↵
y->parent->left=x;↵
}↵
↵
x->right=y;↵
y->parent=x;↵
x->size=y->size;↵
y->size=y->left->size+y->right->size+1;↵
}↵
↵
void insertFixUp(Node *z) {↵
↵
while(z->parent->colour==red) {↵
↵
if(z->parent==z->parent->parent->left) {↵
↵
Node *y=z->parent->parent->right;↵
↵
if(y->colour==red) {↵
↵
z->parent->colour=black;↵
y->colour=black;↵
↵
if(z->parent->parent!=this->root) {↵
↵
z->parent->parent->colour=red;↵
}↵
z=z->parent->parent;↵
} else {↵
↵
if(z==z->parent->right) {↵
↵
z=z->parent;↵
leftRotate(z);↵
}↵
↵
z->parent->colour=black;↵
z->parent->parent->colour=red;↵
rightRotate(z->parent->parent);↵
}↵
} else {↵
↵
Node *y=z->parent->parent->left;↵
↵
if(y->colour==red) {↵
↵
z->parent->colour=black;↵
y->colour=black;↵
↵
if(z->parent->parent!=this->root) {↵
↵
z->parent->parent->colour=red;↵
}↵
z=z->parent->parent;↵
} else {↵
↵
if(z==z->parent->left) {↵
↵
z=z->parent;↵
rightRotate(z);↵
}↵
↵
z->parent->colour=black;↵
z->parent->parent->colour=red;↵
leftRotate(z->parent->parent);↵
}↵
}↵
}↵
}↵
↵
void insertNode(Node *z) {↵
↵
if(this->root==tNil) {↵
↵
z->colour=black;↵
this->root=z;↵
this->root->size=1;↵
return;↵
}↵
↵
Node *y=tNil, *x=this->root;↵
↵
while(x!=tNil) {↵
↵
y=x;↵
x->size++;↵
↵
if(z->data<x->data) {↵
↵
x=x->left;↵
} else {↵
↵
x=x->right;↵
}↵
}↵
↵
z->parent=y;↵
↵
if(z->data<y->data) {↵
↵
y->left=z;↵
} else {↵
↵
y->right=z;↵
}↵
↵
insertFixUp(z);↵
}↵
↵
void transplant(Node *u, Node *v) {↵
↵
if(u->parent==tNil) {↵
↵
this->root=v;↵
} else if(u==u->parent->left) {↵
↵
u->parent->left=v;↵
} else {↵
↵
u->parent->right=v;↵
}↵
v->parent=u->parent;↵
}↵
↵
void deleteFixUp(Node *x) {↵
↵
while(x!=this->root && x->colour==black) {↵
↵
if(x==x->parent->left) {↵
↵
Node *w=x->parent->right;↵
↵
if(w->colour==red) {↵
↵
w->colour=black;↵
x->parent->colour=red;↵
leftRotate(x->parent);↵
↵
w=x->parent->right;↵
}↵
↵
if(w->left->colour==black && w->right->colour==black) {↵
↵
w->colour=red;↵
x=x->parent;↵
} else {↵
↵
if(w->right->colour==black) {↵
↵
w->left->colour=black;↵
w->colour=red;↵
rightRotate(w);↵
↵
w=x->parent->right;↵
}↵
↵
w->colour=x->parent->colour;↵
x->parent->colour=red;↵
w->right->colour=black;↵
leftRotate(x->parent);↵
x=this->root;↵
}↵
} else {↵
↵
Node *w=x->parent->left;↵
↵
if(w->colour==red) {↵
↵
w->colour=black;↵
x->parent->colour=red;↵
rightRotate(x->parent);↵
↵
w=x->parent->left;↵
}↵
↵
if(w->right->colour==black && w->left->colour==black) {↵
↵
w->colour=red;↵
x=x->parent;↵
} else {↵
↵
if(w->left->colour==black) {↵
↵
w->right->colour=black;↵
w->colour=red;↵
leftRotate(w);↵
↵
w=x->parent->left;↵
}↵
↵
w->colour=x->parent->colour;↵
x->parent->colour=red;↵
w->left->colour=black;↵
rightRotate(x->parent);↵
x=this->root;↵
}↵
}↵
}↵
x->colour=black;↵
}↵
↵
void deleteNode(Node *z) {↵
↵
Node *y=z, *x;↵
bool originalColour=y->colour;↵
↵
if(z->left==tNil) {↵
↵
x=z->right;↵
transplant(z, z->right);↵
} else if(z->right==tNil) {↵
↵
x=z->left;↵
transplant(z, z->left);↵
} else {↵
↵
y=findMin(z->right);↵
originalColour=y->colour;↵
↵
x=y->right;↵
↵
if(y->parent==z) {↵
↵
x->parent=y;↵
} else {↵
↵
transplant(y, y->right);↵
y->right=z->right;↵
y->right->parent=y;↵
↵
Node *s=x->parent;↵
↵
while(s!=tNil && s!=y) {↵
↵
s->size--;↵
s=s->parent;↵
}↵
}↵
↵
transplant(z, y);↵
↵
y->left=z->left;↵
y->left->parent=y;↵
y->colour=z->colour;↵
↵
y->size=y->left->size+y->right->size+1;↵
}↵
↵
if(originalColour==black) {↵
↵
deleteFixUp(x);↵
}↵
}↵
↵
void inOrderHelper(Node *node) {↵
↵
if(node==tNil) {↵
↵
return;↵
}↵
↵
inOrderHelper(node->left);↵
↵
std::cout<<node->data<<" ";↵
↵
inOrderHelper(node->right);↵
}↵
↵
public:↵
↵
RBTree() {↵
↵
tNil=new Node();↵
tNil->colour=black;↵
tNil->size=0;↵
↵
tNil->left=tNil;↵
tNil->right=tNil;↵
tNil->parent=tNil;↵
↵
this->root=tNil;↵
}↵
↵
Node* getRoot() {↵
↵
return this->root;↵
}↵
↵
Node* find(ll key) {↵
↵
Node *z=new Node();↵
↵
z->data=key;↵
↵
return findNode(z);↵
}↵
↵
void insert(ll key) {↵
↵
Node *z=new Node();↵
z->data=key;↵
z->colour=red;↵
z->size=1;↵
↵
z->left=tNil;↵
z->right=tNil;↵
z->parent=tNil;↵
↵
insertNode(z);↵
}↵
↵
void erase(ll key) {↵
↵
Node *z=find(key);↵
↵
if(z==tNil) {↵
↵
return;↵
}↵
↵
Node *s=z->parent;↵
↵
while(s!=tNil) {↵
↵
s->size--;↵
s=s->parent;↵
}↵
↵
deleteNode(z);↵
}↵
↵
ll osSelect(Node *x, ll i) {↵
↵
ll r=x->left->size+1;↵
↵
if(i==r) {↵
↵
return x->data;↵
} else if(i<r) {↵
↵
return osSelect(x->left, i);↵
} else {↵
↵
return osSelect(x->right, i-r);↵
}↵
}↵
↵
ll osRank(Node *x) {↵
↵
ll r=x->left->size+1;↵
↵
Node *y=x;↵
↵
while(y!=this->root) {↵
↵
if(y==y->parent->right) {↵
↵
r+=y->parent->left->size+1;↵
}↵
y=y->parent;↵
}↵
↵
return r;↵
}↵
↵
void inOrder() {↵
↵
inOrderHelper(this->root);↵
}↵
};↵
↵
~~~~~↵
========= ↵
↵
I am really so happy to share my custom Order-Statistic Tree using Red Black trees, with the Select(x, i) and Rank(x)...which allow in finding the order statistic and the rank of the key element in log(n) time...↵
↵
Now I do know that PBDS in C++ does exist, but as a challenge I built this..with great hardwork..and also took reference from CLRS which helped me in understanding the working of this data structure...↵
↵
At first I actually encountered this problem in CSES named Josephus Problem, and that could be solved using Circular Doubly Linked Lists (in O(N) time) as well, but even O(NlogN) would suffice so I thought of doing so...A pretty fun experience in building own custom stuff, apart from the STL...↵
↵
Also wanted the opinion of you guys, on how can I improve my work or further make some new functionalities to it in the future, or even build more such data structures allowing iterators like begin() and end() for the same..As far as the debugging part I have submitted the code as well just to be sure of any errors..↵
↵
CSES Josephus Problem 2 (Accepted Code) -> [...](https://pastebin.com/9HuFespD)↵
↵
Thank You So Much! ↵
↵
Have a great day ahead!!!↵
↵
Here is my Code in C++ :↵
↵
↵
~~~~~↵
//MARK:- PRACTICE↵
↵
#define len(a) (ll)a.size()↵
typedef long long ll;↵
typedef long double ld;↵
↵
bool test=false;↵
ll mod1=1e9+7;↵
ll mod2=998244353;↵
ll inf=1e10+5;↵
↵
enum colour {red, black};↵
↵
struct Node {↵
↵
ll data, size;↵
bool colour;↵
Node *parent, *left, *right;↵
};↵
↵
class RBTree {↵
↵
Node *root, *tNil;↵
↵
Node* findNode(Node *z) {↵
↵
Node *x=this->root;↵
↵
while(x!=tNil) {↵
↵
if(x->data==z->data) {↵
↵
return x;↵
} else if(z->data<x->data) {↵
↵
x=x->left;↵
} else {↵
↵
x=x->right;↵
}↵
}↵
↵
return tNil;↵
}↵
↵
Node* findMin(Node *z) {↵
↵
while(z->left!=tNil) {↵
↵
z=z->left;↵
}↵
↵
return z;↵
}↵
↵
void leftRotate(Node *x) {↵
↵
if(x->right==tNil) {↵
↵
return;↵
}↵
↵
Node *y=x->right;↵
x->right=y->left;↵
↵
if(y->left!=tNil) {↵
↵
y->left->parent=x;↵
}↵
↵
y->parent=x->parent;↵
↵
if(x->parent==tNil) {↵
↵
this->root=y;↵
} else if(x==x->parent->left) {↵
↵
x->parent->left=y;↵
} else {↵
↵
x->parent->right=y;↵
}↵
↵
y->left=x;↵
x->parent=y;↵
y->size=x->size;↵
x->size=x->left->size+x->right->size+1;↵
}↵
↵
void rightRotate(Node *y) {↵
↵
if(y->left==tNil) {↵
↵
return;↵
}↵
↵
Node *x=y->left;↵
y->left=x->right;↵
↵
if(x->right!=tNil) {↵
↵
x->right->parent=y;↵
}↵
↵
x->parent=y->parent;↵
↵
if(y->parent==tNil) {↵
↵
this->root=x;↵
} else if(y==y->parent->right) {↵
↵
y->parent->right=x;↵
} else {↵
↵
y->parent->left=x;↵
}↵
↵
x->right=y;↵
y->parent=x;↵
x->size=y->size;↵
y->size=y->left->size+y->right->size+1;↵
}↵
↵
void insertFixUp(Node *z) {↵
↵
while(z->parent->colour==red) {↵
↵
if(z->parent==z->parent->parent->left) {↵
↵
Node *y=z->parent->parent->right;↵
↵
if(y->colour==red) {↵
↵
z->parent->colour=black;↵
y->colour=black;↵
↵
if(z->parent->parent!=this->root) {↵
↵
z->parent->parent->colour=red;↵
}↵
z=z->parent->parent;↵
} else {↵
↵
if(z==z->parent->right) {↵
↵
z=z->parent;↵
leftRotate(z);↵
}↵
↵
z->parent->colour=black;↵
z->parent->parent->colour=red;↵
rightRotate(z->parent->parent);↵
}↵
} else {↵
↵
Node *y=z->parent->parent->left;↵
↵
if(y->colour==red) {↵
↵
z->parent->colour=black;↵
y->colour=black;↵
↵
if(z->parent->parent!=this->root) {↵
↵
z->parent->parent->colour=red;↵
}↵
z=z->parent->parent;↵
} else {↵
↵
if(z==z->parent->left) {↵
↵
z=z->parent;↵
rightRotate(z);↵
}↵
↵
z->parent->colour=black;↵
z->parent->parent->colour=red;↵
leftRotate(z->parent->parent);↵
}↵
}↵
}↵
}↵
↵
void insertNode(Node *z) {↵
↵
if(this->root==tNil) {↵
↵
z->colour=black;↵
this->root=z;↵
this->root->size=1;↵
return;↵
}↵
↵
Node *y=tNil, *x=this->root;↵
↵
while(x!=tNil) {↵
↵
y=x;↵
x->size++;↵
↵
if(z->data<x->data) {↵
↵
x=x->left;↵
} else {↵
↵
x=x->right;↵
}↵
}↵
↵
z->parent=y;↵
↵
if(z->data<y->data) {↵
↵
y->left=z;↵
} else {↵
↵
y->right=z;↵
}↵
↵
insertFixUp(z);↵
}↵
↵
void transplant(Node *u, Node *v) {↵
↵
if(u->parent==tNil) {↵
↵
this->root=v;↵
} else if(u==u->parent->left) {↵
↵
u->parent->left=v;↵
} else {↵
↵
u->parent->right=v;↵
}↵
v->parent=u->parent;↵
}↵
↵
void deleteFixUp(Node *x) {↵
↵
while(x!=this->root && x->colour==black) {↵
↵
if(x==x->parent->left) {↵
↵
Node *w=x->parent->right;↵
↵
if(w->colour==red) {↵
↵
w->colour=black;↵
x->parent->colour=red;↵
leftRotate(x->parent);↵
↵
w=x->parent->right;↵
}↵
↵
if(w->left->colour==black && w->right->colour==black) {↵
↵
w->colour=red;↵
x=x->parent;↵
} else {↵
↵
if(w->right->colour==black) {↵
↵
w->left->colour=black;↵
w->colour=red;↵
rightRotate(w);↵
↵
w=x->parent->right;↵
}↵
↵
w->colour=x->parent->colour;↵
x->parent->colour=red;↵
w->right->colour=black;↵
leftRotate(x->parent);↵
x=this->root;↵
}↵
} else {↵
↵
Node *w=x->parent->left;↵
↵
if(w->colour==red) {↵
↵
w->colour=black;↵
x->parent->colour=red;↵
rightRotate(x->parent);↵
↵
w=x->parent->left;↵
}↵
↵
if(w->right->colour==black && w->left->colour==black) {↵
↵
w->colour=red;↵
x=x->parent;↵
} else {↵
↵
if(w->left->colour==black) {↵
↵
w->right->colour=black;↵
w->colour=red;↵
leftRotate(w);↵
↵
w=x->parent->left;↵
}↵
↵
w->colour=x->parent->colour;↵
x->parent->colour=red;↵
w->left->colour=black;↵
rightRotate(x->parent);↵
x=this->root;↵
}↵
}↵
}↵
x->colour=black;↵
}↵
↵
void deleteNode(Node *z) {↵
↵
Node *y=z, *x;↵
bool originalColour=y->colour;↵
↵
if(z->left==tNil) {↵
↵
x=z->right;↵
transplant(z, z->right);↵
} else if(z->right==tNil) {↵
↵
x=z->left;↵
transplant(z, z->left);↵
} else {↵
↵
y=findMin(z->right);↵
originalColour=y->colour;↵
↵
x=y->right;↵
↵
if(y->parent==z) {↵
↵
x->parent=y;↵
} else {↵
↵
transplant(y, y->right);↵
y->right=z->right;↵
y->right->parent=y;↵
↵
Node *s=x->parent;↵
↵
while(s!=tNil && s!=y) {↵
↵
s->size--;↵
s=s->parent;↵
}↵
}↵
↵
transplant(z, y);↵
↵
y->left=z->left;↵
y->left->parent=y;↵
y->colour=z->colour;↵
↵
y->size=y->left->size+y->right->size+1;↵
}↵
↵
if(originalColour==black) {↵
↵
deleteFixUp(x);↵
}↵
}↵
↵
void inOrderHelper(Node *node) {↵
↵
if(node==tNil) {↵
↵
return;↵
}↵
↵
inOrderHelper(node->left);↵
↵
std::cout<<node->data<<" ";↵
↵
inOrderHelper(node->right);↵
}↵
↵
public:↵
↵
RBTree() {↵
↵
tNil=new Node();↵
tNil->colour=black;↵
tNil->size=0;↵
↵
tNil->left=tNil;↵
tNil->right=tNil;↵
tNil->parent=tNil;↵
↵
this->root=tNil;↵
}↵
↵
Node* getRoot() {↵
↵
return this->root;↵
}↵
↵
Node* find(ll key) {↵
↵
Node *z=new Node();↵
↵
z->data=key;↵
↵
return findNode(z);↵
}↵
↵
void insert(ll key) {↵
↵
Node *z=new Node();↵
z->data=key;↵
z->colour=red;↵
z->size=1;↵
↵
z->left=tNil;↵
z->right=tNil;↵
z->parent=tNil;↵
↵
insertNode(z);↵
}↵
↵
void erase(ll key) {↵
↵
Node *z=find(key);↵
↵
if(z==tNil) {↵
↵
return;↵
}↵
↵
Node *s=z->parent;↵
↵
while(s!=tNil) {↵
↵
s->size--;↵
s=s->parent;↵
}↵
↵
deleteNode(z);↵
}↵
↵
ll osSelect(Node *x, ll i) {↵
↵
ll r=x->left->size+1;↵
↵
if(i==r) {↵
↵
return x->data;↵
} else if(i<r) {↵
↵
return osSelect(x->left, i);↵
} else {↵
↵
return osSelect(x->right, i-r);↵
}↵
}↵
↵
ll osRank(Node *x) {↵
↵
ll r=x->left->size+1;↵
↵
Node *y=x;↵
↵
while(y!=this->root) {↵
↵
if(y==y->parent->right) {↵
↵
r+=y->parent->left->size+1;↵
}↵
y=y->parent;↵
}↵
↵
return r;↵
}↵
↵
void inOrder() {↵
↵
inOrderHelper(this->root);↵
}↵
};↵
↵
~~~~~↵
