* Ufds: Union-Find Disjoint Set :cpp:datastructure:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Write a minimal Ufds class with vector parent, constructor initializing parents to self
** Back
#+begin_src c++
#include <vector>
#include <numeric>

class Ufds {
private:
  std::vector<int> parent;
public:
  Ufds(int n) : parent(n) {
    std::iota(parent.begin(), parent.end(), 0);
  }
};
#+end_src

* Ufds find() with path compression :cpp:datastructure:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Write the ~find()~ method for Ufds with path compression
** Back
#+begin_src c++
int find(int x) {
    if (parent[x] != x) {
        parent[x] = find(parent[x]);
    }
    return parent[x];
}
#+end_src

* Concise Ufds find() :cpp:datastructure:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct? What does it do?
#+begin_src c++
int find(int x) {
    if (parent[x] == x) return x;
    return parent[x] = find(parent[x]);
}
#+end_src
** Back
Yes, correct and equivalent to the longer version.

- Base case: if ~x~ is its own parent, return ~x~
- Recursive case: find root of parent, then assign and return

The assignment ~parent[x] = find(parent[x])~ returns the result while compressing the path.

* Ufds constructor: initializer list vs body :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What is the difference between these two Ufds constructors?
#+begin_src c++
// Initializer list
Ufds(int n) : parent(n) {
  std::iota(parent.begin(), parent.end(), 0);
}

// Body style
Ufds(int n) {
  parent.resize(n);
  std::iota(parent.begin(), parent.end(), 0);
}
#+end_src
** Back
Initializer list: direct constructs ~parent~ with size ~n~ (one allocation)

Body style: default constructs ~parent~, then resize (potential double allocation)

Both produce same result, initializer list is more efficient.

* What does std::vector::resize do? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What does ~resize(n)~ do on a ~std::vector<int>~?
** Back
Resizes the vector to have ~n~ elements:

- If ~n~ > current size: adds elements (value-initialized, usually 0)
- If ~n~ < current size: truncates the vector
- Reallocates if capacity < n

#+begin_src c++
std::vector<int> v;
v.resize(5);  // v = {0, 0, 0, 0, 0}
#+end_src

* Ufds destructor: when to omit :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Should Ufds have a destructor? ~Ufds() {}~ vs ~Ufds() = default~
** Back
Omit entirely if only using ~std::vector~ (auto-cleanup)

If you must write one, prefer ~= default~ to explicitly show intent

Empty ~{}~ works but ~= default~ is clearer intent for future maintenance

* Correct Ufds constructor: is this correct? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct?
#+begin_src c++
Ufds(int n) {
  p.resize(n);
  std::iota(p.begin(), p.end(), 0);
}
#+end_src
** Back
Yes, correct. This is the body-style initialization.

One potential issue: ~p~ is default-constructed first, then ~resize~ may reallocate.

For efficiency, prefer initializer list: ~Ufds(int n) : p(n)~

* Incorrect Ufds constructor: correct or wrong? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct?
#+begin_src c++
std::vector<int> p;
Ufds(int n) {
  p = new std::vector<int>(n);
}
#+end_src
** Back
Wrong.

~new std::vector<int>(n)~ returns a ~vector<int>*~ (pointer), but ~p~ is a ~vector<int>~ (not a pointer).

Can't assign a pointer to a vector.

* What does new return? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What does ~new Type~ return? And ~new Type[n]~?
** Back
~new Type~ returns a pointer to that type: ~Type*~
~new Type[n]~ returns a pointer to an array: ~Type*~

#+begin_src c++
int* p1 = new int;      // single int
int* p2 = new int[10];  // array of 10 ints
#+end_src

* What does delete do? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What does ~delete~ do? ~delete[]~?
** Back
~delete~ frees a single object allocated with ~new~
~delete[]~ frees an array allocated with ~new[]~

#+begin_src c++
int* p1 = new int;
int* p2 = new int[10];
delete p1;   // free single object
delete[] p2; // free array
#+end_src

Mismatching ~delete~ with ~new[]~ causes undefined behavior.

* Is this correct Ufds with C-style array? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct?
#+begin_src c++
class Ufds {
private:
  int* parent;
public:
  Ufds(int n) : parent(new int[n]) {}
  ~Ufds() { delete[] parent; }
};
#+end_src
** Back
Correct. This manually manages the heap-allocated array.

- ~new int[n]~ allocates array of ~n~ ints on heap
- ~delete[] parent~ in destructor frees it

This works but requires manual cleanup — error prone compared to ~std::vector~.

* Equivalent std::array version: correct or wrong? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct?
#+begin_src c++
#include <array>
#include <numeric>

class Ufds {
private:
  std::array<int, 10> parent;
public:
  Ufds() {
    std::iota(parent.begin(), parent.end(), 0);
  }
};
#+end_src
** Back
Correct for compile-time fixed size.

But size ~10~ is hardcoded — not parameterized.

~std::array<T, N>~ requires ~N~ be a compile-time constant.

For runtime size, must use ~std::vector~.

* std::array vs vector vs C-style array :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Compare ~std::array<T, N>~, ~std::vector<T>~, and ~T*~ for Ufds parent array
** Back
| Type             | Size         | Cleanup           | Use when                   |
|------------------+--------------+-------------------+----------------------------|
| ~std::array<T, N>~ | compile-time | automatic         | size known at compile time |
| ~std::vector<T>~   | runtime      | automatic         | size known at runtime      |
| ~T* p = new T[n]~  | runtime      | manual (~delete[]~) | legacy code only           |

* Vector vs Array: is vector backed by array? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is ~std::vector~ backed by an array? How does it support variable length?
** Back
Yes, ~std::vector~ allocates a contiguous memory block (like a heap array).

Typical implementation: three pointers
- ~start~ — pointer to data
- ~finish~ — pointer to last element
- ~end_of_storage~ — pointer to end of allocated capacity

#+begin_src c++
vector<int> v(5);
v.push_back(1);  // may trigger reallocation if capacity exceeded
#+end_src

When capacity is exceeded, vector: allocates larger block, copies elements, deallocates old block.

* Vector size vs capacity :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What is the difference between ~size()~ and ~capacity()~ in ~std::vector~?
** Back
- ~size()~ — number of actual elements stored
- ~capacity()~ — allocated storage space

#+begin_src c++
std::vector<int> v(3);  // size=3, capacity=3
v.push_back(1);        // size=4, capacity may be >=4
v.push_back(1);        // size=5, capacity may be >=5
#+end_src

~reserve(n)~ pre-allocates capacity without resizing.

* Comparison: which Ufds storage to use? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
When would you choose ~std::array~, ~std::vector~, or ~T* new~ for Ufds parent array?
** Back
~std::array<T, N>~ — only if N is known at compile time

~std::vector<T>~ — if size is determined at runtime (typical Ufds case)

~T* new T[n]~ — legacy code only; ~vector~ is safer and equivalent performance

For Ufds: ~std::vector~ is the idiomatic choice because size is runtime-determined.

* C-style array key properties :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What are key properties of C-style arrays (raw arrays)?
** Back
#+begin_src c++
int arr[5];         // fixed size, stack-allocated
int* p = new int[n]; // dynamic size, heap-allocated
#+end_src

- Decay to pointer on function call (lose size info)
- No bounds checking
- ~sizeof(arr)~ gives bytes, not element count
- Must manage lifetime manually for heap arrays

C-style arrays in C++ are generally avoided in favor of ~std::array~/~std::vector~.

* std::iota for Ufds initialization :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
How to use ~std::iota~ to initialize Ufds parent array to ~[0, 1, 2, ..., n-1]~
** Back
#+begin_src c++
#include <numeric>

std::vector<int> parent(n);
std::iota(parent.begin(), parent.end(), 0);
#+end_src

~iota~ fills the range with consecutive values starting from given start value

* Path compression in find() :cpp:datastructure:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What does "path compression" mean in ~find()~?
** Back
After finding the root, point each visited node directly to the root:

#+begin_src c++
parent[x] = find(parent[x]);  // compresses path
#+end_src

This flattens the tree structure, making future ~find()~ calls O(α(n)) ≈ O(1)

* Original Ufds mistakes: is this correct? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
Is this correct?
#+begin_src c++
class Udfs {
  int parent[];
  vector<int> p;
public:
  Ufds(int n) {
    p = new vector<int>;
  }
  ~Ufds() {
    p ? free p;
  }
};
#+end_src
** Back
Wrong. Multiple errors:

1. ~int parent[]~ — illegal incomplete array type

2. ~Ufds(int n)~ constructor but class is ~Udfs~ (typo)

3. ~p = new vector<int>~ — can't assign pointer to vector

4. ~free p~ — can't free a vector, and ~p~ is not a pointer

5. ~Ufds~ destructor but class is ~Udfs~ (typo)

* Heap allocation: what and why? :cpp:cpp:
:PROPERTIES:
:ANKI_NOTE_TYPE: Basic
:END:
** Front
What does "heap allocated" mean? Why use it?
** Back
Heap allocation with ~new~ lives until ~delete~ is called or program ends.

Stack allocation (local variables) is自动 freed when out of scope.

#+begin_src c++
int arr[10];           // stack — freed when function returns
int* p = new int[10]; // heap — lives until delete[]
#+end_src

Heap needed when: size unknown at compile time, or object must outlive scope.