Sets & Multisets

 

1. What is a Set?  

Definition:
Set ek aisa well-defined collection of distinct elements hai, jisme koi bhi element repeat nahi hota. Yani har element unique hota hai aur ek hi baar set me appear hota hai.

Explanation:

  • Set ka order important nahi hota, matlab {1, 2, 3} aur {3, 2, 1} same set hai.

  • Elements kisi bhi type ke ho sakte hain: numbers, alphabets, objects, ya even strings.

  • Set me duplicate elements automatically remove ho jaate hain.

Example:

  • Set of numbers: {1, 2, 3, 4}

  • Set of alphabets: {'a', 'b', 'c'}

  • Set of strings: {"apple", "banana", "orange"}

2. Multiset Kya Hai? (Definition + Explanation)

Definition:
Multiset ek collection hai jisme elements repeat ho sakte hain. Matlab ek element ek se zyada baar appear ho sakta hai.

Explanation:

  • Order abhi bhi important nahi hota.

  • Duplicate elements allow kiye jaate hain.

  • Multiset ka size total elements count karta hai including duplicates.

Example:

  • Multiset of numbers: {1, 2, 2, 3, 3, 3}

  • Multiset of alphabets: {'a', 'a', 'b', 'b', 'b', 'c'}

3. Set ke Operations

  • Union (∪): Dono sets ke saare unique elements ka combination.

    • Example: {1,2} ∪ {2,3} = {1,2,3}

  • Intersection (∩): Dono sets me common elements.

    • Example: {1,2} ∩ {2,3} = {2}

  • Difference (-): Pehle set me jo elements hai aur dusre me nahi hai.

    • Example: {1,2,3} - {2,3,4} = {1}

  • Subset (⊆): Agar saare elements ek set ke dusre set me hain.

    • Example: {1,2} ⊆ {1,2,3} → True

  • Complement: Ek universal set ke hisaab se ek set ke bahar ke elements.

4. Multiset ke Operations

  • Union: Sab elements including duplicates.

  • Intersection: Minimum count of each common element.

  • Addition of elements: Duplicate allowed.

  • Removal of elements: Ek ya sab duplicates remove kar sakte hain.

5. Difference Between Set and Multiset

  • Set me elements unique hote hain, Multiset me duplicates allowed hote hain.

  • Set ka size = unique elements count, Multiset ka size = total elements count including duplicates.

  • Set ke operations simple hote hain, Multiset operations duplicates ke count ke hisaab se hote hain.

6. Use Cases

  • Set: Removing duplicates, membership testing, mathematical operations, fast lookup.

  • Multiset: Counting frequencies, bag of words in NLP, handling duplicate records, inventory management.

    ccplusplus.com: how set and multiset work c++

     

Conclusion:
Sets aur Multisets programming aur mathematics me fundamental concepts hain. Set se duplicate avoid kar sakte hain, aur Multiset se duplicate elements ka counting manage hota hai. Inhe samajhna important hai efficient algorithms aur data handling ke liye.


 

https://amulestack.vercel.app/ 

Comments

Post a Comment

Popular posts from this blog

Data Abstraction

Image
What is Data Abstraction? Data Abstraction ka matlab hota hai: “Sirf zaruri cheez dikhana, aur jo andar ki complex working hai usse chhupa dena.” Programming me hum user ko sirf “What to do” dikhate hain aur “How to do it” chhupa lete hain. Isse system simple, secure aur easy-to-use ban jaata hai.     Real-Life Example: TV Remote TV Remote abstraction ka perfect example hai. Aap remote me bas Volume Up , Channel Change , Power jaisa button dabate ho. Aapko nahi pata hota ki andar circuit kaise signal create karta hai, TV tak kaise pahuchta hai, software usse kaise process karta hai. Aapko sirf zaruri functionality dikh rahi hai → This is Abstraction! Agar company remote ki chip badal bhi de, aapka use karna same hi rahta hai. Programming Me Data Abstraction Coding me Data Abstraction ka matlab hota hai ki hum classes aur functions ko aise design karein ki: User ko sirf use karne layak functions dikhaye dein. Un functions ke andar kya logic chal raha hai, woh poora hid...
Read more

Data Abstraction

Image
  What is Data Abstraction? Data Abstraction means showing only the important information to the user and hiding all the internal working details. In simple words: Show what to do . Hide how it works . This makes a system easy to use, clean, and less confusing.   Real-Life Example: TV Remote When you use a TV remote: You only press buttons like Volume Up, Volume Down, or Channel Change. You do not see how the signal travels inside the remote, how the chip works, or how the TV processes the signal. You only see the basic functions. The internal working is hidden. This is called Abstraction . Data Abstraction in Programming In programming, abstraction means that: The user only sees the required functions or methods. The logic inside those functions remains hidden. Example: When you call saveData(data) in a program: You only know that the data will be saved. You do not know whether it is saved using SQL, NoSQL, a file system, or something else. The internal process is hidden fro...
Read more

Data Structure Ka Parichay Aur Prakar (Introduction and Types of Data Structure)

Image
  1. Data Structure Ki Definition Data Structure ek logical aur systematic tareeka hai jisme data elements ko organize kiya jata hai taki essential operations jaise search, add aur delete efficiently kiye ja sake kam time aur memory mein. Simple Example: Ek library ko consider karo. Books (data) ko shelves (data structures) mein unke subjects ke hisaab se arrange kiya jata hai, taki jab aap koi book dhundho to turant mil jaye. 2. Data Structures Ke Prakar Data Structures mainly do categories mein divide hote hain: Primitive aur Non-Primitive . A. Primitive Data Structures Ye basic data types hote hain jo directly machine level par kaam karte hain. Programming languages inhe pre-defined provide karti hain. Integer (int): Poorn sankhyaon ko store karta hai. Example: 10, -5, 1000 Float/Double: Dashmlav sankhyaon ko store karta hai. Example: 3.14, 0.005 Character (char): Single akshar ya symbol store karta hai. Example: 'A', 'z', '9' Boolean (bo...
Read more