discrete math ppt on how to solve maths easily
- 1. NAME- RANJAN DAS STUDENT CODE- BWU/BTA/22/508 DEPT- B.TECH CSE (AIML) SEC – I SEM- 4th COURSE NAME- DISCRETE MATHEMATICS COURSE CODE- PCC-CSM405 TOPIC – DIVISON ALGORITHM
- 2. • DESCRIPTION • EXAMPLE • ADVANTAGES • APPLICATIONS • CONCLUSION INDEX
- 3. EUCLID'S DIVISON ALGORITHM Division algorithm states that given any two integers a & b with b > 0; There exist unique integers q & r such that a = bq +r, 0<= r<b, q Z. ∈ If r=0 then "b" is the HCF/GCD of "a & b . Ex- a = 50, b = 8 50 = 8 * 6 + 2 q = 6 , r = 2 a=bq+r 8)50( 6 48 2 If r ≠ 0 , then apply Euclid'sdivision lemma to b and r. b = (r*m) + n • For some integers m and n, 0 <= n < r • Continue this process till the remainder is zero. • The divisor which gives you the remainder as 0 is your HCF/GCD
- 6. ADVANTAGES • EFFICIENCY: THE ALGORITHM IS HIGHLY EFFICIENT IN FINDING THE GREATEST COMMON DIVISOR (GCD) OF TWO NUMBERS. ITS TIME COMPLEXITY IS PROPORTIONAL TO THE NUMBER OF DIGITS IN THE SMALLER NUMBER, MAKING IT SUITABLE FOR LARGE INTEGERS. • SIMPLICITY: THE ALGORITHM IS STRAIGHTFORWARD AND EASY TO UNDERSTAND. IT CONSISTS OF A FEW BASIC STEPS, MAKING IT ACCESSIBLE EVEN TO THOSE WITH LIMITED MATHEMATICAL BACKGROUND. • APPLICABILITY: IT HAS BROAD APPLICABILITY ACROSS DIFFERENT FIELDS, INCLUDING MATHEMATICS, COMPUTER SCIENCE, AND CRYPTOGRAPHY. MANY ALGORITHMS AND MATHEMATICAL PROCEDURES RELY ON THE EUCLIDEAN DIVISION ALGORITHM AS A FUNDAMENTAL STEP. • DETERMINISTIC: THE ALGORITHM FOLLOWS A DETERMINISTIC PROCESS, MEANING IT WILL ALWAYS PRODUCE THE SAME RESULT FOR THE SAME INPUT. THIS PROPERTY IS CRUCIAL FOR ITS RELIABILITY AND PREDICTABILITY IN VARIOUS APPLICATIONS
- 7. APPLICATION • COMPUTER SCIENCE (E.G., FINDING MODULAR INVERSES, CRYPTOGRAPHIC ALGORITHMS) • MATHEMATICS (E.G., SIMPLIFYING FRACTIONS, FINDING FACTORS) • ALGORITHM ANALYSIS (EG: SOLVING TIME COMPLEXITY FOR AN ALGORITHM) • ARCHITECTURE AND CONSTRUCTION. • COMPUTER GRAPHICS AND ANIMATION. • MECHANICAL ENGINEERING. • ROBOTICS AND AUTOMATION.
- 8. CONCLUSION • EUCLIDEAN DIVISION ALGORITHM PROVIDES A SYSTEMATIC WAY TO FIND THE GCD OF TWO NUMBERS. • IT IS FUNDAMENTAL IN VARIOUS FIELDS, INCLUDING MATHEMATICS AND COMPUTER SCIENCE. • ITS DETERMINISTIC NATURE AND ABILITY TO HANDLE LARGE NUMBERS MAKE IT INDISPENSABLE IN ALGORITHM DESIGN AND ANALYSIS, SERVING AS A FUNDAMENTAL EXAMPLE IN UNDERSTANDING COMPUTATIONAL COMPLEXITY AND ALGORITHMIC EFFICIENCY.
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