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Question
What is an algorithm?
Solution
Algorithm is a step-by-step procedure for calculations.
For example:
Euclid’s Division Algorithm: In order to compute the HCF of two positive integers say a and b, with a > b by using Euclid’s algorithm, we follow the following steps:
STEP I : Apply Euclid’s Division Lemma to a and b and obtain whole numbers q and `r_1 `,such that `a= bq_1+r_1` ,` 0≤ r_1 < b`
STEP II: If `r_1 =0 `, b is the HCF of a and b.
STEP III: If `r__1 `, apply Euclid’s division lemma to b and `r_1` and obtain whole numbers `q_1` and `r_2`,such that `b= q_1r_1+r_2`
STEP IV: If `r_2=0` , then `r_1` is the HCF of a and b.
STEP V: If `r_2=0 `, then apply Euclid’s division lemma to `r_1` and `r_2` and continue the above process till the remainder `r_n` is zero. The divisor at this stage i.e; `r_n-1` , or the non-zero remainder at the previous stage is the HCF of a and b.
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