Fundamental Computer Science Concepts & Algorithms
Classified in Computers
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Arithmetic Progressions (AP)
Sum of terms = n[(1st term + last term)]/2
Geometric Progressions (GP)
Sum of terms = [1st term(1 - quotientn)/(1 - quotient)] (Swap positions of 1 & quotient if quotient > 1)
Logarithms
- loga(x/y) = logax - logay
- logaxn = nlogax
- logab = (logcb/logca)
Permutations
For a set of n objects: The total number of permutations is n!
For arranging 'r' objects from a set of 'n' objects: The number of permutations is nPr = n! / (n-r)!. (e.g., ways to arrange 3 objects from a set of 5 is 5 * 4 * 3, since there are 5 possibilities for the first object, followed by 4, then 3.)
Combinations
For selecting 'r' objects from a set of 'n' objects: The number of combinations is nCr = n! / (r! * (n-r)!). (Divide by r! since there are r! ways
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