Question

C++ programming

6-1: User Defined Functions I

the C++ cmath library contains several math-related functions. for a general listing of functions contained within this library, review your text or visit Cplusplus.com

(http://www.cplusplus.com/reference/cilbrary/cmath/)

if you had the option to redesign the math library, what other functions would you add to it? for example, do you think a max function or average function might be useful? give a list of at least three functions you think are worth adding to the math collection. provide a description of each new additional function, including what it does, what parameters it takes, and its return value.

Answer 1

• Below are the 3 functions that are very useful but are not inbuilt in math library:

1. nCr(int n, int r): this function is used to calculate combinations when we have to find r unordered outcomes from n available possibilities which takes n and r as the parameters and returns value of nCr i.e, (fact(n)/(fact(r)*fact(n-r)) with return type as int, or long long depending upon the result we get as the result can be very large.
2. nPr(int n, int r):this function is used to calculate total number of permutations when we have to choose r objects from a set of n items which takes n and r as the parameters and returns value of nPr i.e, (fact(n)/fact(n-r)) with return type as int, or long long depending upon the result we get as the result can be very large.
3. power(int base,int exponent,int modulo): this function is used to calculate (base(exponent)) %mod , this method is called modular exponentiation but is not a inbuilt function in c++ math library (in python it is) , it calculates the value in O(log (exponent)) so the time complexity is also very less, and it is used very often. The return type of this function also could be int or long long int depending upon the results as it can also be large.

• fact() in function 1 and 2 is function to calculate factorial of a number, so it can also be added to math library but it is not as important as it is easy to implement.
• Function 1 and 2 mentioned are used oftenly in math problems where we have to put some efforts in buildin the code for that and the function 3 is very important as it is very helpful in solving probabilty problems.
• Also the functions added in the math library should be of best time complexity so that to produce optimal result everytime and they are worth using it.
• average function or max function is not useful in a library as it takes only one line of code to calculate these so why use from a library , the function that should be added should be of huge lines of code and difficult to code at a competitive platform where time is the constraint.

So if you have any queries regarding the above explanation please ask in the comment section and if it seems helpful enough then please upvote , thanks.