Cauchy’s Mean Value Theorem
Suppose f(x) and g(x) are 2 functions satisfying three conditions: 1) f(x), g(x) are continuous in the closed interval a <= x <= b 2)… Read More »
Category Archives: GFacts
Nesbitt’s Inequality
Nesbitt’s inequality is one of the simplest inequalities in mathematics. According to the statement of the inequality, for any 3 given real numbers they satisfy… Read More »
GFact 23 | (Brocard’s problem)
Brocard’s problem is to find values of m and n such that n!+1 = m2 For example, a pair (4, 5) solves the above equation.… Read More »
GFact 22 | (2^x + 1 and Prime)
A number of the form 2x + 1 (where x > 0) is prime if and only if x is a power of 2, i.e.,… Read More »
G-Fact 21 | Collatz Sequence
Starting with any positive integer N, we define the Collatz sequence corresponding to N as the numbers formed by the following operations: N → N/2… Read More »
G-Fact 20 (Cayley’s formula for Number of Labelled Trees)
Consider below questions. How many spanning trees can be there in a complete graph with n vertices? How many labelled Trees (please note trees, not… Read More »
G-Fact 19 (Logical and Bitwise Not Operators on Boolean)
Most of the languages including C, C++, Java and Python provide the boolean type that can be either set to False or True. Consider below… Read More »
G-Fact 18 | Finding nth Fibonacci Number using Golden Ratio
We have discussed different methods to find nth Fibonacci Number.
G-Fact 17
Storage class of a variable determines whether the item has a global or local lifetime. In C, typedef is considered as a storage class like… Read More »
fseek() vs rewind() in C
In C, fseek() should be preferred over rewind().
G-Fact 16
Predict the output of following program.
G-Fact 15
Atomic Operation What is an atomic operation? An idea of atomic operation helps in understanding reentrancy, critical section, thread safety, synchronization primitives, etc… (we will… Read More »
G-Fact 14
In C, a structure cannot have static members, but in C++ a structure can have static members.
G-Fact 13
const Behaviour in C and C++ In C, the const qualified identifiers will have external linkage, where as in C++ it will have internal linkage.… Read More »
G-Fact 12
In C, struct keyword must be used for declaring structure variables, but it is optional in C++.