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Big O (Definition)

We say that g(n) is O(f(n)) - read as, g of n is Big O of f of n when there exists some constants k and n₀(pronounced as n nought, or as n-sub-zero) such that:

g(n) is bound by k * f(n) for problem size n >= n₀.

Given the growth function, g(n) = 2n² + 4n + 3, determine the Big O. Prove that your analysis is correct by finding a constant k, and a constant n₀ that satisfy the definition of Big O.

Given the growth function, g(n) = 4n³ + n + 1, determine the Big O. Prove that your analysis is correct by finding a constant k, and a constant n₀ that satisfy the definition of Big O.

Given the following code segment, determine the Big O. Assume n is the number of elements in the array, myArray.

void myMethod(int myArray[ ], int n)

for(int i = 0; i < n; i++) {

for(int j = 0; j < n; j++) {

int temp = i * j; result += temp;

}

} }