Find the time complexity of the following algorithms in terms of Big O. Explain your answer as well.

1. A function (or set of statements) that doesnt contain loop, recursion and call to any other non-constant time function.
2. A loop or recursion that runs a constant number of times, such as follows:

for (int i = 1; i <= c; i++) // Here c is a constant

{

// some O(1) expressions

}

3. A loop where the loop variables is incremented / decremented by a constant amount, as follows:

// Here c is a positive integer constant

for (int i = 1; i <= n; i += c) {

// some O(1) expressions

}

4. Time complexity of nested loops as follows:

// Here c is a positive integer constant

for (int i = 1; i <=n; i += c) {

for (int j = 1; j <=n; j += c) {

// some O(1) expressions

}

}

5. Time Complexity of a loop if the loop variables is divided / multiplied by a constant amount as follows:

for (int i = 1; i <=n; i *= c) {

// some O(1) expressions

}

6. Time Complexity of a loop if the loop variables is reduced / increased exponentially by a constant amount as follows:

// Here c is a constant greater than 1

for (int i = 2; i <=n; i = pow(i, c)) {

// some O(1) expressions

}

//Here fun is sqrt or cuberoot or any other constant root

for (int i = n; i > 0; i = fun(i)) {

// some O(1) expressions

}