Generally, we need to check several cases:

1. If this line is a simple statement, which means a statement except functions or loops ( for loop or while loop or other loop), we calculate the running of time of this line as constant (we use O(1) to indicate constant running time)

eg. a = a+1

eg. if b > 0

2. If this block is a loop, we calculate the running time of the loop as how many iterations the loop runs.

eg. for i <- 1 to 10      // the for will iterate like i=1, i=2, i=3,...,i=10, so this for loop will iterate 10 times

eg. for i <- 1 to n       //  this for loop will iterate n times, so the running time of this loop is O(n)

eg. i = 10;

while (i > 1 ){

i = i / 3

}        // this while loop will iterate 3 times

3. If this block contains nested loop(s),

eg.

for i <- 1 to n {

      for j <- 1 to n {}

}  

//  second for loop will iterate n times, first for loop will iterate n * n which is n^2 times, so running time is O(n^2)

However, if loops are not nested with each other,

eg. 

for i <- 1 to n {}

for j <- 1 to n {}

// running time is n + n which is 2n , O(n)

4. If a statement is a function call, we need calculate running time of that function. 

If a statement is a recursive function call, it is better to use some methods such as recursion tree method to figure out how many times we call that function.

eg. Merge-Sort

Sometimes mathematical summary formulas will be helpful for some hard questions.

After we know each line or each block 's running time, we pick the highest order terms.