Time-Complexity-using-while-and-if

for i = 1 to n do step 2
{
   stat;
}

while(condition)
{
   stat;
}

do{
}while(condition)

do loop is Posteriori loop，executes statement first then executes condition while loop is prior loop，executes condition first then executes statement

repeat{
   stat;
}until(condition)

repeat will always execute if the condition is false do will always execute if the condition is true

i = 0                     -> 1
while(i < n){             -> n + 1
  stat;                   -> n 
  i ++                    -> n
}

$f(n) = 3n + 2 \Rightarrow O(n) = n$

for(i = 0; i < n; i++)          -> n + 1
{
   stat;                        -> n
}

$f(n) = 2n + 1 \Rightarrow O(n) = n$

a = 1
while(a < b)
{
  stat
  a = a * 2
}

$a \geq b \Rightarrow a = 2^k \Rightarrow 2^k \geq b \Rightarrow k = \log_2b \Rightarrow O(\log_2n)$

i = n
while(i > 1)
{
   stat;
   i = i /2;
}

same as the previous one

$O(\log_2n)$