Running Time of Nested Loops, When inner loop false, - performance

Question

01.) Considering the growth time, When the inner loop of a nested loop is false, is its growth time O (n)?
ex:
for (int i=0; i<n; i++){
for (int j=0; j>n; i++){
//some code
}
}
02.) Considering the growth time, When the inner loop of a nested loop has another array length variable as 'm', is its growth time O (n m)?
ex:
for (int i=0; i<n; i++){
for (int j=0; j<m; i++){
//some code
}
}
What is the running time of the following code? (please explain with steps)
for (int i = 0; i < n; i++) {
for (int j = 0; j > n; j++) {
for (int k = 0; k > n; k++) {
System.out.println("*");
}
}
}
Thank You.

Answer 1

Yes, if it is absolutely clear that inner loop will not be executed due to the conditional's being false regardless of the input size, then time complexity will be O(n).
Yes, a detailed analysis can be found below. However, I assume you incorrectly incremented i in your inner loop.
for (int i=0; i<n; i++){
for (int j=0; j<m; j++){ // j++
//some code
}
}
number of operations performed by inner loop in each iteration of outer loop : m
number of operations performed by outer loop : n
Total number of operations : n*m
Time complexity f(n) ∈ O(n*m)
If the code you posted is not incorrect, then the time complexity analyis:
for (int i=0; i<n; i++){
for (int j=0; j<m; i++){
//some code
}
}
j=0 --> j<m (i++)
If 0<m, then it is an infinite loop. It's pointless to make a time complexity analysis.
If 0>=m, then inner loop is not going to be executed, therefore time complexity will be O(n).
Detailed analysis:
for (int i = 0; i < n; i++) { // n many times
for (int j = 0; j > n; j++) { // n many times
for (int k = 0; k > n; k++) { // n many times
System.out.println("*");
}
}
}
All of the loops are iterated n many times. Most-inner loop will perform n operations. Outer loop will perform n, which makes n*n. And most-outer loop will perform n operations, which makes n*n*n in total.
Time complexity f(n) ∈ O(n^3)