A Program With Nested for Loops

class NestedLoop {
public static void main(String[] args) {
int n = 5; // 1 step
int m = 7; // 1 step
int sum = 0; // 1 step
for (int i = 0; i < n; i++) { // n steps
for (int j = 0; j < m; j++) { // nm steps
sum++; // n
m steps
}
}
System.out.println("Sum: " + sum); // 1 step
}
}

how it is came 1+1+1+6n+4+n(6m+4)+3nm+2… (6n+4)…

Hello,

I hope you’re doing fine. The breakdown is well explained in the slides.
Let’s go through this once again:

• It is 4 till the first intialization in the outer `for` loop.
• In the condition of the outter loop it’s `i<n`, this condition will account for 3(n+1) primitive operations.
• Intialization in the inner `for` loop will take 1 unit of time, but it’s inside a for loop. It’ll be n for this step.
• Just like we did in second step, it will be 3(m+1) for inner loop, but since it’s inside a loop, it’ll be n x 3(m+1).
• `sum++` is three step process, so it is 3m, but since it’s inside a nested loop, it’ll be n x 3m.
• incrementing j is n x 3m
• incrementing i is 3n
• In the end, `print` statement accounts for 2 primitive operations.