What is the total time complexity if each instruction takes A ms. The following is a matlab code extract:

for i=2:n-3
for j=4:n-1
disp(i*J)
end
end

Show all working if possible thanks.

Question

What is the total time complexity if each instruction takes A ms. The following is a matlab code extract:

for i=2:n-3
for j=4:n-1
disp(i*J)
end
end

Show all working if possible thanks.

anonymous · Answer

The time sued for the outer loop will be something like $$t_{outer} = a \cdot n \cdot t_{inner} + b $$ (where a and b are some constants).

Since the inner loop also iterates n times as well, $$t_{inner} = c \cdot n \cdot t_{disp} + d$$

I assume $$t_{disp} = e \cdot 1$$

Now, if we ignore all te constants (like for Big O notation), you'll get something like $$t_{outer} = n \cdot t_{inner} = n \cdot n \cdot t_{disp} = n^2 \cdot 1 = n^2$$

So the complexity of the loop is $$O(n^2)$$