Those are apparently the correct answers but could I get an explaination as to h

Question

Those are apparently the correct answers but could I get an explaination as to how to come to those answers?

Also, how many times do these parts below execute and why?

i <= N

j <= i

k<N

Consider the following code fragment. 01 for (int i 31 i N i++) 02 03 for int j 1 j i j++ 04 for (int k 31 k N k++) 05 06 c [k1 func (i, j, k) 07 08 09 10 Problem 1 Assuming that N is an integer greater than zero, how many times is each of the following operations performed when the code fragment above is executed? Give your answer in each box below as a closed- form function of N on line 01 i N NH j++ on line 03 on line 05 k++

Explanation / Answer

We have 3 FOR loop, all are nested in each other

So, outermost FOR loop runs N times: i=1 to i<=N

and we are doing i++ in outer most FOR loop only,
so i++ will execute N times

In middle FOR loop: for each value of i from outer FOR loop:
   It runs i times: j=1 to j=i

   S0, for i=1
       it runs = 1 times
       for i =2, it runs 2 times
       for i=3 , it runs 3 times

       ----
       for i=N, it runs N times

       Total execution: i + 2 + 3 + .. + n
                       = N(N+1)/2
       So, j++ execute N(N+1)/2 times

Innermost FOR loop runs: (N-1) times for each value of j

   k = 1 to (N-1)

   Since middle FOR loop runs: N(N+1)/2 times
   so, it will run (N-1) * N(N+1)/2

   = (N-1)N(N+1)/2 times

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