How many times does the statement count in line 5 executes in terms of $n$?1.  count=0; 2.  for (i=1; i<=n; i++) { 3.  for (j=1; j<=n; j*=2) { 4.  for (k=1; k<=j; k++) {5.        count = count + 1;6.      }7.    }8.  }For the loop in line 3, we can list the numbers for $j$ as, $2^0,2^1,...,2^{\log n}$Therefore, we can refer to the iterations of the exponents as $r$. Doing so would lead to the summations below for counting the number of executions.$\sum_{i=1}^{n}\sum_{r=0}^{\log n}\sum_{k=1}^{j}1 =\sum_{i=1}^{n}\sum_{r=0}^{\log n}j $I am stuck here, because $\sum_{r=0}^{\log n}$ depends on $j$ but I am not sure how to incorporate them.Thanks in advance.
The number of executions of the count statement; how many?
algorithms;algorithm analysis;time complexity;runtime analysis
Hint: Substitute $j = 2^r$, and use the formula for summing a geometric series.Make sure that you understand why the substitution $j = 2^r$ makes sense.