NOTE : For Calculating the time complexity implemented using loops then try to analyze
how many time #some code is running.
The given loop is nested loop.
Outer Loop is going from i = 1 to i = N and with each iteration it is incremented by 1 only.
Inner loop is going from j = 1 to j = $i^{2}$ and with each iteration it is incremented by the value of i.
For i =1
j = 1 $\rightarrow$ 1 (Increment by +1)
Total Execution of #some code in this Iteration = 1
For i =2
j = 1 $\rightarrow$ 4 (Increment by +2)
1 $\rightarrow$ 3 $\rightarrow$ 5
Total Execution of #some code in this Iteration = 2
For i =3
j = 1 $\rightarrow$ 9 (Increment by +3)
1 $\rightarrow$ 4 $\rightarrow$ 7 $\rightarrow$ 10
Total Execution of #some code in this Iteration = 3
For i =4
j = 1 $\rightarrow$ 16 (Increment by +4)
1 $\rightarrow$ 5 $\rightarrow$ 9 $\rightarrow$ 13 $\rightarrow$ 17
Total Execution of #some code in this Iteration = 4
For i =5
j = 1 $\rightarrow$ 25 (Increment by +5)
1 $\rightarrow$ 6 $\rightarrow$ 11 $\rightarrow$ 16 $\rightarrow$ 21 $\rightarrow$ 26
Total Execution of #some code in this Iteration = 5
Similary,
For i =N
j = 1 $\rightarrow$ $N^{2}$ (Increment by +N)
Total Execution of #some code in this Iteration = N
So, total number of times #some code is executed :
1 + 2 + 3 + 4 + 5 + - - - - - - - - + N
$N(N+1)/2$
$\simeq$ $O(N^{2})$
