Help me walk through a few loops to see how many executions. I need a lesson

I'm having difficulty finding out how many executions these loops operate sum++. i'm not only interested in the answer but how youy figured it out.

 A)   for(i=1 ; i<= 100 ; i++)
         for (j= 1 ; j <= i; j++) sum++;    

 A)   i'm thinking that the first for loop goes through 100 times and the second for loop is also 100 times so 100^2 is correct?? is this right?

B) for(i = 101; i <=200; i++)
       for(j= i - 1;  j <i+1;j++) sum++;

B) I tried walking through it and it seems the first loop starts out and goes through 99 times. hen thew second one is true for 99 times so 99^2
  my thinking was as follows
1st time through j =100 ; 100 < 101 +1; 100++

2nd time  j=101 ; 101 <102+1; 101++
199th time j= 199 ; 199 < 200 +1 ; 200++ so stops here 199-100 = 99 this the right logic??

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objectsConnect With a Mentor Commented:
A) No, the first loop will go 100 times, but the second loop will execute a variable number of time.
first time (i=1) it will execute once, second time (i=2) it will execute twice, etc
So total loops = 1 + 2 + 3 + ... + 100.

B) No, again right for the first loop, but not for the second.
The second loop will execute (i+1) - (i-1) times = 2 times
So total number of loops is 99 x 2 = 198 times.
B) 200!

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No reason to give a wrong answer .....
tyweed420Author Commented:
Objects thanks for the help you get the huge 20 points! may i ask though when you figured out part B how did you know to take (i+1) - (i-1) is that some type of formula or common knowledge proccess you used to take those two arguments and derive 2?

Thanks in advance!
> B) 200!

That is correct, I overlooked the <=.

> how did you know to take (i+1) - (i-1)

just the difference between the upper and lower ranges for the index.
tyweed420Author Commented:
Hey guys one last question for ya regarding counting loops. These two are very difficult for me

1)  for(int i = 100 ; i > 0  ;i--)  
         for(j=i;   j  <  2 * i + 2 ; j++)

         1. i'm thinking the first loop goes through 99 times but then when you get into the second loop it lookslike this

         i=100                 i=99           ....................      i=1
      =======        ========                          =========
       j=100                j=99                                         j=1
      i=202                 i=20                                         i=4                                   so its 3+4+5+6..........+102 = times sum++ is executred is this correct?
     102 times             101 times                                 3 times

2)           for(int i = 0 ; i <10000  ;i++)  
                  for(j=0 ;   j *j*j < i ; j++)

 this one i have no clue can someone walk me through it ?
No, you won't get 2 answers for only 20 points.

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