Solving a Recurrence Relation: T(n) = T(n-1) + n-1
I have been asked to solve that recurrence relation. I got the next solution: https://imgur.com/a/xWoTI40
So I decided to ask my teacher if it was right. He told me that it wasn't; and that this is the right solution: https://imgur.com/a/CGD0ta8
I'm totally clueless right now. The most I try to understand why mine is wrong; the most I think it's actually right.
Can somebody explain?
algorithm recurrence
asked Nov 12 '18 at 21:10
xFunkyTImes
928
add a comment |
I have been asked to solve that recurrence relation. I got the next solution: https://imgur.com/a/xWoTI40
So I decided to ask my teacher if it was right. He told me that it wasn't; and that this is the right solution: https://imgur.com/a/CGD0ta8
I'm totally clueless right now. The most I try to understand why mine is wrong; the most I think it's actually right.
Can somebody explain?
algorithm recurrence
asked Nov 12 '18 at 21:10
xFunkyTImes
928
I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
2
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
2
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10
add a comment |
I have been asked to solve that recurrence relation. I got the next solution: https://imgur.com/a/xWoTI40
So I decided to ask my teacher if it was right. He told me that it wasn't; and that this is the right solution: https://imgur.com/a/CGD0ta8
I'm totally clueless right now. The most I try to understand why mine is wrong; the most I think it's actually right.
Can somebody explain?
algorithm recurrence
asked Nov 12 '18 at 21:10
xFunkyTImes
928
I have been asked to solve that recurrence relation. I got the next solution: https://imgur.com/a/xWoTI40
So I decided to ask my teacher if it was right. He told me that it wasn't; and that this is the right solution: https://imgur.com/a/CGD0ta8
I'm totally clueless right now. The most I try to understand why mine is wrong; the most I think it's actually right.
Can somebody explain?
algorithm recurrence
algorithm recurrence
asked Nov 12 '18 at 21:10
xFunkyTImes
928
asked Nov 12 '18 at 21:10
xFunkyTImes
928
asked Nov 12 '18 at 21:10
xFunkyTImes
928
asked Nov 12 '18 at 21:10
xFunkyTImes
928
asked Nov 12 '18 at 21:10
xFunkyTImes
928
928
I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
2
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
2
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10
add a comment |
I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
2
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
2
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10
I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
2
2
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
2
2
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10
add a comment |
1 Answer
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Your solution is correct. Here's a different approach with the same result:
t(1) = 0 (given)
t(2) = t(1) + 1 = 1
t(3) = t(2) + 2 = 1 + 2 = 3
t(4) = t(3) + 3 = 1 + 2 + 3 = 6
...
t(n) = 1 + 2 + ... + (n-1) = n * (n - 1) / 2 = Theta(n^2).
The teacher's solution is wrong after the second = sign. Here's what the teacher wrote:
t(n-1) + n - 1 = t(n-2) + n - 1 - 2
But actually the following is correct:
t(n-1) + n - 1 = ( t(n-2) + n - 2 ) + n - 1
which is actually exactly what you got. It appears that the teacher dropped an n term.
In fact, the teacher's solution ends with a dominant term of -n^2 which is clearly wrong, as t(n) >= 0 for all n >= 0.
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Your solution is correct. Here's a different approach with the same result:
t(1) = 0 (given)
t(2) = t(1) + 1 = 1
t(3) = t(2) + 2 = 1 + 2 = 3
t(4) = t(3) + 3 = 1 + 2 + 3 = 6
...
t(n) = 1 + 2 + ... + (n-1) = n * (n - 1) / 2 = Theta(n^2).
The teacher's solution is wrong after the second = sign. Here's what the teacher wrote:
t(n-1) + n - 1 = t(n-2) + n - 1 - 2
But actually the following is correct:
t(n-1) + n - 1 = ( t(n-2) + n - 2 ) + n - 1
which is actually exactly what you got. It appears that the teacher dropped an n term.
In fact, the teacher's solution ends with a dominant term of -n^2 which is clearly wrong, as t(n) >= 0 for all n >= 0.
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
add a comment |
Your solution is correct. Here's a different approach with the same result:
t(1) = 0 (given)
t(2) = t(1) + 1 = 1
t(3) = t(2) + 2 = 1 + 2 = 3
t(4) = t(3) + 3 = 1 + 2 + 3 = 6
...
t(n) = 1 + 2 + ... + (n-1) = n * (n - 1) / 2 = Theta(n^2).
The teacher's solution is wrong after the second = sign. Here's what the teacher wrote:
t(n-1) + n - 1 = t(n-2) + n - 1 - 2
But actually the following is correct:
t(n-1) + n - 1 = ( t(n-2) + n - 2 ) + n - 1
which is actually exactly what you got. It appears that the teacher dropped an n term.
In fact, the teacher's solution ends with a dominant term of -n^2 which is clearly wrong, as t(n) >= 0 for all n >= 0.
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
add a comment |
Your solution is correct. Here's a different approach with the same result:
t(1) = 0 (given)
t(2) = t(1) + 1 = 1
t(3) = t(2) + 2 = 1 + 2 = 3
t(4) = t(3) + 3 = 1 + 2 + 3 = 6
...
t(n) = 1 + 2 + ... + (n-1) = n * (n - 1) / 2 = Theta(n^2).
The teacher's solution is wrong after the second = sign. Here's what the teacher wrote:
t(n-1) + n - 1 = t(n-2) + n - 1 - 2
But actually the following is correct:
t(n-1) + n - 1 = ( t(n-2) + n - 2 ) + n - 1
which is actually exactly what you got. It appears that the teacher dropped an n term.
In fact, the teacher's solution ends with a dominant term of -n^2 which is clearly wrong, as t(n) >= 0 for all n >= 0.
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
Your solution is correct. Here's a different approach with the same result:
t(1) = 0 (given)
t(2) = t(1) + 1 = 1
t(3) = t(2) + 2 = 1 + 2 = 3
t(4) = t(3) + 3 = 1 + 2 + 3 = 6
...
t(n) = 1 + 2 + ... + (n-1) = n * (n - 1) / 2 = Theta(n^2).
The teacher's solution is wrong after the second = sign. Here's what the teacher wrote:
t(n-1) + n - 1 = t(n-2) + n - 1 - 2
But actually the following is correct:
t(n-1) + n - 1 = ( t(n-2) + n - 2 ) + n - 1
which is actually exactly what you got. It appears that the teacher dropped an n term.
In fact, the teacher's solution ends with a dominant term of -n^2 which is clearly wrong, as t(n) >= 0 for all n >= 0.
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
answered Nov 13 '18 at 0:14
pkpnd
4,5711140
4,5711140
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
add a comment |
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
This is exactly what I was looking for. Thank you a lot @pkpnd
– xFunkyTImes
Nov 13 '18 at 8:30
add a comment |
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I'm voting to close this question as off-topic because it is a mathematics question, not a programming question.
– Raymond Chen
Nov 12 '18 at 21:50
2
You should ask to close this one as well @RaymondChen: stackoverflow.com/questions/2752977/how-to-solve-tn-tn-1-n
– xFunkyTImes
Nov 12 '18 at 21:55
2
The second solution seems incorrect to me, specially because for a large value of n it would be negative.
– Ari
Nov 12 '18 at 22:15
@xFunkyTimes Done, thanks.
– Raymond Chen
Nov 13 '18 at 2:10