Solving the reccurence method by using substitution
0
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I am having trouble in understanding this example(as the attached the picture below). I basically have 2 questions which these questions are related to each other.
- Is T(N) for N = 1 must equal to 1 for any reccurences case in substitution method by using induction(in basis step)?
- If it is not, then why in the example is equal to 1?
Because if I put N = 1 to the
>> T(N)=2T(N/2)+N the result is not equal to 1 instead of 2.
Can someone explain? Example of attached picture
induction computational-complexity substitution
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
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add a comment |
0
$begingroup$
I am having trouble in understanding this example(as the attached the picture below). I basically have 2 questions which these questions are related to each other.
- Is T(N) for N = 1 must equal to 1 for any reccurences case in substitution method by using induction(in basis step)?
- If it is not, then why in the example is equal to 1?
Because if I put N = 1 to the
>> T(N)=2T(N/2)+N the result is not equal to 1 instead of 2.
Can someone explain? Example of attached picture
induction computational-complexity substitution
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
$endgroup$
$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55
add a comment |
0
0
0
$begingroup$
I am having trouble in understanding this example(as the attached the picture below). I basically have 2 questions which these questions are related to each other.
- Is T(N) for N = 1 must equal to 1 for any reccurences case in substitution method by using induction(in basis step)?
- If it is not, then why in the example is equal to 1?
Because if I put N = 1 to the
>> T(N)=2T(N/2)+N the result is not equal to 1 instead of 2.
Can someone explain? Example of attached picture
induction computational-complexity substitution
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
$endgroup$
I am having trouble in understanding this example(as the attached the picture below). I basically have 2 questions which these questions are related to each other.
- Is T(N) for N = 1 must equal to 1 for any reccurences case in substitution method by using induction(in basis step)?
- If it is not, then why in the example is equal to 1?
Because if I put N = 1 to the
>> T(N)=2T(N/2)+N the result is not equal to 1 instead of 2.
Can someone explain? Example of attached picture
induction computational-complexity substitution
induction computational-complexity substitution
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
edited Jan 25 at 3:24
Marfin. F
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
asked Jan 25 at 3:05
Marfin. FMarfin. F
134
134
$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55
add a comment |
$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55
$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55
add a comment |
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$begingroup$
No, it doesn't have to be $1.$ This is the problem statement. It might be anything.
$endgroup$
– saulspatz
Jan 25 at 3:26
$begingroup$
@saulspatz I just noticed it was a problem statement. So is it somekind of hint to guess the answer quicker?
$endgroup$
– Marfin. F
Jan 25 at 3:45
$begingroup$
No, not at all. This is the data for the problem to be solved. We have a function $T$ that obeys the two equations equations given, and we want to find an explicit formula for $T$.
$endgroup$
– saulspatz
Jan 25 at 3:47
$begingroup$
@saulspatz Ah I see. I am actually use this example to solve other reccurence problem which only has 1 equation with similar problem. That is why I am confused by this example but thanks for your explanation, indeed.
$endgroup$
– Marfin. F
Jan 25 at 3:55