# Linked Questions

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### $T(n)=2T(n/2)+n\log n$ and the Master theorem [duplicate]

According to Introduction to algorithms by Cormen et al, $$T(n)=2T(n/2)+n\log n$$ is not case 3 of Master Theorem. Can someone explain me why? And which case of master theorem is it?
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### Recurrence relation T(n) = 3T(n-1) + n [duplicate]

I'm trying to solve the recurrence relation T(n) = 3T(n-1) + n and I think the answer is O(n^3) because each new node spawns three child nodes in the recurrence tree. Is this correct? And, in terms of ...
3answers
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### Solve recurrence T(n)=2T(n-1)+n for n greater than 1 and T(1)=1 [duplicate]

Problem statement: Solve $T(n)$ for $T(n)=2T(n-1)+n$, $n > 1$, and $T(1)=1$. My attempt: I tried back substituting but I am unable to find a general pattern: \begin{align*} T(n) &=2^2 T(n-2)...
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### recurrence - Iteration method T(n)=T(n-a)+n [duplicate]

I really need help to solve the following: T(n)=T(n-a)+n where a is a constant greather or equal 1. So I started to iterate T(n)=T(n-a)+n =T(((n-a)+n)-a)+n =T(3n-3a)+n =T(((3n-3a)+n)-...
2answers
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### Recurrence Problem $T(n) = 3T(n/3) + n$ [duplicate]

My question here is dealing with the residual that I get. We are trying to prove $T(n) = 3T(n/3) + n$ is $O(n*\log n)$. So where I get is $T(n) \le cn[\log n - \log 3] + n$. So my residual is \$-cn\log ...
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### Proving number of calls made in cut-rod algorithm [duplicate]

I was reading dynamic programming chapter from famous book Introduction To Algorithm In rod cutting problem it gives simple algorithm as follows: ...
1answer
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### How can I solve for T(n) recurrence equations? [duplicate]

Solve the following recurrence equations a. T(n) = T(n/2) + 18 b. T(n) = 2T(n/2) + 5n c. T(n) = 3T(n/2) + 5n d. T(n) = T(n/2) + 5n This is only a sample of what I was given but I am not sure what ...
1answer
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### Recurrence of T(n) = T(n/3) + T(2n/3) [duplicate]

I've searched online for this but I only seem to find answers for a similar equation: T(n) = T(n/3) + T(2n/3) + cn But the one I'm trying to solve is: ...
1answer
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### How do you solve a recurrence relation with multiple subproblems of different sizes? [duplicate]

For instance, consider the following recurrence relation. T(n) = T(n/2) + T(n/3) + T(n/4) + n Would you use the substitution method for this?

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