Question

Use recursion trees to solve each of the following recurrences. Each tree should show levels 0, 1, 2, and 𝑖, as we did in class. From that tree, derive the asymptotic running time (e.g., 𝑂(𝑛) or 𝑂(𝑛 lg 𝑛)). Assume that 𝑇(0) = 𝑇(1) = 1 for each recurrence. a) 𝑇(𝑛) = 2𝑇(𝑛/4) + 𝑛 b) 𝑇(𝑛) = 3𝑇(𝑛/3) + 𝑛 c) 𝑇(𝑛) = 4𝑇(𝑛/2) + βˆšπ‘›

          Use recursion trees to solve each of the following recurrences. Each tree should show levels
0, 1, 2, and 𝑖, as we did in class. From that tree, derive the asymptotic running time
(e.g., 𝑂(𝑛) or 𝑂(𝑛 lg 𝑛)). Assume that 𝑇(0) = 𝑇(1) = 1 for each recurrence.
a) 𝑇(𝑛) = 2𝑇(𝑛/4) + 𝑛
b) 𝑇(𝑛) = 3𝑇(𝑛/3) + 𝑛
c) 𝑇(𝑛) = 4𝑇(𝑛/2) + βˆšπ‘›
        
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Added by Rosa H.

Computer Science and Information Technology
Computer Science and Information Technology
Trishna Knowledge Systems 2018 Edition
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Use recursion trees to solve each of the following recurrences. Each tree should show levels 0, 1, 2, and 𝑖, as we did in class. From that tree, derive the asymptotic running time (e.g., 𝑂(𝑛) or 𝑂(𝑛 lg 𝑛)). Assume that 𝑇(0) = 𝑇(1) = 1 for each recurrence. a) 𝑇(𝑛) = 2𝑇(𝑛/4) + 𝑛 b) 𝑇(𝑛) = 3𝑇(𝑛/3) + 𝑛 c) 𝑇(𝑛) = 4𝑇(𝑛/2) + βˆšπ‘›
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Transcript

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00:01 To everyone.
00:02 So, here a n equals to 2 a n by 4 plus b n.
00:11 So, recursion tree for a n, a n by 4, a n by 16, a 1.
00:36 So, each level divide by, divide n by 4.
00:44 So, here it is log 4 n plus 1.
00:50 So, the cost of each level, cost of each level is o v n.
01:00 Therefore, total cost, total cost is o v n log 4 n.
01:09 Second one, for b n equals to 2 b n by 4 plus n.
01:16 So, tree for b n, b n.
01:20 So, after b n by 4, b n by 16, b 1...
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