• Determine a formula that expresses the height of the tree. Answer: General Recursion Tree: 1 1 = 2° 2 = 2! T(n/2) T(n/2) 4 = 22 T(n/4) T(n/4) T(n/4) T(n/4) log n T(n/8) T(n/8) T(n/8) T(n/8) T(n/8)...


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• Determine a formula that expresses the height of the tree.<br>Answer: General Recursion Tree:<br>1<br>1 = 2°<br>2 = 2!<br>T(n/2)<br>T(n/2)<br>4 = 22<br>T(n/4)<br>T(n/4)<br>T(n/4)<br>T(n/4)<br>log n<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>T(n/8)<br>8 = 23<br>T(1)<br>T(1)<br>T(1)<br>T(1)<br>T(1)<br>T(1)<br>n= 2k<br>........<br>Therefore the height of the binary tree is log2 n<br>And because we have a binary tree the formula to find the number of nodes would<br>be 2-1 – 1 = 2logn+1 - 1<br>

Extracted text: • Determine a formula that expresses the height of the tree. Answer: General Recursion Tree: 1 1 = 2° 2 = 2! T(n/2) T(n/2) 4 = 22 T(n/4) T(n/4) T(n/4) T(n/4) log n T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) 8 = 23 T(1) T(1) T(1) T(1) T(1) T(1) n= 2k ........ Therefore the height of the binary tree is log2 n And because we have a binary tree the formula to find the number of nodes would be 2-1 – 1 = 2logn+1 - 1

Jun 11, 2022
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