computer science

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bekalay674379 · Answer

Hey! The answers are below and ans for 4th Q attached. If you have more questions pm me! And hit the 5 stars, regards!Q1: RECURSE-INSERTION-SORT(A, n)
if n > 1    
 RECURSE-INSERTION-SORT(A, n - 1)    
 INSERT(A, n)Q2: INSERT(A, k)
key = A[k]
index = k - 1
while index > 0 and A[index] > key    
  A[index + 1] = A[index]    
  index = index - 1
A[index + 1] = key
Q3: Let us assume that for n = 1n=1, T(n) = c_1T(n)=c1, where c_1c1 is some constant. And on average for n > 1n>1, inserting an element in its proper position in a sorted array requires shifting half of the elements, i.e. c_2n/2 + c_3c2n/2+c3 time (c_2n/2c2n/2 for shifting the elements and c_3c3 for inserting the element). $ T(n) & = T(n - 1) + c_2(n - 1)/2 + c_3 \ & = T(n - 2) + c_2(n - 2)/2 + c_3 + \{c_2(n - 1)/2 + c_3\} \ & = T(1) + \cdot \cdot \cdot + \{c_2(n - 2)/2 + c_3\} + \{c_2(n - 1)/2 + c_3\} \ & = c_1 + \frac {c_2} 2 \{1 + 2 + \cdot \cdot \cdot + (n - 1)\} + c_3(n - 1) \ & = c_1 + \frac {c_2} 2 \cdot \frac {n(n - 1)} 2 + c_3(n - 1) \ & = \Theta(n^2)$

expertsolution · Answer

Please find attachment. Read this well and use it to enhance as well as develop your understanding and knowledge about the given assignment. If you have any queries feel free to send me a message. Thank you very much!Kindly leave healthy feedback with 5stars as this is my real reward of all hard working.
BEST OF LUCK :)
regards,Dr. Charles Kennedy (expertsolution)

expertsolution · Answer

Please find attachment. Read this well and use it to enhance as well as develop your understanding and knowledge about the given assignment. If you have any queries feel free to send me a message. Thank you very much!Kindly leave healthy feedback with 5stars as this is my real reward of all hard working.
BEST OF LUCK :)
regards,Dr. Charles Kennedy (expertsolution)

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