Write a recurrence relation describing the worst case running time of each the following algorithms and...
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Write a recurrence relation describing the worst case running time of each the following algorithms and make a guess about the asymptotic complexity of the functions defined by the recurrence relation using either expanding into a series or a recursion tree. Justify your solutions using the substitution method. A[i j] represents an array of n = j i +1 numbers starting at index i and ending at index j and A[k] represents the value at index k. (20 points each) 3.) FUNCTION F3(A[1...n]) IF n 5 THEN RETURN(A[n]) x0 FOR 1 TO 5 DO BEGIN (FOR i) END FOR j1 TO n - 4 DO A[i] A[j] + A[j+2] x x + F3(A[1 .. [n/2]]) RETURN(x) 4.) FUNCTION F(A[i... j]) nj-i+1 IF n 1 THEN RETURN(A[i]) x F(A[i.. [i + 2n/3]]) FOR in/4] TO [n/4] + 12 DO x+x+A[i] RETURN(x) Write a recurrence relation describing the worst case running time of each the following algorithms and make a guess about the asymptotic complexity of the functions defined by the recurrence relation using either expanding into a series or a recursion tree. Justify your solutions using the substitution method. A[i j] represents an array of n = j i +1 numbers starting at index i and ending at index j and A[k] represents the value at index k. (20 points each) 3.) FUNCTION F3(A[1...n]) IF n 5 THEN RETURN(A[n]) x0 FOR 1 TO 5 DO BEGIN (FOR i) END FOR j1 TO n - 4 DO A[i] A[j] + A[j+2] x x + F3(A[1 .. [n/2]]) RETURN(x) 4.) FUNCTION F(A[i... j]) nj-i+1 IF n 1 THEN RETURN(A[i]) x F(A[i.. [i + 2n/3]]) FOR in/4] TO [n/4] + 12 DO x+x+A[i] RETURN(x)
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The pseudocode represents a function F which performs the following steps If the size of the array n ... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
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