Tutorial_6_Sol-for-viewing-printing

Tutorial_6_Sol-for-viewing-printing - CC2203 Data...

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CC2203 Data Structures and Algorithms Sem 2, 2009-2010 Page 1 of 3 Tutorial 6 Solutions Exercise 1 Answer (a) The method computeSum() computes the sums of all the elements in the subarrays and the array that begin at index 0. In this example, it computes the following: Sum = 5 for the subarray [5] Sum = 9 for the subarray [5, 4] Sum = 12 for the subarray [5, 4, 3] Sum = 23 for the subarray [5, 4, 3, 11] Sum = 32 for the array [5, 4, 3, 11, 9] (b) In the inner for loop, the statement sum += item[j] is executed i times where i {1, 2, …, n}. In this example, n = e.length = 5. At the 1 st inner for loop, i = 0, sum += item[j] is not executed . At the 2 nd inner for loop, i = 1, sum += item[j] is executed once. . . At the (n-1)-th inner for loop, i = n-2, sum += item[j] is executed n-2 times. At the n-th inner for loop, i = n-1, sum += item[j] is executed n-1 times. Therefore, sum += item[j] is executed ( ) 2 / 1 1 1 - = - = n n i n i times. Since 0 1 lim 2 / 2 / lim 2 = = n n n n n , 2 / n is asymptotically smaller than 2 / 2 n .
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