Algorithm Evaluate (A[0,...n-1])//Input: An array A[0,...n-1]) of real numbersminval A[0]; maxval A[0]for i 1 to n-1 doif A[i] < minvalminval A[i]if A[i] > minvalmaxnval A[i]return maxval - minvala. What does the algorithm compute?b. what is the basic operation?c. How many time is the basic operation executed?d. What is the efficiency class of the algorithm?e. Suggest an improvement or a better algorithm altogether and indicate its efficiency class.
Question
Algorithm Evaluate (A[0,...n-1])//Input: An array A[0,...n-1]) of real numbersminval A[0]; maxval A[0]for i 1 to n-1 doif A[i] < minvalminval A[i]if A[i] > minvalmaxnval A[i]return maxval - minvala. What does the algorithm compute?b. what is the basic operation?c. How many time is the basic operation executed?d. What is the efficiency class of the algorithm?e. Suggest an improvement or a better algorithm altogether and indicate its efficiency class.
Solution
a. The algorithm computes the difference between the maximum and minimum values in an array of real numbers.
b. The basic operation is the comparison operation where each element of the array is compared with the current minimum and maximum values.
c. The basic operation is executed (n-1) times, where n is the number of elements in the array. This is because the algorithm starts from the second element (index 1) and goes up to the last element (index n-1).
d. The efficiency class of the algorithm is O(n), where n is the number of elements in the array. This is because each element in the array is visited once.
e. The algorithm is already efficient with a time complexity of O(n). However, an improvement can be made in terms of space complexity. Instead of storing the entire array in memory, we can process the numbers as they come in (for example, if they are being read from a file or a stream). This would reduce the space complexity to O(1). The time complexity would remain O(n).
Similar Questions
Algorithm Compute (A[0,...n-1, 0,....n-1])//Input: An matrix A[0,...n-1, 0,.....n-1]) of real numbersfor i 0 to n-2 dofor j i+1 to n-1 doif A[i,j] A[j,i]return falsereturn truea. What does the algorithm compute?b. what is the basic operation?c. How many time is the basic operation executed?d. What is the efficiency class of the algorithm?e. Suggest an improvement or a better algorithm altogether and indicate its efficiency class.
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