We are given an array A with 2n + 1 distinct elements. Suppose that we are...

 

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We are given an array A with 2n + 1 distinct elements. Suppose that we are using the randomized selection algorithm to find the median. In a worst-case scenario of this algorithm, the median is found at the very last step, where each step before that gets rid of only one element in the array. How many different worst-case scenarios are there for finding the median in A? Example: Suppose that we have A = [4, 5, 1, 3, 2]. One of the worst-case scenarios is to pick the following elements as the pivots in this order 1, 2, 4, 5. Because (randomly but unluckily) if we pick these numbers in this order as the pivots, we will get rid of only the pivot in each step, and only at the very end (when we have only the element 3 remaining, which is the median of the original input array) we will find the median. The other worst-case scenarios are: 1,5,2,4 1,5,4,2 5,1,4,2 5,1,2,4 5,4,1,2 Activate We are given an array A with 2n + 1 distinct elements. Suppose that we are using the randomized selection algorithm to find the median. In a worst-case scenario of this algorithm, the median is found at the very last step, where each step before that gets rid of only one element in the array. How many different worst-case scenarios are there for finding the median in A? Example: Suppose that we have A = [4, 5, 1, 3, 2]. One of the worst-case scenarios is to pick the following elements as the pivots in this order 1, 2, 4, 5. Because (randomly but unluckily) if we pick these numbers in this order as the pivots, we will get rid of only the pivot in each step, and only at the very end (when we have only the element 3 remaining, which is the median of the original input array) we will find the median. The other worst-case scenarios are: 1,5,2,4 1,5,4,2 5,1,4,2 5,1,2,4 5,4,1,2 Activate We are given an array A with 2n + 1 distinct elements. Suppose that we are using the randomized selection algorithm to find the median. In a worst-case scenario of this algorithm, the median is found at the very last step, where each step before that gets rid of only one element in the array. How many different worst-case scenarios are there for finding the median in A? Example: Suppose that we have A = [4, 5, 1, 3, 2]. One of the worst-case scenarios is to pick the following elements as the pivots in this order 1, 2, 4, 5. Because (randomly but unluckily) if we pick these numbers in this order as the pivots, we will get rid of only the pivot in each step, and only at the very end (when we have only the element 3 remaining, which is the median of the original input array) we will find the median. The other worst-case scenarios are: 1,5,2,4 1,5,4,2 5,1,4,2 5,1,2,4 5,4,1,2 Activate

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In the given worstcase scenario for the randomized selection algorithm the median is found at the ve... View the full answer