To analyze the complexity of binary search, we can use a recurrence relation. Let's consider the following options:

1. T(n) = T(n / 2) + n^2
2. T(n) = T(n / 2) + log n
3. T(n) = 2T(n / 2) + k, where k is a constant
4. T(n) = T(n / 2) + k

To determine the correct recurrence relation, we need to understand the steps involved in binary search. In each step, we divide the search space in half, which corresponds to the n / 2 term in the recurrence relation.

Additionally, we need to consider the work done at each step. In binary search, we compare the target element with the middle element of the current search space. If the target is smaller, we continue the search in the left half; if it is larger, we continue in the right half. This comparison and decision-making process takes constant time, represented by the k term in the recurrence relation.

Now, let's analyze the options:

1. T(n) = T(n / 2) + n^2: This option suggests that the work done at each step is proportional to n^2, which is not the case in binary search. Therefore, this option is not correct.

2. T(n) = T(n / 2) + log n: This option suggests that the work done at each step is proportional to log n, which is correct for binary search. Therefore, this option is a valid recurrence relation for the complexity of binary search.

3. T(n) = 2T(n / 2) + k: This option suggests that we perform twice the work at each step compared to the previous step. This is not the case in binary search, as we only divide the search space in half at each step. Therefore, this option is not correct.

4. T(n) = T(n / 2) + k: This option suggests that we perform the same amount of work at each step, which is correct for binary search. Therefore, this option is also a valid recurrence relation for the complexity of binary search.

In conclusion, the correct recurrence relations for the complexity of binary search are options 2 and 4, which are:

2. T(n) = T(n / 2) + log n
4. T(n) = T(n / 2) + k

Question

To analyze the complexity of binary search, we can use a recurrence relation. Let's consider the following options:

1. T(n) = T(n / 2) + n^2
2. T(n) = T(n / 2) + log n
3. T(n) = 2T(n / 2) + k, where k is a constant
4. T(n) = T(n / 2) + k

To determine the correct recurrence relation, we need to understand the steps involved in binary search. In each step, we divide the search space in half, which corresponds to the n / 2 term in the recurrence relation.

Additionally, we need to consider the work done at each step. In binary search, we compare the target element with the middle element of the current search space. If the target is smaller, we continue the search in the left half; if it is larger, we continue in the right half. This comparison and decision-making process takes constant time, represented by the k term in the recurrence relation.

Now, let's analyze the options:

1. T(n) = T(n / 2) + n^2: This option suggests that the work done at each step is proportional to n^2, which is not the case in binary search. Therefore, this option is not correct.

2. T(n) = T(n / 2) + log n: This option suggests that the work done at each step is proportional to log n, which is correct for binary search. Therefore, this option is a valid recurrence relation for the complexity of binary search.

3. T(n) = 2T(n / 2) + k: This option suggests that we perform twice the work at each step compared to the previous step. This is not the case in binary search, as we only divide the search space in half at each step. Therefore, this option is not correct.

4. T(n) = T(n / 2) + k: This option suggests that we perform the same amount of work at each step, which is correct for binary search. Therefore, this option is also a valid recurrence relation for the complexity of binary search.

In conclusion, the correct recurrence relations for the complexity of binary search are options 2 and 4, which are:

2. T(n) = T(n / 2) + log n
4. T(n) = T(n / 2) + k

Knowee AI · Accepted Answer

To analyze the complexity of binary search, we can use a recurrence relation. Let's consider the following options:

1. T(n) = T(n / 2) + n^2
2. T(n) = T(n / 2) + log n
3. T(n) = 2T(n / 2) + k, where k is a constant
4. T(n) = T(n / 2) + k

To determine the correct recurrence relation, we need to understand the steps involved in binary search. In each step, we divide the search space in half, which corresponds to the n / 2 term in the recurrence relation.

Additionally, we need to consider the work done at each step. In binary search, we compare the target element with the middle element of the current search space. If the target is smaller, we continue the search in the left half; if it is larger, we continue in the right half. This comparison and decision-making process takes constant time, represented by the k term in the recurrence relation.

Now, let's analyze the options:

1. T(n) = T(n / 2) + n^2: This option suggests that the work done at each step is proportional to n^2, which is not the case in binary search. Therefore, this option is not correct.

2. T(n) = T(n / 2) + log n: This option suggests that the work done at each step is proportional to log n, which is correct for binary search. Therefore, this option is a valid recurrence relation for the complexity of binary search.

3. T(n) = 2T(n / 2) + k: This option suggests that we perform twice the work at each step compared to the previous step. This is not the case in binary search, as we only divide the search space in half at each step. Therefore, this option is not correct.

4. T(n) = T(n / 2) + k: This option suggests that we perform the same amount of work at each step, which is correct for binary search. Therefore, this option is also a valid recurrence relation for the complexity of binary search.

In conclusion, the correct recurrence relations for the complexity of binary search are options 2 and 4, which are:

2. T(n) = T(n / 2) + log n
4. T(n) = T(n / 2) + k

The recurrence relation that arises in relation with the complexity of binary search is:1.T(n) = T(n / 2) + n2.T(n) = T(n / 2) + log n3.T(n) = 2T(n/ 2) + k , where k is constant4.T(n) = T(n / 2) + k

Question

Solution

Similar Questions

Upgrade your grade with Knowee