Question

Exercise 5 (Binary Search). Let a = [a0, a1,..., an-1] be an array of n integers. Assume the array is sorted: a0 ? a1 ?...? an-1. 1. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by the following binary search implementation? 1 static int search(int[] a, int y) { 2 int lo = 0, hi = a.length - 1; 3 while (lo < hi) { 4 int mid = lo + (hi - lo) / 2; 5 if (a[mid] < y) lo = mid + 1; 6 else hi = mid; 7 } 8 return lo; 9} 2. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by the following binary search implementation? 1 static int search2(int[] a, int y) { 2 int lo = 0, hi = a.length - 1; 3 while (lo < hi) { 4 int mid = lo + (hi - lo) / 2; 5 if (a[mid] > y) hi = mid; 6 else lo = mid + 1; 7 } 8 return hi - 1; 9} 3. Give a simple logarithmic time algorithm, taking as input a sorted array of integers as well as some integer y, and which returns the number of occurrences of y in the array (and -1 if there are none).

          Exercise 5 (Binary Search). Let a = [a<sub>0</sub>, a<sub>1</sub>,..., a<sub>n-1</sub>] be an array of n integers. Assume the array
is sorted: a<sub>0</sub> ? a<sub>1</sub> ?...? a<sub>n-1</sub>.
1. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by
the following binary search implementation?
1 static int search(int[] a, int y) {
2 int lo = 0, hi = a.length - 1;
3 while (lo < hi) {
4 int mid = lo + (hi - lo) / 2;
5 if (a[mid] < y) lo = mid + 1;
6 else hi = mid;
7 }
8 return lo;
9}
2. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by
the following binary search implementation?
1 static int search2(int[] a, int y) {
2 int lo = 0, hi = a.length - 1;
3 while (lo < hi) {
4 int mid = lo + (hi - lo) / 2;
5 if (a[mid] > y) hi = mid;
6 else lo = mid + 1;
7 }
8 return hi - 1;
9}
3. Give a simple logarithmic time algorithm, taking as input a sorted array of integers as well
as some integer y, and which returns the number of occurrences of y in the array (and -1 if
there are none).

Exercise 5 (Binary Search). Let a = [a<sub>0</sub>, a<sub>1</sub>,..., a<sub>n-1</sub>] be an array of n integers. Assume the array
is sorted: a<sub>0</sub> ? a<sub>1</sub> ?...? a<sub>n-1</sub>.
1. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by
the following binary search implementation?
1 static int search(int[] a, int y)
2 int lo = 0, hi = a.length - 1;
3 while (lo < hi)
4 int mid = lo + (hi - lo) / 2;
5 if (a[mid] < y) lo = mid + 1;
6 else hi = mid;
7
8 return lo;
9
2. Suppose the array a has multiple occurrences of y. Which of the occurrences is returned by
the following binary search implementation?
1 static int search2(int[] a, int y)
2 int lo = 0, hi = a.length - 1;
3 while (lo < hi)
4 int mid = lo + (hi - lo) / 2;
5 if (a[mid] > y) hi = mid;
6 else lo = mid + 1;
7
8 return hi - 1;
9
3. Give a simple logarithmic time algorithm, taking as input a sorted array of integers as well
as some integer y, and which returns the number of occurrences of y in the array (and -1 if
there are none).

Added by Monique S.

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