Find last position of target element in sorted array

Problem

Given a sorted array and an element, find last occurrence of element in array. 

Examples

Example 1:

Input: a = [1, 4, 4, 10, 10, 15, 20], target = 10
Output: 4

This problem is similar to [Find first position of target element in sorted array](find-first-position-of-target-element-in-sorted-array).

Solution

A brute force solution involves scanning the entire array and comparing each A[index] with the key. If A[index] is equal to the key and the next element is different, return the index. The worst-case time complexity of this method is ( O(N) ). Can we improve this? And the answer is yes, using [Binary Search on Sorted Array](binary-search-on-sorted-array).

Method 1 - Binary Search

If target == a[mid], update lastPosition to mid. However, to find the very last occurrence of the target, continue checking the right part of the array to see if the target appears at a higher position.

Code

Java

public int binarySearchLastPosition(int[] a, int target) {
	int start = 0;
	int end = a.length-1;

	int lastPosition = -1;
	while(start <= end) {
		int mid = (start + end)/2;

		if(target == a[mid]) {
			// Found target, update lastPosition and move to the right to find a higher position by setting start=mid+1
			lastPosition = mid;
			start = mid+1;
		} else if (target < a[mid]) {
			end = mid-1;
		} else {
			start = mid+1;
		}
	}

	return lastPosition;
}