Using Binary Search with sorted Array with duplicates

Question

I've been tasked with creating a method that will print all the indices where value x is found in a sorted array.

I understand that if we just scanned through the array from 0 to N (length of array) it would have a running time of O(n) worst case. Since the array that will be passed into the method will be sorted, I'm assuming that I can take advantage of using a Binary Search since this will be O(log n). However, this only works if the array has unique values. Since the Binary Search will finish after the first "find" of a particular value. I was thinking of doing a Binary Search for finding x in the sorted array, and then checking all values before and after this index, but then if the array contained all x values, it doesn't seem like it would be that much better.

I guess what I'm asking is, is there a better way to find all the indices for a particular value in a sorted array that is better than O(n)?

public void PrintIndicesForValue42(int[] sortedArrayOfInts)
{
    // search through the sortedArrayOfInts

    // print all indices where we find the number 42. 
}

Ex: sortedArray = { 1, 13, 42, 42, 42, 77, 78 } would print: "42 was found at Indices: 2, 3, 4"

Answer 1

You will get the result in O(lg n)

public static void PrintIndicesForValue(int[] numbers, int target) {
    if (numbers == null)
        return;

    int low = 0, high = numbers.length - 1;
    // get the start index of target number
    int startIndex = -1;
    while (low <= high) {
        int mid = (high - low) / 2 + low;
        if (numbers[mid] > target) {
            high = mid - 1;
        } else if (numbers[mid] == target) {
            startIndex = mid;
            high = mid - 1;
        } else
            low = mid + 1;
    }

    // get the end index of target number
    int endIndex = -1;
    low = 0;
    high = numbers.length - 1;
    while (low <= high) {
        int mid = (high - low) / 2 + low;
        if (numbers[mid] > target) {
            high = mid - 1;
        } else if (numbers[mid] == target) {
            endIndex = mid;
            low = mid + 1;
        } else
            low = mid + 1;
    }

    if (startIndex != -1 && endIndex != -1){
        for(int i=0; i+startIndex<=endIndex;i++){
            if(i>0)
                System.out.print(',');
            System.out.print(i+startIndex);
        }
    }
}