Modified binary search - find smallest index - need to evaluate the idea to find smallest index.

BinarySearch_FindSmallestIndex.cs

using System;

class Solution
{
    public static int IndexEqualsValueSearch(int[] arr)
    {
      if (arr.Length == 0)
      {
        return -1;
      }

      var startIndex = 0;
      var endIndex   = arr.Length - 1;
      var found = -1;
      
      while(endIndex - startIndex >= 0)
      {
        var middle = startIndex + (endIndex - startIndex)/2;
        
        if (arr[middle] == middle)
        {
          found = middle;
          endIndex = middle - 1;
        }
        else if(arr[middle] < middle)
        {
          startIndex = middle + 1;
        }
        else
        {
          endIndex = middle - 1;
        }
      }
      
      return found;
    }

    static void Main(string[] args)
    {
      Console.WriteLine(IndexEqualsValueSearch(new int[]{1, 2, 3, 7, 8, 9, 10}));
    }
}

/*
[-8, 0, 2, 5] sorted distince arr[i] < arr[j], increment at least 1

[0, 1, 2, 3]  always increment one. 

[-8, -1, 0, 2] -> are you supposed to check that it is not descending?

return lowest index i 

*/