Searcher.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Sample.WithLimits
{
    class UppercaseSearcher
    {
        internal static int[] Search(string source)
        {
            return Search(source, 0);
        }

        internal static int[] Search(string source, int index)
        {
            if (IsOutOfBounds(source, index))
            {
                return new int[0];
            }

            if (char.IsUpper(source, index))
            {
                return new int[] { index }
                    .Concat(Search(source, index + 1))
                    .ToArray();
            }
            else
            {
                return Search(source, index + 1)
                    .ToArray();
            }
        }

        private static bool IsOutOfBounds(string source, int index)
        {
            return source.Length == 0 || index >= source.Length;
        }
    }
}

Test.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Xunit;

namespace Sample.WithLimits
{
    public class TestClass
    {
        [Fact]
        public void ShouldReturnEmptyArray()
        {
            //Arrange, act, assert
            Assert.Equal(new int[0], UppercaseSearcher.Search(""));
        }

        [Fact]
        public void ShouldReturn0IfOneLetterIsUppercase()
        {
            //Arrange, act, assert
            Assert.Equal(new int[] {0}, UppercaseSearcher.Search("A"));
        }

        [Fact]
        public void ShouldReturn1IfSecondLetterIsUppercase()
        {
            //Arrange, act, assert
            Assert.Equal(new int[] { 1 }, UppercaseSearcher.Search("bA"));
        }
    }
}