def find_longest_substring(string):
    # Dictionary that maps characters (treated as keys) to their most recent index,
    # so we don't re-examine them later. This speeds up the process of checking if a character was added in the current window.
    seen_indices = {}
    
    longest_start, longest_end = 0, 0
    for i, char in enumerate(string):
        # If this is a new start position (i.e., we're starting from an existing match and then see something new), save it to the dictionary.
        if string[longest_start:longest_end+1] == longest_match:
            seen_indices[char] = max(seen_indices.get(char, 0), i - len(longest_match))
        
        # If this is a new character that hasn't been added before, start with an index of the current position.
        else:
            seen_indices[char] = i
        
        if i == longest_end:  # This means we've reached the end of our match.
            longest_start += len(longest_match) + 1
            longest_end += len(longest_match)
            
    return string[longest_start : longend]

# Test it out!
print(find_longest_substring("abcabcbb"))  # Should print "abc"