We use a flexible sliding window template because the best window length is not known in advance. Let l be the left boundary and let last_occurrence[ch] store the most recent index of each character in the current window. As we move r from left to right, we update last_occurrence[s[r]] = r.

The window is valid when it contains at most two distinct characters. If adding s[r] makes the map size 3, the window is invalid and we must remove one character type completely. The best character type to remove is the one with the smallest last occurrence, because it appears farthest to the left. So we set l = min(last_occurrence.values()) + 1 and delete that character from the map. After this update, the window is valid again and still as large as possible.

On each step, update max_len with r - l + 1.

Implementation

def lengthOfLongestSubstringTwoDistinct(self, s):
    last_occurrence = dict()
    max_len, l = 0, 0
    for r in range(len(s)):
        last_occurrence[s[r]] = r
        r += 1
        if len(last_occurrence) == 3:
            l = min(last_occurrence.values())+1
            del last_occurrence[s[l-1]]
        max_len = max(max_len, r - l)
    return max_len

We want to use a sliding window to find the substrings with two distint characters.