## Determine Whether Two Strings Are Isomorphic ### Problem Implement `areIsomorphic(source, target) -> result`. Two strings are isomorphic when every character in `source` can be replaced consistently to obtain `target`, while preserving position. Each source character must map to exactly one target character, and two different source characters may not map to the same target character. Return `true` when the strings are isomorphic and `false` otherwise. ### Function Contract - Python: `def areIsomorphic(source: str, target: str) -> bool` - JavaScript: `function areIsomorphic(source, target)` returns a Boolean. - Java: `boolean areIsomorphic(String source, String target)` - C++: `bool areIsomorphic(const string& source, const string& target)` ### Portable Contract - Each input contains only printable ASCII characters U+0020 through U+007E. - `0 <= source.length, target.length <= 90,000`. - Different lengths return `false`; two empty strings return `true`. - Character identity is exact and case-sensitive. - Spaces and punctuation are ordinary characters and participate in the mapping. - Do not modify either string. - Let `B` be the compact UTF-8 JSON byte length of `[source,target]`, with no whitespace outside strings. Quotes and reverse solidus characters use their shortest required JSON escapes, and every bracket, comma, quote, escape, and character byte is counted. Inputs satisfy `B <= 96,000`. - The serialized Boolean result uses four or five bytes, so input plus output is at most `96,005` bytes. - Target `O(source.length + target.length)` time and `O(1)` auxiliary space for the fixed printable-ASCII alphabet. ### Examples ```text source = "egg" target = "add" result = true ``` ```text source = "foo" target = "bar" result = false ``` ```text source = "paper" target = "title" result = true ``` ```text source = "ab" target = "aa" result = false ``` ```hint Check the relationship in both directions Consistency from source to target is not enough when two distinct source characters try to claim the same target character. ``` ### Discussion Requirements 1. State the invariant maintained after processing each aligned character pair. 2. Explain why one forward map alone accepts an invalid many-to-one mapping. 3. Cover empty strings, unequal lengths, repeated characters, spaces, punctuation, and case differences. 4. Explain how fixed-size ASCII tables keep memory constant as input grows. 5. Describe how to process very large strings in synchronized chunks without resetting mapping state between chunks.