Return a new string that sorts between two given strings

Question

Given two strings a and b, where a is lexicographically < b, I\'d like to return a string c such that a < c < b. The use case is inserting a node in a database sort

Answer 1

This is a very simple way to achieve this and probably far from optimal (depending on what you call optimal of course).

I use only a and b. I suppose you could generalise this to use more letters.

Two simple observations:

1. Creating a new string that comes after another string is easy: just append one or more letters. E.g., abba < abbab.
2. Creating a new string that comes before another string x is only always guaranteed to be possible if x ends with b. Now, replace that b by an a and append one or more letters. E.g., abbab > abbaab.

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The algorithm is now very simple. Start with a and b as sentinels. Inserting a new key between two existing keys x and y:

• If x is a prefix of y: the new key is y with the ending b replaced by ab.
• If x is not a prefix of y: the new key is x with a b appended.

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Example run:

a, b
a, ab*, b
a, aab*, ab, b
a, aab, ab, abb*, b
a, aab, ab, abab*, abb, b
a, aaab*, aab, ab, abab, abb, b