如何用正则表达式求解方程3x+2y=14？求技术解答

Great question—using regular expressions to solve linear Diophantine equations is such a clever, counterintuitive trick! Let’s unpack both of your confusion points clearly:

Why match a string of 14 '1's? #

The core idea here is to translate the algebraic equation into a counting problem with strings. Let’s break it down:

• 3x represents x groups of 3 identical items (we use '1's here for simplicity)
• 2y represents y groups of 2 identical items
• The total number of items adds up to 14

By creating a string of 14 consecutive '1's, we give the regex a concrete "pool" of items to split into groups of 3 and 2. If the regex can successfully match the entire string by splitting it into these groups, that means we’ve found valid non-negative integers x and y that satisfy the equation.

What regex goes in const r = /.../? #

The regex needs to match any combination of 3-'1' groups and 2-'1' groups that add up to exactly 14 characters. Here’s the correct pattern:

const r = /^(?:111)*(?:11)*$/;

Let’s break down each part:

• ^ and $: Anchors that ensure the regex matches the entire string (no extra characters before or after)
• (?:111)*: A non-capturing group that matches 0 or more sequences of three '1's. The number of times this group repeats is your x value.
• (?:11)*: Another non-capturing group that matches 0 or more sequences of two '1's. The number of times this group repeats is your y value.

This regex will only match strings where the total length is 3x + 2y. Since we’re feeding it a 14-'1' string, it will only return a match if x and y are valid solutions to 3x + 2y = 14 (like x=4, y=1; x=2, y=4; x=0, y=7).

If you wanted to extract the actual values of x and y, you could modify the regex to use capturing groups and count the matches, but the core pattern above is what checks for valid solutions.

内容的提问来源于stack exchange，提问作者FrankDrebbin