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fix: resolve binary addition and substring issues in Karatsuba algorithm #2851

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fix: resolve binary addition and substring issues in Karatsuba algorithm #2851

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Commits on Oct 17, 2024

  1. fix: resolve binary addition and substring issues in Karatsuba algorithm 

    fix: correct binary addition and substring handling in the Karatsuba algorithm

- Fixed the `add_strings` function to handle binary addition correctly.
- Improved the `safe_substr` function to manage leading zeros and extract substrings properly.
- Ensured correct bit shifting by using `1LL <<` for 64-bit integers.
- Added comprehensive self-tests to verify functionality.

This fixes incorrect results from the Karatsuba algorithm for binary multiplication.
    @ShanawazAlam007
    ShanawazAlam007 authored Oct 17, 2024
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