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    <title>Bipartite-Matching on iAlgorithm</title>
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      <title>Hall&#39;s Marriage Theorem: Intuition, Proofs, and Competitive Programming Applications</title>
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      <description>A complete guide to Hall&amp;#39;s Marriage Theorem for bipartite matching, featuring two rigorous proofs (Halmos–Vaughan induction and augmenting paths), generalizations to k-matching and defect formulas, and a full walkthrough of AtCoder ARC106E - Medals.</description>
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