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The following recurrence often arises in divide-and-conquer algorithms, where the processes involve dividing, solving, and combining....

The following recurrence often arises in divide-and-conquer algorithms, where the processes involve dividing, solving, and combining.

?(1) = 1

?(?) = 2 ?(?/2) + ? log?, ??? ?>1, Where ? is a power of 2. Prove that ?(?)= ? (? (log ?)^2) using substitution method.

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