We can make a sorting routine using merge. Divide and conquer is a technique for solving a large problem by breaking it into two smaller problems, until the problems become easy. If we cut the problem in half each time, the solution will be O(log(n)) or O(n · log(n)).

• If divide-and-conquer cuts the problem in half at each step, the problem size will decrease very fast: by a factor of 1,000 in 10 steps, a factor of 1,000,000 in 20 steps, a factor of 1,000,000,000 in 30 steps.

• We soon reach a problem of size 1, which is usually easy to solve.

• Time will be O(log(n)) if we only process one of the halves, as in binary search.

• Time will be O(n · log(n)) if we process both halves, as in sorting.

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