You have n identical flowers, which you would like to place into k vases, according to the following rules: • Each flowe

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You have n identical flowers, which you would like to place intok vases, according to the following rules: • Each flower must beplaced in a vase. • The ith vase (where 1 ≤ i ≤ k) must contain atleast 1 and at most fi flowers. • No two vases are allowed tocontain the same number of flowers. Your goal is to assign a numberof flowers to each vase following the above rules, or to determinethat no such assignment exists. 1.1 [10 marks] Suppose that f1 = .. . = fk = n. Design an algorithm which runs in O(k) time andachieves the goal. 1.2 [10 marks] Now we return to the originalproblem, in which the fi can take any positive integer values.Design an algorithm which runs in O(k log k) time and achieves thegoal.
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