Question: Consider distinct numbers x 1 ,,x n each also with a positive weight w 1 ,,w n such that . The weighted median is the

Consider distinct numbers x₁,,x_n each also with a positive weight w₁,,w_n such that Consider distinct numbers x1,,xn each also with a positive weight w1,,wn such . The weighted median is the item x_k that satisfies that . The weighted median is the item xk that satisfies and and a) Show how to compute the weighted median of n items in

a) Show how to compute the weighted median of n items in worst case time O(nlogn) using sorting. Provide the algorithm and the efficiency analysis.

b) Show how to compute the weighted median in worst case time O(n) using a linear time median-finding algorithm as a black-box. Provide the algorithm and the efficiency analysis.

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