Question $1$: Cousider the Dufferentrated Set Coteruge Problem

Input: $n$ items, $U=(1,2,$dots,$n),$ covriage requirments of the items $f=(f_1,f_2,$dots,$f_0)m$ rets, $S_1,S_2,$dots,$S_m.$ price of the sets $p=(p_1,B_2$dots..,$p_2)$

Let $x=(x_1,x_2$dots,$x_n)$ be the selection derision of the $a_t,x_{1}in\{0,1\}.$

Output: A minimum price selection $x$ of the sets $S_1,S_2,$dots,$S_n$ that can cover the items. $U$ at least $f$ times

Ex: Let $n=5$ and $U=($:$1,2,3,4,5$:$)$ having coverage requirements $f=(1,2,1,2,1).$

Let $m=5$ and $S_1=\{1,2\},S_2=\{2,3,4\},S_3=\{2,5\},S_4=\{3,4\},S_3=\{1,4\}$ wit prices $p=(5,6,10,2,4).$

For instance, item $j=2$inU should be covered by at least $f_2=2$ different sets $S_{.}.$ note that item $2$ can be covered by $S_1$ with price $p_1=5$ by $S_2$ with price $p_2=6$ and by with price $p_3=10$

Determine a greedy selection rule for the sets. Design a greedy algoritim for th Differentiated Set Conerage Problem and report the pseudocode.

Discuss the time complexity of your greody algorithm Is it efficient? Can you algorithm find fie optimum solution?

Irrploment your algoritim in Python. Use the input given in the example ard repor the console outputs and your Python code scripts.