algorithm

4. Consider the problem of weighing an integer amount n using the fewest number of weight pieces. We have 4 types of weight pieces; 1kg,5kg,10kg, and 25kg. Assume any weight piece is infinitely available. A greedy algorithm iteratively selects the largest weight piece that does not take us past the amount to be weighed, decreases the amount to be weighed by the weight of the selected piece, and continues iteratively. For instance to weigh 123 kilograms, the greedy algorithm selects the weight pieces in the following order: 25+25+25+25+10+ 10+1+1+1, making use of a total of 9 weight pieces. Prove or disprove whether the greedy algorithm provides the optimum solution for any value of n. 5. Repeat Question 4, this time assuming that the available types of weights are w0,w1,,wk for some integers w>1,k1. 6. [10pts] Consider the same problem defined in Question 4. This time give a set of types of weights for which the greedy algorithm does not yield an optimal solution. Note that your set should include 1kg weights so that there is a solution for every value of n