[Solved]Let S Say Two Arrays M N Containing Characters Set B C D E Assume Character Set Cost Assoc Q37132766

Let’s say we have two arrays m and n containing the charactersfrom the set a, b, c , d, e. Assume each character in the set has acost associated with it, consider the costs to be a=1, b=3, c=4,d=5, e=7.

for example

m = [‘a’, ‘b’, ‘c’, ‘d’, ‘d’, ‘e’, ‘a’]n = [‘b’, ‘b’, ‘b’, ‘a’, ‘c’, ‘e’, ‘d’]

Suppose we would like to merge m and n to form a larger arrays.

An example of s array could be

s = [‘a’, ‘b’, ‘c’, ‘d’, ‘d’, ‘e’, ‘a’, ‘b’, ‘b’, ‘b’, ‘a’, ‘c’, ‘e’, ‘d’]

or

s = [‘b’, ‘a’, ‘d’, ‘d’, ‘d’, ‘b’, ‘e’, ‘c’, ‘b’, ‘a’, ‘b’, ‘a’, ‘c’, ‘e’]

If there are two or more identical characters adjacent to eachother a penalty is applied which is equal to: number of adjacentcharacters of the same type * the cost for that character. Considerthe second example for s above which contains a sub-array [‘d’,’d’, ‘d’]. In this case a penalty of 3*5 will be applied becausethe cost associated with d is 5 and the number of repetitions of dis 3.

I need to design a dynamic programming algorithm which minimisesthe cost associated with s. What would the subproblems, recurrencesand base cases be? Any pointers on how this might be done would beappreciated!

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