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POParenthesizing a string so that expression takes a given value
 

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    <p>The following problem is from the chapter on Dynamic Programming by Vazirani et. al.</p> <hr> <p>[6.6]Let us define a multiplication operation(×) on three symbols a; b; c according to the following table:</p> <p><img src="https://i.imgur.com/HcUWS.png" alt="Multiplication table"></p> <p>Therefore, a × a = b , a × b = b etc.</p> <p>Find an efficient algorithm that examines a string of these symbols, say bbbbac, and decides whether or not it is possible to parenthesize the string in such a way that the value of the resulting expression is a. For example, on input bbbbac your algorithm should return yes because ((b(bb))(ba))c = a.</p> <hr> <p>Here is my approach: Map it to the problem of counting the number of boolean parenthesizations as given <strong><a href="https://stackoverflow.com/questions/6701812/counting-boolean-parenthesizations-implementation">here</a></strong>. In that problem, you are given a boolean expression of the form</p> <p>T <em>or</em> F <em>and</em> T <em>xor</em> T</p> <p>and you need to find the number of ways of parenthesizing this so that it evaluates to true. </p> <p>We can think of <em>or</em> , <em>and</em> , <em>xor</em> as operators which follow certain rules (T <em>xor</em> F = T etc.) and act on operands taking values T or F. For our original problem, we can think of a,b,c as operands with multiplication(x) <em>as defined by the given table</em> as providing the rules. </p> <p>Does the above approach make sense or is there a simpler approach ? </p>
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    1. COIf it's from a chapter on dynamic programming.. you should try using dynamic programming.
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    2. CO@Nabb: The boolean parenthesization problem I mention already has a dynamic programming formulation. My question contains the link to the SO question which shows the DP formulation.
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