GATE CS 2014 Set 2 — Question 49
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Programming & Data Structures → Stacks & Queues → Expression Evaluation
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Question
Consider the expression tree shown. Each leaf represents a numerical value, which can either be 0 or 1. Over all possible choices of the values at the leaves, the maximum possible value of the expression represented by the tree is ___.
Correct answer
6 to 6
Solution
Let the values at the leaves be denoted by variables. Let's trace the operations from the bottom up or expand the expression from the root down.Let the leaves from left to right be .The structure of the tree is:
To maximize this expression, we should assign to variables with a positive coefficient and to variables with a negative coefficient.Positive coefficients: (Total 6 variables).
Negative coefficients: (Total 2 variables).Set and .Maximum Value .
- Root is .
- Left child of Root is . Right child of Root is .
- Left child () has children: Left () and Right ().
- The Left () has children . Value: .
- The Right () has children . Value: .
- So, Left Subtree Value = .
- Right child () has children: Left () and Right ().
- The Left () has children . Value: .
- The Right () has children . Value: .
- So, Right Subtree Value = .
- Root Value = Left Subtree Value + Right Subtree Value
To maximize this expression, we should assign to variables with a positive coefficient and to variables with a negative coefficient.Positive coefficients: (Total 6 variables).
Negative coefficients: (Total 2 variables).Set and .Maximum Value .
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