GATE2014-2-39

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 ___. 

Answer 1

An Expression Tree is a binary tree in which each internal node corresponds to operator and each leaf node corresponds to operand so for example expression tree for 3 + ((5+9)*2) would be:. Below diagram shows values to pick to get the maximum value in expresison tree

Comments

Can someone give me a good approach of how to think about such questions.It seems difficult to derive the correct answer in exam time.

Answer 2

ans is $6$

at left  leafs

$+$   $---> (1,1)=2$         intermediate $+ ---->  2-(-1)=3  $  

$-$   $---->(0,1)=-1$

at right leafs

$-$  minus $---->(1,0)=1$       intermediate   $+$    $----> 1+2=3$

$+$     $---->(1,1)=2$

 

at root   $+ ---> 3+3=6$

Answer 3

lets say every leaf denoted by x

then expression look like this (x + x)-(x - x)+(x - x)+(x +x )

                                        =  1     1  0   1     1   0    1   1 (this combination will give maxiumum value)

                                         = (1 + 1)-(0-1) + (1-0) + (1+1)=6

So answer is 6

Answer 4

A = B + C 

For A to be maximum, both B and C should be maximum

B = D - E

For B to be maximum, D should be maximum and E should be minimum

C = F + G

For C to be maximum, both F and G should be maximum

The maximum value of D is ( 1 + 1 = 2 )

The minimum  value of E is ( 0 - 1 = -1 )

The maximum value of F is 1 ( 1 - 0 = 1 )

The maximum value of G is 2 ( 1 + 1 = 2 )

B = 2 - ( -1 ) = 2 + 1 = 3

C = 1 + 2 = 3

A = B + C = 3 + 3 = 6

6  is the answer 

Answer 5

consider the leaves as any variable, let-Y

now use bottom up parsing method and traverse from  top to down and left to right and evaluate the expression in such a manner so that it will give maximum output. here it is :

[(Y+Y)-(Y-Y)]+[(Y-Y)+(Y+Y)] then select the values such that it will give you maximum throughput.

here values are 1  1 0 1 1 0 1 1      ,

so if you will put these values respectively in above expression you will get maximum output:  6

Answer 6

lets number the nodes from left to right as a,b,c,d,e,f,,g,h, respectively now the expression tree reduces to ((a+b)-(c-d))+((e-f)+(g+h))now we can easily see the possible values of variables to get the maximum value. here a+b so we can take a=b=1 and then -(c-d) so we would like to get negative value from c-d so that it becomes positive  and add to a+b value and so on...

Answer 7

answer - 5

for addition operation we have to maximize operands

for subtraction operation we have to minimize minuend

use these values to maximize value of expression

leftmost leaves = (1,1)

second leftmost leaves = (0, 0)

third left most leaves = (1, 0)

rightmost leaves = (1, 1)