34 votes

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 ___.

15 votes

Best answer

$A = B + C$

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 $2\;( 1 + 1 = 2 )$

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

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

19 votes

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 $+ ---> 3+3=6$

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 $+ ---> 3+3=6$

11 votes

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

0

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.

5

check this @sutanay3

for clarity image https://drive.google.com/open?id=188C6_9ckbY637fKagbg76fUKS-fxpqNv

5 votes

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

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

1 vote

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**

1 vote

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...