Brackets around expression max value
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I was working on a problem https://www.spoj.com/problems/LISA/
In the problem, the expression is given which has only operators (+,*). Putting brackets we need to get maximum value possible. First thing came in my mind putting brackets around + will maximize the value. But it's not working for all cases. Like in below example
1+2*3+4*5 = (1+2)*(3+4)*5 = 105
2*0*3+7+1*0*3 = 2*((0*3+7+1*0)*3) = 42 ( putting bracket arount not solve the problem )
Can you help me to derive the best way to put brackets around the expression?
I came across a dynamic problem way of solving the problem
f(ci,cj) = Max( f(i,j-1) operator c(i,j) , f( i+1,j-1) operator c(i,i) )
Like 3,5 = Max of [ (3,4) * (5,5) or (3,3)+(4,5) ]
= Max of [ 7*5 or 3+20 ]
= Max of [ 35,23 ] = 35
-----------------------------------
C1 C2 C3 C4 C5
C1 1 3 9 13 105
C2 2 6 14 70
C3 3 7 35
C4 4 20
C5 5
Above DP table gives correct result can someone provide proof that it gives maximum value?
linear-algebra abstract-algebra logic dynamic-programming
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up vote
0
down vote
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I was working on a problem https://www.spoj.com/problems/LISA/
In the problem, the expression is given which has only operators (+,*). Putting brackets we need to get maximum value possible. First thing came in my mind putting brackets around + will maximize the value. But it's not working for all cases. Like in below example
1+2*3+4*5 = (1+2)*(3+4)*5 = 105
2*0*3+7+1*0*3 = 2*((0*3+7+1*0)*3) = 42 ( putting bracket arount not solve the problem )
Can you help me to derive the best way to put brackets around the expression?
I came across a dynamic problem way of solving the problem
f(ci,cj) = Max( f(i,j-1) operator c(i,j) , f( i+1,j-1) operator c(i,i) )
Like 3,5 = Max of [ (3,4) * (5,5) or (3,3)+(4,5) ]
= Max of [ 7*5 or 3+20 ]
= Max of [ 35,23 ] = 35
-----------------------------------
C1 C2 C3 C4 C5
C1 1 3 9 13 105
C2 2 6 14 70
C3 3 7 35
C4 4 20
C5 5
Above DP table gives correct result can someone provide proof that it gives maximum value?
linear-algebra abstract-algebra logic dynamic-programming
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I was working on a problem https://www.spoj.com/problems/LISA/
In the problem, the expression is given which has only operators (+,*). Putting brackets we need to get maximum value possible. First thing came in my mind putting brackets around + will maximize the value. But it's not working for all cases. Like in below example
1+2*3+4*5 = (1+2)*(3+4)*5 = 105
2*0*3+7+1*0*3 = 2*((0*3+7+1*0)*3) = 42 ( putting bracket arount not solve the problem )
Can you help me to derive the best way to put brackets around the expression?
I came across a dynamic problem way of solving the problem
f(ci,cj) = Max( f(i,j-1) operator c(i,j) , f( i+1,j-1) operator c(i,i) )
Like 3,5 = Max of [ (3,4) * (5,5) or (3,3)+(4,5) ]
= Max of [ 7*5 or 3+20 ]
= Max of [ 35,23 ] = 35
-----------------------------------
C1 C2 C3 C4 C5
C1 1 3 9 13 105
C2 2 6 14 70
C3 3 7 35
C4 4 20
C5 5
Above DP table gives correct result can someone provide proof that it gives maximum value?
linear-algebra abstract-algebra logic dynamic-programming
I was working on a problem https://www.spoj.com/problems/LISA/
In the problem, the expression is given which has only operators (+,*). Putting brackets we need to get maximum value possible. First thing came in my mind putting brackets around + will maximize the value. But it's not working for all cases. Like in below example
1+2*3+4*5 = (1+2)*(3+4)*5 = 105
2*0*3+7+1*0*3 = 2*((0*3+7+1*0)*3) = 42 ( putting bracket arount not solve the problem )
Can you help me to derive the best way to put brackets around the expression?
I came across a dynamic problem way of solving the problem
f(ci,cj) = Max( f(i,j-1) operator c(i,j) , f( i+1,j-1) operator c(i,i) )
Like 3,5 = Max of [ (3,4) * (5,5) or (3,3)+(4,5) ]
= Max of [ 7*5 or 3+20 ]
= Max of [ 35,23 ] = 35
-----------------------------------
C1 C2 C3 C4 C5
C1 1 3 9 13 105
C2 2 6 14 70
C3 3 7 35
C4 4 20
C5 5
Above DP table gives correct result can someone provide proof that it gives maximum value?
linear-algebra abstract-algebra logic dynamic-programming
linear-algebra abstract-algebra logic dynamic-programming
asked Nov 20 at 7:48
Sumeet
1156
1156
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