Sum of subsets problem by backtracking

Sum of Subsets Problem
By
Backtracking
Presentation by
Hasanain ALshadoodee
Backtracking

Learning Outcomes
At the end of session viewers will be to
 Apply backtracking approach to solve sum of subsets problem
Presentation by_Hasanain ALshadoodee
2

3
Introduction
 We are given n distinct positive numbers (weights)
 The objective is to find all combination of weights whose
sum is equal to given weights m
 State space tree is generated for all the possibilities of
the subsets
 Generate the tree by keeping weight <= m

Example
Consider the example given below
n= 4
W{1:4}= {5,10,15,20}
m= 25
Find the sum of subset equal to m
4

Example
n= 4
W{1:4}= {5,10,15,20}
m= 25
5
0,50
5,45
15,35
30,20 15,20
35, 0 15, 0
5,35
5,20
25, 0
X1=1
X2=1
X3=1
X2=0
X3=0
X4=1 X4=0
X3=0
X4=1
Solution
X1,x2,x3,x4={1,0,0,1}
First node two value one the
value is the subset=0
And second value
Summation of all value
=5+10+15+20
=50
0+5=5 50-5=45
45-10=35
5+10=15

Think and Write
6
Find another subset which is equal to m where
n= 4
W{1:4}= {5,10,15,20}
m= 25
0,50
0,45
10,35
25,20
25, 0
Solution
X1,x2,x3,x4={0,1,1,0}
X1=0
X2=1
X3=1
X4=0
Without increase 50-5=45
45-10=35
0+10=10

subset sum problem using
backtracking python Code Answer
7

Another Example
8
the problem is to find a subset of a given set
S={S1,S2,……,Sn} of n positive integers whose sum is
equal to a given positive integer “ d “.
S1<=S2<=…….<=Sn

9
Ex.. For S={1,3,4,5} 2d=8
SLo={1,3,4}=8 SLo={3,5}=8
0
1
4
8 4
1
5 1
0
3
7 3
0
4 0
6 1 8
State Space Tree
X=3
X=1
X=4
X=5
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Presentation by_HasanainALshadoodee 10

Sum of subsets problem by backtracking

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