Sum of subsets problem by backtracking
- 1. Sum of Subsets Problem By Backtracking Presentation by Hasanain ALshadoodee Backtracking
- 2. 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. Presentation by_Hasanain ALshadoodee 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
- 4. 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 Presentation by_Hasanain ALshadoodee 4
- 5. Example n= 4 W{1:4}= {5,10,15,20} m= 25 Presentation by_Hasanain ALshadoodee 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
- 6. Think and Write Presentation by_Hasanain ALshadoodee 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
- 7. subset sum problem using backtracking python Code Answer Presentation by_Hasanain ALshadoodee 7
- 8. Another Example Presentation by_Hasanain ALshadoodee 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. Presentation by_Hasanain ALshadoodee 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 3