Subset Sum Problem (Backtracking)
Find if there exists a subset of given array that sums to a target value
Subset Sum Problem
The Subset Sum problem asks whether there exists a subset of a given set of integers that sums to a specific target value.
Theory & Concepts
Definition:
Given a set of positive integers and a target sum, determine if there exists a subset whose elements sum exactly to the target.
Key Points:
- NP-Complete problem - no known polynomial solution
- Backtracking explores all possible subset combinations
- Pruning optimization: stop if current sum exceeds target
- Can be solved using dynamic programming for optimization
Applications:
- Partition problems in computer science
- Resource allocation and budget planning
- Cryptography and number theory
- Combinatorial optimization problems
University Guidelines
Exam Weightage
6-8 marks MarksSyllabus Coverage:
- Subset sum problem formulation
- Backtracking approach implementation
- Include/exclude decision tree
- Pruning strategies and optimization
- Complexity analysis
Common Questions:
- Find subset with given sum using backtracking
- Trace algorithm execution with decision tree
- Implement subset sum with pruning
- Compare with dynamic programming approach
Exam Tips:
Show include/exclude decisions clearly
Demonstrate pruning when sum exceeds target
Draw decision tree for small examples
Mention exponential time complexity O(2^n)
Algorithm Details
O(2^n) - explores all possible subsets
Time Complexity
O(n) for recursion stack depth
Space Complexity
Algorithm Steps:
- 1Start with empty subset, index 0, sum 0
- 2For each element, make two recursive calls:
- 3 1. Include current element (add to subset and sum)
- 4 2. Exclude current element (move to next index)
- 5Base cases: sum equals target (found) or index >= array length
- 6Pruning: if current sum > target, stop exploration
- 7Return true if any path finds the target sum
Configure Subset Sum
Current Problem:
Array:
3[0]
34[1]
4[2]
12[3]
5[4]
2[5]
Target Sum:9
Array Sum:60
Search Results
🎯
Configure the array and target sum, then click "Find Subset" to start the search