Problem Statement
Partition Equal Subset Sum
Given an integer array nums, return true if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or false otherwise.
Examples
Example 1:
Input: nums = [1, 5, 11, 5]
Output: true
Explanation: The array can be partitioned as [1, 5, 5] and [11].
Example 2:
Input: nums = [1, 2, 3, 5]
Output: false
Explanation: The array cannot be partitioned into equal sum subsets.
Constraints
- 1 <= nums.length <= 200
- 1 <= nums[i] <= 100
Problem Breakdown
To solve this problem, we need to:
- This problem is equivalent to finding if there exists a subset of the array with a sum equal to half of the total sum.
- If the total sum is odd, it's impossible to partition the array into two equal subsets.
- This is a variation of the 0/1 Knapsack problem, which can be solved using dynamic programming.
- We can use a 1D or 2D DP array to keep track of which sums are possible to achieve with the given numbers.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Partition Equal Subset Sum
Given an integer array nums, return true if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or false otherwise.
Examples
Example 1:
The array can be partitioned as [1, 5, 5] and [11].
Example 2:
The array cannot be partitioned into equal sum subsets.
Problem Breakdown
Constraints:
- 1 <= nums.length <= 200
- 1 <= nums[i] <= 100
Key Insights:
This problem is equivalent to finding if there exists a subset of the array with a sum equal to half of the total sum.
If the total sum is odd, it's impossible to partition the array into two equal subsets.
This is a variation of the 0/1 Knapsack problem, which can be solved using dynamic programming.
We can use a 1D or 2D DP array to keep track of which sums are possible to achieve with the given numbers.
Real-World Application
This problem has several practical applications:
Resource Allocation
Dividing resources equally among two groups, such as assigning tasks to two teams with equal workload.
Load Balancing
Distributing data or processing load evenly across multiple servers or systems.
Fair Division
Dividing assets or items fairly between two parties, such as in divorce settlements or inheritance divisions.