Partition Equal Subset Sum in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Partition Equal Subset Sum problem?

To determine if a given list of positive integers can be split into two subsets with equal sums.

beginner

Why do we check if the total sum of the array is even in Partition Equal Subset Sum?

Because if the total sum is odd, it's impossible to split the array into two equal sum subsets.

intermediate

What does the dynamic programming table represent in the Partition Equal Subset Sum solution?

It represents whether a subset with a specific sum is possible using elements up to a certain index.

intermediate

In the DP approach, what does dp[i][j] = true mean?

It means that using the first i numbers, we can form a subset with sum exactly j.

intermediate

What is the time complexity of the typical DP solution for Partition Equal Subset Sum?

O(n * sum/2), where n is the number of elements and sum is the total sum of the array.

What should you do first when solving Partition Equal Subset Sum?

A Check if the total sum is even

B Sort the array

C Find the maximum element

D Calculate the product of all elements

Checking if the total sum is even helps quickly decide if partitioning is possible.

If the total sum of the array is 20, what sum should each subset have for equal partition?

A 20

B 10

C 5

D 15

Each subset must sum to half of the total sum, so 20 / 2 = 10.

In DP, what does it mean if dp[i][j] is false?

A Subset sum j is zero

B Subset sum j is possible with first i elements

C Sum j is greater than total sum

D No subset of first i elements sums to j

False means no subset with sum j can be formed using first i elements.

Which approach is commonly used to solve Partition Equal Subset Sum efficiently?

A Dynamic Programming

B Brute Force without memoization

C Greedy Algorithm

D Divide and Conquer

Dynamic Programming efficiently checks subset sums avoiding repeated work.

What is the space optimization technique often applied in DP for this problem?

A Use recursion without memoization

B Sort the array first

C Use a 1D boolean array instead of 2D

D Use a stack to store subsets

A 1D boolean array can track achievable sums, reducing space from O(n*sum) to O(sum).

Explain how dynamic programming helps solve the Partition Equal Subset Sum problem.

Think about how you track which sums can be formed as you add numbers.

Describe the steps to determine if an array can be partitioned into two equal sum subsets.

Start with sum checks, then focus on subset sum problem.

Practice

1. What does the Partition Equal Subset Sum problem ask you to find?

easy

A. If the array can be split into two subsets with equal sums

B. If the array contains any duplicate elements

C. If the array is sorted in ascending order

D. If the array has an even number of elements

Solution

1. Step 1: Understand the problem goal

   The problem asks whether the given array can be divided into two parts where the sum of elements in both parts is the same.

2. Step 2: Clarify what is being checked

   It is not about duplicates, sorting, or count of elements, but about equal sum partitioning.

3. Final Answer:

   If the array can be split into two subsets with equal sums -> Option A

4. Quick Check:

   Partition Equal Subset Sum = Split into equal sum subsets [OK]

Hint: Focus on equal sum subsets, not element order or duplicates [OK]

Common Mistakes:

• Thinking it checks for duplicates
• Confusing with sorting problems
• Assuming it checks array length parity

2. Which of the following TypeScript function signatures correctly represents a function to solve Partition Equal Subset Sum?

easy

A. function canPartition(nums: boolean[]): boolean

B. function canPartition(nums: string): number

C. function canPartition(nums: number): string

D. function canPartition(nums: number[]): boolean

Solution

1. Step 1: Identify correct parameter type

   The input is an array of numbers, so nums: number[] is correct.

2. Step 2: Identify correct return type

   The function returns true or false, so return type is boolean.

3. Final Answer:

   function canPartition(nums: number[]): boolean -> Option D

4. Quick Check:

   Input array of numbers, output boolean [OK]

Hint: Input is number array, output is boolean for yes/no [OK]

Common Mistakes:

• Using wrong input type like string or boolean array
• Returning number instead of boolean
• Incorrect function signature syntax

3. What is the output of the following TypeScript code?

function canPartition(nums: number[]): boolean {
  const total = nums.reduce((a, b) => a + b, 0);
  if (total % 2 !== 0) return false;
  const target = total / 2;
  const dp = new Array(target + 1).fill(false);
  dp[0] = true;
  for (const num of nums) {
    for (let j = target; j >= num; j--) {
      dp[j] = dp[j] || dp[j - num];
    }
  }
  return dp[target];
}

console.log(canPartition([1, 5, 11, 5]));

medium

A. Runtime error

B. true

C. undefined

D. false

Solution

1. Step 1: Calculate total sum and check parity

   The sum is 1+5+11+5 = 22, which is even, so continue.

2. Step 2: Use dynamic programming to check subset sum

   The code checks if a subset sums to 11 (half of 22). The subset [11] or [5,5,1] sums to 11, so dp[11] becomes true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Sum even and subset exists = true [OK]

Hint: Check if half sum subset exists using dp array [OK]

Common Mistakes:

• Not checking if total sum is even
• Confusing dp array update direction
• Assuming false because of large numbers

4. Find the bug in this TypeScript code for Partition Equal Subset Sum:

function canPartition(nums: number[]): boolean {
  const total = nums.reduce((a, b) => a + b);
  if (total % 2 !== 0) return false;
  const target = total / 2;
  const dp = new Array(target + 1).fill(false);
  dp[0] = true;
  for (const num of nums) {
    for (let j = num; j <= target; j++) {
      dp[j] = dp[j] || dp[j - num];
    }
  }
  return dp[target];
}

medium

A. Missing initial value in reduce causes error on empty array

B. dp array size is incorrect

C. Loop direction in inner for loop should be reversed

D. No bug, code is correct

Solution

1. Step 1: Check reduce usage

   Reduce lacks initial value, but if array is non-empty, it works. Not the main bug.

2. Step 2: Check inner loop direction

   The inner loop runs from num to target increasing, but it should run backward from target down to num to avoid using updated dp values in the same iteration.

3. Final Answer:

   Loop direction in inner for loop should be reversed -> Option C

4. Quick Check:

   Inner loop must go backward to avoid dp overwrite [OK]

Hint: Inner loop for dp must run backward to prevent reuse [OK]

Common Mistakes:

• Not reversing inner loop causes wrong dp updates
• Assuming reduce always needs initial value
• Ignoring dp array size correctness

5. Given the array [2, 2, 3, 7], which of the following subsets can be one half of the partition if the array can be split into two equal sum subsets?

hard

A. [2, 2, 3]

B. [2, 3]

C. [5]

D. [3, 5]

Solution

1. Step 1: Calculate total sum

   Sum = 2 + 2 + 3 + 7 = 14. Half sum = 7.

2. Step 2: Find subset summing to 7

   Check each option:
   A: [2,3] = 5 ≠ 7
   B: [2,2,3] = 7 == 7
   C: [5] = 5 ≠ 7 (5 not in array)
   D: [3,5] = 8 ≠ 7 (5 not in array)
   B works, with remaining [7] also 7.

3. Final Answer:

   [2, 2, 3] -> Option A

4. Quick Check:

   Sum half is 7, B sums to 7 [OK]

Hint: Sum array, find subset with half sum [OK]

Common Mistakes:

• Not calculating half sum correctly
• Choosing subsets that don't sum to half
• Ignoring that partition may not exist