Introduction

In this blog post, we will explore how to solve the LeetCode problem "494" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer array nums and an integer target. You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers. For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1". Return the number of different expressions that you can build, which evaluates to target. Example 1: Input: nums = [1,1,1,1,1], target = 3 Output: 5 Explanation: There are 5 ways to assign symbols to make the sum of nums be target 3. -1 + 1 + 1 + 1 + 1 = 3 +1 - 1 + 1 + 1 + 1 = 3 +1 + 1 - 1 + 1 + 1 = 3 +1 + 1 + 1 - 1 + 1 = 3 +1 + 1 + 1 + 1 - 1 = 3 Example 2: Input: nums = [1], target = 1 Output: 1 Constraints: 1 <= nums.length <= 20 0 <= nums[i] <= 1000 0 <= sum(nums[i]) <= 1000 -1000 <= target <= 1000

Explanation

Here's the breakdown of the solution and the Python code:

• High-Level Approach:

  • The problem can be transformed into a subset sum problem. Instead of assigning '+' or '-', we can think of dividing the array into two subsets: one where we add the numbers (positive subset) and one where we subtract the numbers (negative subset).
  • The sum of the positive subset (sum_positive) and the sum of the negative subset (sum_negative) must satisfy sum_positive - sum_negative = target. Also, sum_positive + sum_negative = sum(nums). Solving for sum_positive, we get sum_positive = (target + sum(nums)) / 2.
  • The problem now becomes finding the number of subsets of nums that sum up to sum_positive. We can solve this using dynamic programming.

• Complexity:

  • Runtime: O(n * sum), where n is the length of nums and sum is the sum of elements in nums.
  • Storage: O(sum)

Code

    def findTargetSumWays(nums, target):
    """
    Finds the number of different expressions that can be built from nums
    to evaluate to target.
    """
    total_sum = sum(nums)

    # If the target is unreachable
    if (total_sum + target) < 0 or (total_sum + target) % 2 != 0:
        return 0

    subset_sum = (total_sum + target) // 2

    # Initialize DP table
    dp = [0] * (subset_sum + 1)
    dp[0] = 1  # Empty subset sums to 0 in one way

    # Iterate over numbers
    for num in nums:
        for j in range(subset_sum, num - 1, -1):  # Iterate backwards to avoid overcounting
            dp[j] += dp[j - num]

    return dp[subset_sum]