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Number of Ways to Split Array - Step-by-Step Explanation

This README provides a detailed explanation of the solution for the problem "Number of Ways to Split Array". Below, we go through the thought process and steps for each implementation in C++, Java, JavaScript, Python, and Go.

🚀 Problem Description

Given an array nums, count the number of ways to split the array into two non-empty parts such that the sum of the left part is greater than or equal to the sum of the right part.

🧠 Intuition

The idea is to calculate the sum of the left and right parts of the array for each split point and check if the left sum is greater than or equal to the right sum. By using prefix sums, we can avoid recalculating sums repeatedly and ensure the solution is efficient.

🛠️ Approach

  1. Calculate the total sum of the entire array.
  2. Use a prefix sum to keep track of the cumulative sum of elements from the start up to the current index.
  3. At each split point (from index 0 to n-2), calculate the right sum as the difference between the total sum and the prefix sum.
  4. Check if the left sum (prefix sum) is greater than or equal to the right sum. If yes, increase the count of valid splits.
  5. Return the final count of valid splits.

📚 Step-by-Step Explanation

C++ Implementation

  1. Calculate the total sum: Start by iterating through the array to compute the total sum of all elements.
  2. Initialize variables: Use a prefix_sum to store the cumulative sum of the left part and a count to keep track of valid splits.
  3. Iterate through the array: For each split point, update the prefix sum with the current element.
  4. Compute the right sum: Subtract the prefix sum from the total sum to get the right part's sum.
  5. Check the condition: Compare the prefix sum with the right sum. If the prefix sum is greater than or equal to the right sum, increment the count.
  6. Return the result: Once the loop finishes, return the count of valid splits.

Java Implementation

  1. Calculate the total sum: Use a loop to compute the total sum of all elements in the array.
  2. Initialize variables: Create variables for prefixSum (to track the cumulative left sum) and count (to count valid splits).
  3. Iterate through the array: Loop from the start of the array to the second-to-last element.
  4. Update the prefix sum: Add the current element to the prefixSum during each iteration.
  5. Compute the right sum: Subtract the prefixSum from the totalSum to get the right part's sum dynamically.
  6. Check the condition: If the prefixSum is greater than or equal to the right sum, increment the count.
  7. Return the count: After the loop, return the total number of valid splits.

JavaScript Implementation

  1. Calculate the total sum: Use the reduce() function to compute the sum of all elements in the array.
  2. Initialize variables: Create variables prefixSum for the cumulative left sum and count to track valid splits.
  3. Iterate through the array: Use a for loop to traverse the array, stopping at the second-to-last element.
  4. Update the prefix sum: Add the current element to prefixSum in each iteration.
  5. Compute the right sum: Subtract prefixSum from totalSum to dynamically calculate the sum of the right part.
  6. Check the condition: Compare prefixSum with the right sum. If prefixSum is greater than or equal to the right sum, increment count.
  7. Return the count: At the end of the loop, return the total count of valid splits.

Python Implementation

  1. Calculate the total sum: Use Python's sum() function to find the sum of all elements in the array.
  2. Initialize variables: Create prefix_sum for the cumulative left sum and count to store the number of valid splits.
  3. Iterate through the array: Loop through the array, stopping before the last element.
  4. Update the prefix sum: Add the current element to prefix_sum during each iteration.
  5. Compute the right sum: Subtract the prefix_sum from the total_sum to get the right part's sum.
  6. Check the condition: If the prefix_sum is greater than or equal to the right sum, increment the count.
  7. Return the count: After the loop finishes, return the total count of valid splits.

Go Implementation

  1. Calculate the total sum: Use a for loop to compute the sum of all elements in the array.
  2. Initialize variables: Create prefixSum to store the left cumulative sum and count to track valid splits.
  3. Iterate through the array: Loop through the array, stopping before the last element.
  4. Update the prefix sum: Add the current element to prefixSum in each iteration.
  5. Compute the right sum: Subtract prefixSum from totalSum to dynamically compute the right sum.
  6. Check the condition: Compare prefixSum and the right sum. If prefixSum is greater than or equal to the right sum, increment count.
  7. Return the count: At the end of the loop, return the total number of valid splits.

⚙️ Complexity Analysis

  • Time Complexity:
    The algorithm runs in (O(n)) time, where (n) is the size of the array. This is because we iterate through the array once to calculate the total sum and once more to evaluate valid splits.

  • Space Complexity:
    The solution uses (O(1)) extra space since we only use a few variables (total_sum, prefix_sum, count).

✨ Conclusion

This approach ensures optimal performance with minimal space usage, making it well-suited for large inputs. The use of prefix sums significantly reduces redundant computations, achieving (O(n)) efficiency across all implementations.