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Running Sum of 1D Array

Certification: Basic Level Accuracy: 0% Submissions: 1 Points: 5

Write a Java program to compute the running sum of a 1D array. A running sum (also known as a cumulative sum) is defined as the sum of all elements up to a given index in an array, inclusive. For example, given an array nums = [1, 2, 3, 4], the running sum is [1, 1+2, 1+2+3, 1+2+3+4] = [1, 3, 6, 10].

Example 1
     
  • Input: nums = [1, 2, 3, 4]
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  • Output: [1, 3, 6, 10]
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  • Explanation: 
       
    • Step 1: Initialize a new array to store the running sum values.
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    • Step 2: The first element of the running sum array is the same as the first element of the input: 1.
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    • Step 3: For the second element, add the second element of the input to the previous running sum: 1 + 2 = 3.
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    • Step 4: For the third element, add the third element of the input to the previous running sum: 3 + 3 = 6.
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    • Step 5: For the fourth element, add the fourth element of the input to the previous running sum: 6 + 4 = 10.
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    • Step 6: Return the running sum array [1, 3, 6, 10].
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    •
Example 2
     
  • Input: nums = [3, 1, 2, 10, 1]
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  • Output: [3, 4, 6, 16, 17]
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  • Explanation: 
       
    • Step 1: Initialize a new array to store the running sum values.
      •  
    • Step 2: The first element of the running sum array is the same as the first element of the input: 3.
      •  
    • Step 3: For the second element, add the second element of the input to the previous running sum: 3 + 1 = 4.
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    • Step 4: For the third element, add the third element of the input to the previous running sum: 4 + 2 = 6.
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    • Step 5: For the fourth element, add the fourth element of the input to the previous running sum: 6 + 10 = 16.
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    • Step 6: For the fifth element, add the fifth element of the input to the previous running sum: 16 + 1 = 17.
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    • Step 7: Return the running sum array [3, 4, 6, 16, 17].
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    •
Constraints
     
  • 1 ≤ nums.length ≤ 1000
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  • -10^6 ≤ nums[i] ≤ 10^6
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  • Time Complexity: O(n)
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  • Space Complexity: O(1) excluding the output array
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Solution

Solution Hints

    
  
  • Create an output array of the same size as the input array
    • 
  
  • The first element of the output array will be the same as the first element of the input
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  • For each subsequent element at index i, add the value of the previous running sum (at index i-1) to the current element value
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  • Iterate through the array once to compute the running sum
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  • Return the running sum array
    •

Steps to solve by this approach:

 Step 1: Create a new array of the same length as the input array to store the running sum.
 Step 2: Set the first element of the output array equal to the first element of the input array.
 Step 3: Initialize a loop starting from the second element (index 1) to the end of the array.
 Step 4: For each element, calculate the running sum by adding the current element to the previous running sum.
 Step 5: Store this running sum in the output array at the current index.
 Step 6: Continue until the end of the array is reached.
 Step 7: Return the output array containing the running sums.

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