# Solution: Running Sum of 1d Array

*This is part of a series of Leetcode solution explanations ( ). If you liked this solution or found it useful,* *please like**this post and/or* *upvote**my solution post on Leetcode's forums.*

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Leetcode Problem #1480 (*Easy*): Running Sum of 1d Array

####
*Description:*

*Description:*

(*Jump to*: *Solution Idea* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

Given an array

`nums`

. We define a running sum of an array as`runningSum[i] = sum(nums[0]…nums[i])`

.Return the running sum of

`nums`

.

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*Examples:*

*Examples:*

Example 1: Input: nums = [1,2,3,4] Output: [1,3,6,10] Explanation: Running sum is obtained as follows: [1, 1+2, 1+2+3, 1+2+3+4].

Example 2: Input: nums = [1,1,1,1,1] Output: [1,2,3,4,5] Explanation: Running sum is obtained as follows: [1, 1+1, 1+1+1, 1+1+1+1, 1+1+1+1+1].

Example 3: Input: nums = [3,1,2,10,1] Output: [3,4,6,16,17]

####
*Constraints:*

*Constraints:*

`1 <= nums.length <= 1000`

`-10^6 <= nums[i] <= 10^6`

####
*Idea:*

*Idea:*

(*Jump to*: *Problem Description* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

While this is not a terribly challenging problem, it's a good introduction to the concept of a **prefix sum array**. Prefix sum arrays have many uses in more complex algorithms and can sometimes help reduce the time complexity of a advanced solution by an order of magnitude.

In a prefix sum array, we will create a duplicate array which contains the running sum of the elements **0** to **i** of our original array (**nums**) for each index **i** of our prefix sum array (**ans**). *( Note: We can lower the space complexity by using an in-place approach with nums directly and mutating it into its own prefix sum array, if there is no compelling reason to avoid modifying a function argument.)*

Since we'll need to build on a previous running total, we should start our iteration at **i = 1** and copy over the first element from **nums** to **ans**. Then we just iterate through **nums** and add each element (**nums[i]**) to the previous running total (**ans[i-1]**) to create the new running total (**ans[i]**).

When we're done, we can **return ans**.

**Time Complexity: O(N)**where**N**is the length of nums-
**Space Complexity: O(N)**for our running sum array*or***O(1)**with an in-place approach

####
*Javascript Code:*

*Javascript Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
var runningSum = function(nums) {
let ans = new Array(nums.length)
ans[0] = nums[0]
for (let i = 1; i < nums.length; i++)
ans[i] = ans[i-1] + nums[i]
return ans
};
```

####
*Python Code:*

*Python Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution:
def runningSum(self, nums: List[int]) -> List[int]:
ans = [0] * len(nums)
ans[0] = nums[0]
for i in range(1, len(nums)):
ans[i] = ans[i-1] + nums[i]
return ans
```

####
*Java Code:*

*Java Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution {
public int[] runningSum(int[] nums) {
int[] ans = new int[nums.length];
ans[0] = nums[0];
for (int i = 1; i < nums.length; i++)
ans[i] = ans[i-1] + nums[i];
return ans;
}
}
```

####
*C++ Code:*

*C++ Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution {
public:
vector<int> runningSum(vector<int>& nums) {
vector<int> ans(nums.size());
ans[0] = nums[0];
for (int i = 1; i < nums.size(); i++)
ans[i] = ans[i-1] + nums[i];
return ans;
}
};
```

#### Project: algorithms

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