How to Compute Running Sum of 1d Array using std::partial_sum in

  • Time:2020-09-08 11:19:41
  • Class:Weblog
  • Read:15

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.

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:
1 <= nums.length <= 1000
-10^6 <= nums[i] <= 10^6

Hints:
Think about how we can calculate the i-th number in the running sum from the (i-1)-th number.

Accumulate Prefix Sum

A traditional approach to compute the running sum would be to accumulate the prefix sum. You can use an additional variable to keep the sum, or simply we can update in place (use previous element in the array) to store the prefix sum.

1
2
3
4
5
6
7
8
9
class Solution {
public:
    vector<int> runningSum(vector<int>& nums) {
        for (int i = 1; i < nums.size(); ++ i) {
            nums[i] += nums[i - 1];
        }
        return nums;
    }
};
class Solution {
public:
    vector<int> runningSum(vector<int>& nums) {
        for (int i = 1; i < nums.size(); ++ i) {
            nums[i] += nums[i - 1];
        }
        return nums;
    }
};

C++ std::partial_sum

The C++ std::partial_sum does exactly this job. The function computes the partial sums of the elements in the range specified by [first, last) and update them to the range begining at third parameter.

1
2
3
4
5
6
7
class Solution {
public:
    vector<int> runningSum(vector<int>& nums) {
        partial_sum(begin(nums), end(nums), begin(nums));
        return nums;
    }
};
class Solution {
public:
    vector<int> runningSum(vector<int>& nums) {
        partial_sum(begin(nums), end(nums), begin(nums));
        return nums;
    }
};

The std::partial_sum may be implemented as follows:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
template<class InputIt, class OutputIt>
constexpr // since C++20
OutputIt partial_sum(InputIt first, InputIt last, 
                     OutputIt d_first)
{
    if (first == last) return d_first;
 
    typename std::iterator_traits<inputit>::value_type sum = *first;
    *d_first = sum;
 
    while (++first != last) {
       sum = std::move(sum) + *first; // std::move since C++20
       *++d_first = sum;
    }
    return ++d_first;
 
    // or, since C++14:
    // return std::partial_sum(first, last, d_first, std::plus<>());
}
template<class InputIt, class OutputIt>
constexpr // since C++20
OutputIt partial_sum(InputIt first, InputIt last, 
                     OutputIt d_first)
{
    if (first == last) return d_first;
 
    typename std::iterator_traits<inputit>::value_type sum = *first;
    *d_first = sum;
 
    while (++first != last) {
       sum = std::move(sum) + *first; // std::move since C++20
       *++d_first = sum;
    }
    return ++d_first;
 
    // or, since C++14:
    // return std::partial_sum(first, last, d_first, std::plus<>());
}

The loops can be unrolled as the following:

1
2
3
4
5
*(d_first)   = *first;
*(d_first+1) = *first + *(first+1);
*(d_first+2) = *first + *(first+1) + *(first+2);
*(d_first+3) = *first + *(first+1) + *(first+2) + *(first+3);
...
*(d_first)   = *first;
*(d_first+1) = *first + *(first+1);
*(d_first+2) = *first + *(first+1) + *(first+2);
*(d_first+3) = *first + *(first+1) + *(first+2) + *(first+3);
...

–EOF (The Ultimate Computing & Technology Blog) —

Recommend:
How to use the Leetcode’s Mock Interview Overview to Nail
Replace Harddrives when CrystalDiskInfo Shows Caution Health Sta
Finding the Predecessor and Successor Node of a Binary Search Tr
Algorithms to Detect Pattern of Length M Repeated K or More Time
Using the stdout to debug print the solution in the leetcode con
Tutorial: How to Set Up a API Load Balancer by Using CloudFlare
Introducing the Pancake Sorting Algorithm
What Should You Blog About During the Pandemic and Beyond?
6 Tips For Starting a Business During a Pandemic
Will Your Blog be affected by the Current Facebook Ad Boycott?
Share:Facebook Twitter
Comment list
Comment add