accumulate() and partial_sum() in C++ STL : Numeric header

The numeric header is part of the numeric library in C++ STL. This library consists of basic mathematical functions and types, as well as optimized numeric arrays and support for random number generation. Some of the functions in the numeric header:

• iota
• accumulate
• reduce
• inner_product
• partial_sum etc.

This article explains accumulate() and partial_sum() in the numeric header which can be used during competitive programming to save time and effort. 
1) accumulate(): This function returns the sum of all the values lying in a range between [first, last) with the variable sum. We usually find out the sum of elements in a particular range or a complete array using a linear operation which requires adding all the elements in the range one by one and storing it into some variable after each iteration.

Syntax:

accumulate(first, last, sum);

or

accumulate(first, last, sum, myfun); 

Parameters:

• first, last: first and last elements of range whose elements are to be added
• sum:  initial value of the sum
• myfun: a function for performing any specific task. 

For example, we can find the product of elements between the first and last.

CPP

// C++ program to demonstrate working of accumulate()
#include <iostream>
#include <numeric>
using namespace std;

// User defined function
int myfun(int x, int y)
{
    // for this example we have taken product
    // of adjacent numbers
    return x * y;
}

int main()
{
    // Initialize sum = 1
    int sum = 1;
    int a[] = { 5, 10, 15 };

    // Simple default accumulate function
    cout << "\nResult using accumulate: ";
    cout << accumulate(a, a + 3, sum);

    // Using accumulate function with
    // defined function
    cout << "\nResult using accumulate with"
            "user-defined function: ";
    cout << accumulate(a, a + 3, sum, myfun);

    // Using accumulate function with
    // pre-defined function
    cout << "\nResult using accumulate with "
            "pre-defined function: ";
    cout << accumulate(a, a + 3, sum, std::minus<int>());

    return 0;
}

Output

Result using accumulate: 31
Result using accumulate withuser-defined function: 750
Result using accumulate with pre-defined function: -29

Note: For adding larger values beyond the int range the sum should be initialized with 0ll or a user-defined sum with the suffix ll,  else the sum will be overflown. (here ll refers to long long int)
Example: accumulate(a,a+n,0ll)

See this Example Problem for more reference: Sum of all elements between k1’th and k2’th smallest elements

2) partial_sum( ): This function assigns a partial sum of the corresponding elements of an array to every position of the second array. It returns the partial sum of all the sets of values lying between [first, last) and stores it in another array b. 
For example, if x represents an element in [first, last) and y represents an element in the result, the ys can be calculated as:

y0 = x0 
y1 = x0 + x1 
y2 = x0 + x1 + x2 
y3 = x0 + x1 + x2 + x3 
y4 = x0 + x1 + x2 + x3 + x4

Syntax:

partial_sum(first, last, b);

or

partial_sum(first, last, b, myfun);

Parameters:

• first, last: first and last element of the range whose elements are to be added
• b: index of array where  corresponding partial sum will be stored
• myfun: a user-defined function for performing any specific task

CPP

// C++ program to demonstrate working of partial_sum()
#include <iostream>
#include <numeric>
using namespace std;

// user defined function
int myfun(int x, int y)
{
    // the sum of element is twice of its
    // adjacent element
    return x + 2 * y;
}

int main()
{
    int a[] = { 1, 2, 3, 4, 5 };
    int b[5];

    // Default function
    partial_sum(a, a + 5, b);

    cout << "Partial Sum - Using Default function: ";
    for (int i = 0; i < 5; i++)
        cout << b[i] << ' ';
    cout << '\n';

    // Using user defined function
    partial_sum(a, a + 5, b, myfun);

    cout << "Partial sum - Using user defined function: ";
    for (int i = 0; i < 5; i++)
        cout << b[i] << ' ';
    cout << '\n';

    return 0;
}

Output

Partial Sum - Using Default function: 1 3 6 10 15 
Partial sum - Using user defined function: 1 5 11 19 29 

Explanation of code :

without myfun:

simply, ith  element of a array + i-1th element of array b makes equal to ith element of b

i.e. b[i]=a[i]+b[i-1] 

b[0] =1+no ele=> 1

b[1] =2+1=> 3

b[2]= 3+3=> 6

b[3]=6+4=10 and   so on

with myfun:

 in the same way : 

b[i]=a[i]+2*b[i-1]

means b[0]= 1+2*0 => 1

b[1] = 1+2*2=> 5 

b[2]= 5+3*2=> 11

b[3]=11+4*2=> 19 and so on upto last. 

This article is contributed by Abhinav Tiwari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.