Accumulate() and partial_sum() in C++ STL Numeric header

The C++ STL's numeric library includes the numeric header. This library provides efficient numeric arrays, support for random number generation, and fundamental mathematical operations and types. Several of the numeric header's functions include the following:

• Iota
• Accumulate
• Reduce
• Inner_product
• Partial _ sum etc.

This article describes the numeric header functions accumulate() and partial sum(), which can be used to expedite and simplify competitive programming.

1. accumulate ()

With the variable sum, this function returns the total of all values falling inside the range [first, last]. We often use a linear operation to calculate the sum of the items in a certain range or an entire array. This entails adding each element in the range individually and saving the result in a variable after each iteration.

Syntax:

Accumulate (first, last, sum)

Or

Accumulate (first, last, sum, myfun);

Parameters

• first, last: It specifiesstart and end components of the range to which elements are being added.
• sum: It specifiesstarting point of the total
• myfun: It specifiesa method for carrying out any certain operation.

For instance, we can determine the combination of the first and last element.

Example:

#include <iostream>
#include <numeric>
usingnamespace std;
intmyfun(int x, int y)
{
    // combination of two adjacent numbers are taken
    return x * y;
}
 
int main()
{
    // Initial sum = 1
    int sum = 1;
    inta[] = { 5, 10, 15 };
 
    cout<< "\nResult using accumulate: ";
    cout<<accumulate(a, a + 3, sum);
 
    //with the help of accumulatefunction with
    // function def
    cout<< "\nResult using accumulate with"
            "user-defined function: ";
    cout<< accumulate(a, a + 3, sum, myfun);
 
    // with the help of accumulate function with
    // functionpre-defined
    cout<< "\nResult using accumulate with "
            "pre-defined function: ";
    cout<<accumulate (a, a + 3, sum, std::minus<int>());
 
    return0;
}

Output:

Sum of all elements between k1^th and k2^th smallest elements

Given two numbers, k1 and k2, and an array of integers Find the total number of elements in the array between the two provided smallest elements, k1 and k2. One may suppose that all of the array's elements are distinct and that (1 = k1 k2 = n).

Sorting:

#include <bits/stdc++.h>
 
usingnamespacestd;
 


intsumBetweenTwoKth (intarr [], intn, intk1, intk2)
{
    
    sort (arr, arr + n);
 
    
     int result = 0;
     for (int i=k1; i<k2-1; i++)
      result += arr[i]; */
    returnaccumulate (arr + k1, arr + k2 - 1, 0);
}
 


intmain ()
{
    intarr[] = {20, 8, 22, 4, 12, 10, 14 };
    intk1 = 3, k2 = 6;
    intn = sizeof(arr) / sizeof (arr[0]);
    cout<<sumBetweenTwoKth(arr, n, k1, k2);
    return0;
}

Output:

The outcome obtained is 26

2. partial_sum ()

Each point of the second array is given a partial sum of the corresponding elements of an array by this function. It returns and keeps in another array b the partial sum of each set of values falling between [first, last].

For instance, the ys can be calculated as follows if x represents an element in [first, last] and y represents an element in the outcome:

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: range's start and last components to which more elements are to be appended.
• b: index of the array containing the corresponding partial sum.
• myfun: a function established by the user to carry out any task.

Example:

#include <iostream>
#include <numeric>
usingnamespacestd;
 


intmyfun (intx, inty)
{
   
  
    returnx + 2 * y;
}
 
intmain ()
{
    inta [] = {1, 2, 3, 4, 5 };
    intb [5];
 
    
    partial_sum(a, a + 5, b);
 
    cout<< "Partial Sum - Using Default function: ";
    for(inti = 0; i< 5; i++)
        cout<< b[i] << ' ';
    cout<< '\n';
 
    
    partial_sum(a, a + 5, b, myfun);
 
    cout<< "Partial sum - Using user defined function: ";
    for(inti = 0; i< 5; i++)
        cout<< b[i] << ' ';
    cout<< '\n';
 
    return0;
}

Output:

Adding partially – with the help of attribute default: 1 3 6 10 15
Adding partially_ with the help of user defined attribute: 1 5 11 19 29


Y00 = x0 
y1 = x0 + x1 
y2 = x0 + x1 + x2 
y3 = x0 + x1 + x2 + x3 
y4 = x0 + x1 + x2 + x3 + x4