numeric header in C++ STL | Set 2 (adjacent_difference(), inner_product() and iota())

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.

See this article for more reference: accumulate() and partial_sum() in C++ STL :  Numeric header

This article explains adjacent_difference(), inner_product(), and iota in the numeric header which can be used during competitive programming to save time and effort. 

1) adjacent_difference(): This function assigns the difference between the corresponding elements of an array to another array. It returns the adjacent difference of all the sets of values lying between [ First, last ). 
For Example: If a[] represents an element in the provided range [first, last) and b[] represents the result. 

b[0] = a[0] 
b[1] = a[1] – a[0] 
b[2] = a[2] – a[1] 
b[3] = a[3] – a[2] 
b[4] = a[4] – a[3] 
... ... ...

Syntax: 

adjacent_difference(first, last, b);
adjacent_difference(first, last, b, myfun );
adjacent_difference(first, last, b, multiplies() );

Parameters:

• first, last: address of first and last element of 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
• multiplies(): a pre-defined function.

// CPP Program to demonstrate adjacent_difference()
#include <functional>
#include <iostream>
#include <numeric>
using namespace std;

int myfun(int x, int y) { return x + y; }

// Driver Code
int main()
{
    int a[] = { 1, 2, 3, 4, 5, 6 };
    int b[6];

    // using adjacent_difference function
    adjacent_difference(a, a + 6, b);
    cout << "\nResult using adjacent_difference: ";
    for (int i = 0; i < 6; i++)
        std::cout << b[i] << ' ';

    // using adjacent_difference function
    // user defined function
    adjacent_difference(a, a + 6, b, myfun);
    cout << "\nResult using accumulate with user-"
            "defined function: ";
    for (int i = 0; i < 6; i++)
        std::cout << b[i] << ' ';

    // using adjacent_difference with pre-defined function
    adjacent_difference(a, a + 6, b, multiplies<int>());

    cout << "\nResult using accumulate with pre-defined "
            "function: ";
    for (int i = 0; i < 6; i++)
        std::cout << b[i] << ' ';

    return 0;
}

Result using adjacent_difference: 1 1 1 1 1 1 
Result using accumulate with user-defined function: 1 3 5 7 9 11 
Result using accumulate with pre-defined function: 1 2 6 12 20 30 

2) inner_product(): This function returns the result of the addition of var with the inner products of the pairs formed by the elements of two ranges starting at first1 and first2.
Syntax: 

inner_product(first, last, b, var) ;
inner_product(a, a+3, b, var, fun, fun1) ;
inner_product(a , a+3, b, init, minus (), divides () );

Parameters:

• first, last: address of first and last element of range whose elements are to be added
• b: index of array where  corresponding partial sum will be stored;
• fun, fun1: a user-defined function for performing any specific task
• minus(), divides(): pre defined function.

// CPP Program to demonstrate inner_product()
#include <functional>
#include <iostream>
#include <numeric>
using namespace std;

int fun(int x, int y) { return x - y; }

int fun1(int x, int y) { return x + y; }

// Driver Code
int main()
{
    int var = 200;
    int a[] = { 10, 15, 20 };
    int b[] = { 1, 3, 5 };

    cout << "\nResult using inner_product ";

    // inner_product with default method
    cout << inner_product(a, a + 3, b, var);

    // inner_product with pre-defined function
    cout << "\nResult using inner_product with pre-defined "
            "function: ";
    cout << inner_product(a, a + 3, b, var, minus<int>(),
                          divides<int>());

    // inner_product with user defined function
    cout << "\nResult using inner_product with "
            "user-defined function: ";
    cout << inner_product(a, a + 3, b, var, fun, fun1);

    return 0;
}

Result using inner_product 355
Result using inner_product with pre-defined function: 181
Result using inner_product with user-defined function: 146

3) iota(): This function assigns a value to the elements in the range [first, last ) of the array which is incremented at each step by val++.
Syntax:

iota(first, last,val) ;

Parameters:

• first, last: address of first and last element of range whose elements are to be added
• val: initial value to store, the expression ++value must be well-formed

// CPP Program to demonstrate iota()
#include <iostream>
#include <numeric>
using namespace std;

// Driver Code
int main()
{
    int a[7];

    // using iota function to store 100, 101, 102,...
    iota(a, a + 7, 100);
    cout << " a : ";
    for (int& x : a)
        cout << ' ' << x;

    return 0;
}

 a :  100 101 102 103 104 105 106