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
#include <functional>
#include <iostream>
#include <numeric>
using namespace std;
int myfun( int x, int y) { return x + y; }
int main()
{
int a[] = { 1, 2, 3, 4, 5, 6 };
int b[6];
adjacent_difference(a, a + 6, b);
cout << "\nResult using adjacent_difference: " ;
for ( int i = 0; i < 6; i++)
std::cout << b[i] << ' ' ;
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] << ' ' ;
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;
}
|
Output
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
#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; }
int main()
{
int var = 200;
int a[] = { 10, 15, 20 };
int b[] = { 1, 3, 5 };
cout << "\nResult using inner_product " ;
cout << inner_product(a, a + 3, b, var);
cout << "\nResult using inner_product with pre-defined "
"function: " ;
cout << inner_product(a, a + 3, b, var, minus< int >(),
divides< int >());
cout << "\nResult using inner_product with "
"user-defined function: " ;
cout << inner_product(a, a + 3, b, var, fun, fun1);
return 0;
}
|
Output
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
#include <iostream>
#include <numeric>
using namespace std;
int main()
{
int a[7];
iota(a, a + 7, 100);
cout << " a : " ;
for ( int & x : a)
cout << ' ' << x;
return 0;
}
|
Output
a : 100 101 102 103 104 105 106
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