Step by Step solution about How to resolve the algorithm Trabb Pardo–Knuth algorithm step by step in the C++ programming language

This code is a C++ program that takes 11 numbers as input and applies a mathematical function to each number. The function is defined by the expression sqrt( abs( n ) ) + 5 * pow( n , 3 ), where n is the input number. The program then outputs the result of applying the function to each number, along with a message indicating whether the result is "too large" or not.

Here is a breakdown of the code:

• The program includes several standard libraries, including <iostream>, <cmath>, <vector>, <algorithm>, and <iomanip>. These libraries provide the functionality needed to read input from the console, perform mathematical operations, store data in vectors, apply transformations to collections of data, and format output.

• The main function is the entry point of the program. It declares two vectors, input and results, each of which can hold 11 double values.

• The program prompts the user to enter 11 numbers and reads them into the input vector using a for loop.

• The program uses the std::transform function to apply the mathematical function to each number in the input vector and store the results in the results vector. The std::transform function takes three arguments: an input iterator, an output iterator, and a function that defines the transformation to be applied to each element. In this case, the input iterator is input.begin(), the output iterator is results.begin(), and the function is a lambda expression that defines the mathematical function.

• The program then uses a for loop to iterate over the results vector in reverse order (from index 10 to 0). For each number in the results vector, the program prints a message to the console that includes the input number, the result of applying the mathematical function to the input number, and a message indicating whether the result is "too large" or not. The program uses the std::setw function to format the output so that the input numbers and results are aligned in columns.

• The program returns 0 to indicate successful execution.

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
#include <iomanip>

int main( ) {
   std::vector<double> input( 11 ) , results( 11 ) ;
   std::cout << "Please enter 11 numbers!\n" ;
   for ( int i = 0 ; i < input.size( ) ; i++ ) 
      std::cin >> input[i];
      
   std::transform( input.begin( ) , input.end( ) , results.begin( ) ,
	 [ ]( double n )-> double { return sqrt( abs( n ) ) + 5 * pow( n , 3 ) ; } ) ;
   for ( int i = 10 ; i > -1 ; i-- ) {
      std::cout << "f( " << std::setw( 3 ) << input[ i ] << " ) : " ; 
      if ( results[ i ] > 400 ) 
	 std::cout << "too large!" ;
      else 
	 std::cout << results[ i ] << " !" ;
      std::cout << std::endl ;
   }
   return 0 ;
}