Step by Step solution about How to resolve the algorithm Display a linear combination step by step in the C programming language

The provided C code takes a vector of real numbers as input and prints the vector in a simplified and readable format. Here's how the code works:

• It includes several standard libraries:

  • <stdlib.h> for general purpose functions like malloc and free.
  • <stdio.h> for input and output operations.
  • <math.h> for mathematical functions like fabs, labs, and abs, which are used for handling floating-point numbers.

• The main function is the entry point of the program:

  • It checks if the number of command-line arguments (argC) is less than or equal to 1. If so, it prints usage information and exits.
  • If there are command-line arguments, it processes and prints the vector:
    • It initializes variables:
      • i: A loop counter.
      • zeroCount: Counts the number of zero elements in the vector.
      • firstNonZero: Stores the index of the first non-zero element in the vector.
    • It allocates memory for a double-precision floating-point array (vector) to store the vector components.
    • It iterates through the command-line arguments (starting from index 1, skipping the program name) and does the following for each argument:
      • Converts the argument from a string to a double using atof.
      • Stores the converted value in the vector array.
      • Checks if the value is zero and increments zeroCount if so.
      • If the value is non-zero and firstNonZero is still -1, it updates firstNonZero to the current index.
    • It handles special cases:
      • If zeroCount is equal to argC, it prints "0" to represent a zero vector.
      • Otherwise, it iterates through the vector array and prints each element in a simplified form:
        • If the element is 1, it prints "e".
        • If the element is -1, it prints "-e".
        • If the element is a non-zero floating-point number, it prints "e" or "-e" based on the sign of the element.
        • For elements other than the first non-zero element, it prints a sign ("+" or "-") and the simplified form of the element.
    • Finally, it frees the allocated memory for the vector array.

In summary, this code simplifies and prints a vector of real numbers in a more readable format, highlighting the non-zero elements and their positions in the vector.

#include<stdlib.h>
#include<stdio.h>
#include<math.h> /*Optional, but better if included as fabs, labs and abs functions are being used. */

int main(int argC, char* argV[])
{
	
	int i,zeroCount= 0,firstNonZero = -1;
	double* vector;
	
	if(argC == 1){
		printf("Usage : %s <Vector component coefficients seperated by single space>",argV[0]);
	}
	
	else{
		
		printf("Vector for [");
		for(i=1;i<argC;i++){
			printf("%s,",argV[i]);
		}
		printf("\b] -> ");
		
		
		vector = (double*)malloc((argC-1)*sizeof(double));
		
		for(i=1;i<=argC;i++){
			vector[i-1] = atof(argV[i]);
			if(vector[i-1]==0.0)
				zeroCount++;
			if(vector[i-1]!=0.0 && firstNonZero==-1)
				firstNonZero = i-1;
		}

		if(zeroCount == argC){
			printf("0");
		}
		
		else{
			for(i=0;i<argC;i++){
				if(i==firstNonZero && vector[i]==1)
					printf("e%d ",i+1);
				else if(i==firstNonZero && vector[i]==-1)
					printf("- e%d ",i+1);
				else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])>0.0)
					printf("- %lf e%d ",fabs(vector[i]),i+1);
				else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])==0.0)
					printf("- %ld e%d ",labs(vector[i]),i+1);
				else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])>0.0)
					printf("%lf e%d ",vector[i],i+1);
				else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])==0.0)
					printf("%ld e%d ",vector[i],i+1);
				else if(fabs(vector[i])==1.0 && i!=0)
					printf("%c e%d ",(vector[i]==-1)?'-':'+',i+1);
				else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])>0.0)
					printf("%c %lf e%d ",(vector[i]<0)?'-':'+',fabs(vector[i]),i+1);
				else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])==0.0)
					printf("%c %ld e%d ",(vector[i]<0)?'-':'+',labs(vector[i]),i+1);				
			}
		}
	}
	
	free(vector);
	
	return 0;
}