Step by Step solution about How to resolve the algorithm Babbage problem step by step in the C programming language

The code you provided is the implementation of the Babbage Problem in C programming language.

The Babbage Problem is a problem in mathematics that asks for the smallest number whose square ends in a given string of digits. In this case, the given string of digits is 269696.

The code starts by initializing two variables, current and square, to 0. Then, it enters a while loop that continues as long as the following two conditions are met:

• the square of current does not end in 269696
• current is less than the maximum possible integer value

Inside the loop, current is incremented by 1 and the square of current is calculated and stored in square.

If the loop terminates because current is equal to the maximum possible integer value, then the code prints a message saying that the condition was not satisfied before the maximum integer value was reached. Otherwise, the code prints a message saying that the smallest number whose square ends in 269696 is current.

Here is an example of how the code would work:

current = 0
square = 0

square = current * current
square = 0

current = 1
square = current * current
square = 1

current = 2
square = current * current
square = 4

current = 3
square = current * current
square = 9

current = 4
square = current * current
square = 16

current = 5
square = current * current
square = 25

current = 6
square = current * current
square = 36

current = 7
square = current * current
square = 49

The loop continues in this manner until square ends in 269696. In this case, current will be equal to 7, and the code will print the following message:

The smallest number whose square ends in 269696 is 7

// This code is the implementation of Babbage Problem

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
 
int main() {
	int current = 0, 	//the current number 
	    square;		//the square of the current number

	//the strategy of take the rest of division by 1e06 is
	//to take the a number how 6 last digits are 269696
	while (((square=current*current) % 1000000 != 269696) && (square<INT_MAX)) {
		current++;
	}

        //output
	if (square>+INT_MAX)
	    printf("Condition not satisfied before INT_MAX reached.");
	else		   
	    printf ("The smallest number whose square ends in 269696 is %d\n", current);
	   
        //the end
	return 0 ;
}