Detailed analysis of algorithms runtime over different sizes of inputs using plots and graphs on this algorithm:

#include

using namespace std;

bool ifValid(const string& cardNo)

{

int Digits= cardNo.length();

int Sum= 0, rmDigit = false;

for (int i= Digits-1; i>=0; i--) {

int digit= cardNo[i] - '0';

if (rmDigit== true)

digit= digit*2;

Sum+= digit/10;

Sum+= digit%10;

rmDigit= !rmDigit;

}

return (Sum%10 == 0);

}

int main()

{ string cardNo = "371449635398431";

if (ifValid(cardNo))

printf("The card is Valid!");

else

printf("The card is not Valid!");

return 0;

}