Luhn algorithm

26 May, 2021
The Luhn algorithm, also known as the modulus 10 or mod 10 algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, Canadian Social Insurance Numbers. The LUHN formula was created in the late 1960s by a group of mathematicians. Shortly thereafter, credit card companies adopted it. Because the algorithm is in the public domain, it can be used by anyone. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers. It was designed to protect against accidental errors, not malicious attacks.
Let’s understand the algorithm with an example: Consider the example of an account number “79927398713“. Step 1 – Starting from the rightmost digit, double the value of every second digit, 
Step 2 – If doubling of a number results in a two digit number i.e greater than 9(e.g., 6 × 2 = 12), then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6), to get a single digit number. 
Step 3 – Now take the sum of all the digits.
Step 4 – If the total modulo 10 is equal to 0 (if the total ends in zero) then the number is valid according to the Luhn formula; else it is not valid. 
Since the sum is 70 which is a multiple of 10, the account number is possibly valid. 
The idea is simple; we traverse from the end. For every second digit, we double it before adding it. We add two digits of the number obtained after doubling.  
C++
Java
Python3
C#
Javascript
// C++ program to implement Luhn algorithm#include <bits/stdc++.h>using namespace std; // Returns true if given card number is validbool checkLuhn(const string& cardNo){    int nDigits = cardNo.length();     int nSum = 0, isSecond = false;    for (int i = nDigits - 1; i >= 0; i--) {         int d = cardNo[i] - '0';         if (isSecond == true)            d = d * 2;         // We add two digits to handle        // cases that make two digits after        // doubling        nSum += d / 10;        nSum += d % 10;         isSecond = !isSecond;    }    return (nSum % 10 == 0);} // Driver codeint main(){    string cardNo = "79927398713";    if (checkLuhn(cardNo))        printf("This is a valid card");    else        printf("This is not a valid card");    return 0;}
// Java program to implement// Luhn algorithmimport java.io.*; class GFG {     // Returns true if given// card number is validstatic boolean checkLuhn(String cardNo){    int nDigits = cardNo.length();     int nSum = 0;    boolean isSecond = false;    for (int i = nDigits - 1; i >= 0; i--)    {         int d = cardNo.charAt(i) - '0';         if (isSecond == true)            d = d * 2;         // We add two digits to handle        // cases that make two digits        // after doubling        nSum += d / 10;        nSum += d % 10;         isSecond = !isSecond;    }    return (nSum % 10 == 0);}     // Driver code    static public void main (String[] args)    {        String cardNo = "79927398713";        if (checkLuhn(cardNo))            System.out.println("This is a valid card");        else            System.out.println("This is not a valid card");         }} // This Code is contributed by vt_m.
# Python3 program to implement# Luhn algorithm # Returns true if given card# number is validdef checkLuhn(cardNo):         nDigits = len(cardNo)    nSum = 0    isSecond = False         for i in range(nDigits - 1, -1, -1):        d = ord(cardNo[i]) - ord('0')             if (isSecond == True):            d = d * 2          # We add two digits to handle        # cases that make two digits after        # doubling        nSum += d // 10        nSum += d % 10          isSecond = not isSecond         if (nSum % 10 == 0):        return True    else:        return False # Driver code  if __name__=="__main__":         cardNo = "79927398713"         if (checkLuhn(cardNo)):        print("This is a valid card")    else:        print("This is not a valid card") # This code is contributed by rutvik_56
// C# program to implement// Luhn algorithmusing System; class GFG {     // Returns true if given// card number is validstatic bool checkLuhn(String cardNo){    int nDigits = cardNo.Length;     int nSum = 0;    bool isSecond = false;    for (int i = nDigits - 1; i >= 0; i--)    {          int d = cardNo[i] - '0';         if (isSecond == true)            d = d * 2;         // We add two digits to handle        // cases that make two digits        // after doubling        nSum += d / 10;        nSum += d % 10;         isSecond = !isSecond;    }    return (nSum % 10 == 0);}     // Driver code    static public void Main()    {        String cardNo = "79927398713";        if (checkLuhn(cardNo))            Console.WriteLine("This is a valid card");        else            Console.WriteLine("This is not a valid card");         }} // This Code is contributed by vt_m.
<script>    // Javascript program to implement Luhn algorithm         // Returns true if given    // card number is valid    function checkLuhn(cardNo)    {        let nDigits = cardNo.length;         let nSum = 0;        let isSecond = false;        for (let i = nDigits - 1; i >= 0; i--)        {             let d = cardNo[i].charCodeAt() - '0'.charCodeAt();             if (isSecond == true)                d = d * 2;             // We add two digits to handle            // cases that make two digits            // after doubling            nSum += parseInt(d / 10, 10);            nSum += d % 10;             isSecond = !isSecond;        }        return (nSum % 10 == 0);    }         let cardNo = "79927398713";    if (checkLuhn(cardNo))      document.write("This is a valid card");    else      document.write("This is not a valid card");     </script>
Output: 
This is a valid card
The Luhn algorithm detects any single-digit error, as well as almost all transpositions of adjacent digits.  
This article is contributed by Vishal Kumar Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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