检查一个大数是否能被 9 整除

原文:https://www . geesforgeks . org/check-大数-整除-9-not/

给定一个数，任务是找出这个数是否能被 9 整除。输入的数字可能很大，即使我们使用 long long int 也可能无法存储。

示例:

Input  : n = 69354
Output : Yes

Input  : n = 234567876799333
Output : No

Input  : n = 3635883959606670431112222
Output : No

因为输入的数字可能非常大，所以我们不能用 n % 9 来检查一个数字是否能被 9 整除，尤其是在像 C/C++这样的语言中。这个想法基于以下事实。

A number is divisible by 9 if sum of its digits is divisible by 9.

插图:

For example n = 9432
Sum of digits = 9 + 4 + 3 + 2
             = 18
Since sum is divisible by 9,
answer is Yes.

这是如何工作的？

Let us consider 1332, we can write it as
1332 = 1*1000 + 3*100 + 3*10 + 2

The proof is based on below observation:
Remainder of 10i divided by 9 is 1
So powers of 10 only results in remainder 1 
when divided by 9.

Remainder of "1*1000 + 3*100 + 3*10 + 2"
divided by 9 can be written as : 
1*1 + 3*1 + 3*1 + 2 = 9
The above expression is basically sum of
all digits.

Since 9 is divisible by 9, answer is yes.

以下是上述想法的实现。

C++

// C++ program to find if a number is divisible by
// 9 or not
#include<bits/stdc++.h>
using namespace std;

// Function to find that number divisible by 9 or not
int check(string str)
{
    // Compute sum of digits
    int n = str.length();
    int digitSum = 0;
    for (int i=0; i<n; i++)
        digitSum += (str[i]-'0');

    // Check if sum of digits is divisible by 9.
    return (digitSum % 9 == 0);
}

// Driver code
int main()
{
    string str = "99333";
    check(str)?  cout << "Yes" : cout << "No ";
    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find if a number is
// divisible by 9 or not
class IsDivisible
{
    // Function to find that number
    // is divisible by 9 or not
    static boolean check(String str)
    {
        // Compute sum of digits
        int n = str.length();
        int digitSum = 0;
        for (int i=0; i<n; i++)
            digitSum += (str.charAt(i)-'0');

        // Check if sum of digits is divisible by 9.
        return (digitSum % 9 == 0);
    }

    // main function
    public static void main (String[] args)
    {
        String str = "99333";
        if(check(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python 3

# Python 3 program to
# find if a number is
# divisible by
# 9 or not

# Function to find that
# number divisible by 9
# or not
def check(st) :

    # Compute sum of digits
    n = len(st)
    digitSum = 0

    for i in range(0,n) :
        digitSum = digitSum + (int)(st[i])

    # Check if sum of digits
    # is divisible by 9.
    return (digitSum % 9 == 0)

# Driver code
st = "99333"

if(check(st)) :
    print("Yes")
else :
    print("No")

# This code is contributed by Nikita Tiwari.

C

// C# program to find if a number is
// divisible by 9 or not.
using System;

class GFG {

    // Function to find that number
    // is divisible by 9 or not
    static bool check(String str)
    {

        // Compute sum of digits
        int n = str.Length;
        int digitSum = 0;
        for (int i = 0; i < n; i++)
            digitSum += (str[i] - '0');

        // Check if sum of digits is
        // divisible by 9.
        return (digitSum % 9 == 0);
    }

    // main function
    public static void Main ()
    {
        String str = "99333";
        if(check(str))
            Console.Write("Yes");
        else
            Console.Write("No");
    }
}

// This code is Contributed by
// nitin mittal.

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP program to find if a number
// is divisible by 9 or not

// Function to find that
// number divisible by 9 or not
function check($str)
{

    // Compute sum of digits
    $n = strlen($str);
    $digitSum = 0;
    for ($i = 0; $i < $n; $i++)
        $digitSum += ($str[$i] - '0');

    // Check if sum of digits
    // is divisible by 9.
    return ($digitSum % 9 == 0);
}

// Driver code
$str = "99333";
$x = check($str) ? "Yes" : "No ";
echo($x);

// This code is contributed by Ajit.
?>

java 描述语言

<script>

// Javascript program to find if a number
// is divisible by 9 or not

// Function to find that
// number divisible by 9 or not
function check(str)
{

    // Compute sum of digits
    let n = str.length;
    let digitSum = 0;

    for(let i = 0; i < n; i++)
        digitSum += (str[i] - '0');

    // Check if sum of digits
    // is divisible by 9.
    return (digitSum % 9 == 0);
}

// Driver code
let str = "99333";
let x = check(str) ? "Yes" : "No ";

document.write(x);

// This code is contributed by _saurabh_jaiswal.

</script>

输出:

Yes

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