检查一个大数是否能被 5 整除
给定一个数，任务是检查数是否能被 5 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 = 56945255
Output : Yes
Input : n = 1234567589333150
Output : Yes
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 % 5 来检查一个数字是否能被 5 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 5 if its
digits last digit will be 0 or 5 .
插图:
For example, let us consider 769555
Number formed by last digit is = 5
Since 5 is divisible by 5 , answer is YES.
这是如何工作的？
Let us consider 5335, we can write it as
5335 = 5*1000 + 3*100 + 3*10 + 5
The proof is based on below observation:
Remainder of 10i divided by 5 is 0 if i greater
than or equal to one. Note than 10, 100, 1000,
... etc lead to remainder 0 when divided by 5.
So remainder of " 5*1000 + 3*100 +
3*10 + 5" divided by 5 is equivalent to remainder
of following :
0 + 0 + 0 + 5 = 5
Since 5 is divisible by 5, answer is yes.
以下是上述想法的实现。
C++
// C++ program to find if a number is
// divisible by 5 or not
#include<bits/stdc++.h>
using namespace std;
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
bool isDivisibleBy5(string str)
{
int n = str.length();
return ( ((str[n-1]-'0') == 0) ||
((str[n-1]-'0') == 5));
}
// Driver code
int main()
{
string str = "76955";
isDivisibleBy5(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 5 or not
class IsDivisible
{
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
static boolean isDivisibleBy5(String str)
{
int n = str.length();
return ( ((str.charAt(n-1)-'0') == 0) ||
((str.charAt(n-1)-'0') == 5));
}
// main function
public static void main (String[] args)
{
String str = "76955";
if(isDivisibleBy5(str))
System.out.println("Yes");
else
System.out.println("No");
}
}
计算机编程语言
# Python program to find if a number is
# divisible by 5 or not
# Function to find that number divisible
# by 5 or not. The function assumes that
# string length is at least one.
def isDivisibleBy5(st) :
n = len(st)
return ( (st[n-1] == '0') or
(st[n-1] == '5'))
# Driver code
st = "76955"
if isDivisibleBy5(st) :
print "Yes"
else :
print "No "
# This code is contributed by Nikita Tiwari.
C
// C# program to find if a number is
// C# program to find if a number
// is divisible by 5 or not.
using System;
class IsDivisible
{
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
static bool isDivisibleBy5(String str)
{
int n = str.Length;
return (((str[n - 1] - '0') == 0) ||
((str[n - 1] - '0') == 5));
}
// Driver Code
public static void Main ()
{
String str = "76955";
if(isDivisibleBy5(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 5 or not
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function isDivisibleBy5($str)
{
$n = strlen($str);
return ( (($str[$n-1]-'0') == 0) ||
(($str[$n-1]-'0') == 5));
}
// Driver code
$str = "76955";
$x = isDivisibleBy5($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 5 or not
// Function to find that number divisible
// by 5 or not. The function assumes that
// string length is at least one.
function isDivisibleBy5(str)
{
n = str.length;
return (((str[n - 1] - '0') == 0) ||
((str[n - 1] - '0') == 5));
}
// Driver Code
var str = "76955";
var x = isDivisibleBy5(str) ? "Yes" : "No";
document.write(x);
// This code is contributed by bunnyram19
</script>
输出:
Yes
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