检查一个大数是否能被 25 整除
给定一个数字，任务是检查这个数字是否能被 25 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 = 56945250
Output : Yes
Input : n = 1234567589333100
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 % 25 来检查一个数字是否能被 25 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 25 if its digits
last two digits will be 0 or divisible by 25 .
插图:
For example, let us consider 769575
Number formed by last two digits is = 75
Since 75 is divisible by 25 , answer is YES.
Let us consider 5325, we can write it as
5325 = 5*1000 + 3*100 + 2*10 + 5
The proof is based on below observation:
Remainder of 10i divided by 25 is 0 if i greater
than or equal to two. Note than 100, 1000,
... etc lead to remainder 0 when divided by 25.
So remainder of " 5*1000 + 3*100 + 2*10 + 5"
divided by 25 is equivalent to remainder
of following :
0 + 0 + 20 + 5 = 25
Since 25 is divisible by 25, answer is yes.
C++
// C++ program to find if a number is
// divisible by 25 or not
#include<bits/stdc++.h>
using namespace std;
// Function to find that number divisible
// by 25 or not.
bool isDivisibleBy25(string str)
{
// If length of string is single digit then
// it's not divisible by 25
int n = str.length();
if (n == 1)
return false;
return ( (str[n-1]-'0' == 0 &&
str[n-2]-'0' == 0) ||
((str[n-2]-'0')*10 + (str[n-1]-'0'))%25 == 0 );
}
// Driver code
int main()
{
string str = "76955";
isDivisibleBy25(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 25 or not
class IsDivisible
{
// Function to find that number divisible
// by 25 or not.
static boolean isDivisibleBy25(String str)
{
// If length of string is single digit then
// it's not divisible by 25
int n = str.length();
if (n == 1)
return false;
return ( (str.charAt(n-1)-'0' == 0 &&
str.charAt(n-2)-'0' == 0) ||
((str.charAt(n-2)-'0')*10 + (str.charAt(n-1)-'0'))%25 == 0 );
}
// main function
public static void main (String[] args)
{
String str = "76955";
if(isDivisibleBy25(str))
System.out.println("Yes");
else
System.out.println("No");
}
}
Python 3
# Python 3 program to find if
# a number is divisible by 25
# or not
# Function to find that
# number divisible by 25 or not.
def isDivisibleBy25(st) :
# If length of string is
# single digit then it's
# not divisible by 25
n = len(st)
if (n == 1) :
return False
return ((int)(st[n-1]) == 0 and ((int)(st[n-2])== 0) or
((int)(st[n-2])*10 + (int)(st[n-1])%25 == 0))
# Driver code
st = "76955"
if(isDivisibleBy25(st)) :
print("Yes")
else :
print("No")
# This code is contributed by Nikita Tiwari.
C
// C# program to find if a number
// is divisible by 25 or not
using System;
class IsDivisible
{
// Function to find that number
// divisible by 25 or not.
static bool isDivisibleBy25(String str)
{
// If length of string is single digit then
// then it's not divisible by 25
int n = str.Length;
if (n == 1)
return false;
return ((str[n - 1] - '0' == 0 &&
str[n - 2] - '0' == 0) ||
((str[n - 2] - '0') * 10 +
(str[n - 1] - '0')) % 25 == 0);
}
// Driver Code
public static void Main ()
{
String str = "76955";
if(isDivisibleBy25(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 25 or not
// Function to find that number
// divisible by 25 or not.
function isDivisibleBy25($str)
{
// If length of string
// is single digit then
// it's not divisible by 25
$n = strlen($str);
if ($n == 1)
return false;
return ( ($str[$n - 1] -'0' == 0 &&
$str[$n - 2] -'0' == 0) ||
(($str[$n - 2] -'0') * 10 +
($str[$n - 1] - '0')) % 25 == 0 );
}
// Driver code
$str = "76955";
$x = isDivisibleBy25($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 25 or not
// Function to find that number
// divisible by 25 or not
function isDivisibleBy25(str)
{
// If length of string
// is single digit then
// it's not divisible by 25
n = str.length;
if (n == 1)
return false;
return ((str[n - 1] -'0' == 0 &&
str[n - 2] -'0' == 0) ||
((str[n - 2] -'0') * 10 +
(str[n - 1] - '0')) % 25 == 0);
}
// Driver Code
var str = "76955";
var x = isDivisibleBy25(str) ? "Yes" : "No";
document.write (x);
// This code is contributed by bunnyram19
</script>
输出:
No
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