Kaprekar数是一个数字,当将其分为两部分时,其平方为零,使得部分的总和等于原始数字,并且所有部分的值都不为0。(来源:Wiki)
给定一个数字,任务是检查它是否是Kaprekar数字。
例子:
Input : n = 45
Output : Yes
Explanation : 452 = 2025 and 20 + 25 is 45
Input : n = 13
Output : No
Explanation : 132 = 169. Neither 16 + 9 nor 1 + 69 is equal to 13
Input : n = 297
Output : Yes
Explanation: 2972 = 88209 and 88 + 209 is 297
Input : n = 10
Output : No
Explanation: 102 = 100. It is not a Kaprekar number even if
sum of 100 + 0 is 100. This is because of the condition that
none of the parts should have value 0.
- 求n的平方并计算平方中的位数。
- 在不同位置拆分正方形,并查看任何拆分中的两个部分的总和是否等于n。
以下是该想法的实现。
C++
//C++ program to check if a number is Kaprekar number or not
#include
using namespace std;
// Returns true if n is a Kaprekar number, else false
bool iskaprekar(int n)
{
if (n == 1)
return true;
// Count number of digits in square
int sq_n = n * n;
int count_digits = 0;
while (sq_n)
{
count_digits++;
sq_n /= 10;
}
sq_n = n*n; // Recompute square as it was changed
// Split the square at different poitns and see if sum
// of any pair of splitted numbers is equal to n.
for (int r_digits=1; r_digits
Java
// Java program to check if a number is
// Kaprekar number or not
class GFG
{
// Returns true if n is a Kaprekar number, else false
static boolean iskaprekar(int n)
{
if (n == 1)
return true;
// Count number of digits in square
int sq_n = n * n;
int count_digits = 0;
while (sq_n != 0)
{
count_digits++;
sq_n /= 10;
}
sq_n = n*n; // Recompute square as it was changed
// Split the square at different poitns and see if sum
// of any pair of splitted numbers is equal to n.
for (int r_digits=1; r_digits
Python
# Python program to check if a number is Kaprekar number or not
import math
# Returns true if n is a Kaprekar number, else false
def iskaprekar( n):
if n == 1 :
return True
#Count number of digits in square
sq_n = n * n
count_digits = 1
while not sq_n == 0 :
count_digits = count_digits + 1
sq_n = sq_n / 10
sq_n = n*n # Recompute square as it was changed
# Split the square at different poitns and see if sum
# of any pair of splitted numbers is equal to n.
r_digits = 0
while r_digits< count_digits :
r_digits = r_digits + 1
eq_parts = (int) (math.pow(10, r_digits))
# To avoid numbers like 10, 100, 1000 (These are not
# Karprekar numbers
if eq_parts == n :
continue
# Find sum of current parts and compare with n
sum = sq_n/eq_parts + sq_n % eq_parts
if sum == n :
return True
# compare with original number
return False
# Driver method
i=1
while i<10000 :
if (iskaprekar(i)) :
print i," ",
i = i + 1
# code contributed by Nikita Tiwari
C#
// C# program to check if a number is
// Kaprekar number or not
using System;
class GFG {
// Returns true if n is a Kaprekar
// number, else false
static bool iskaprekar(int n)
{
if (n == 1)
return true;
// Count number of digits
// in square
int sq_n = n * n;
int count_digits = 0;
while (sq_n != 0) {
count_digits++;
sq_n /= 10;
}
// Recompute square as it was changed
sq_n = n * n;
// Split the square at different poitns
// and see if sum of any pair of splitted
// numbers is equal to n.
for (int r_digits = 1; r_digits < count_digits;
r_digits++)
{
int eq_parts = (int)Math.Pow(10, r_digits);
// To avoid numbers like 10, 100, 1000
// These are not Karprekar numbers
if (eq_parts == n)
continue;
// Find sum of current parts and compare
// with n
int sum = sq_n / eq_parts + sq_n % eq_parts;
if (sum == n)
return true;
}
// compare with original number
return false;
}
// Driver method
public static void Main()
{
Console.WriteLine("Printing first few "
+ "Kaprekar Numbers using iskaprekar()");
for (int i = 1; i < 10000; i++)
if (iskaprekar(i))
Console.Write(i + " ");
}
}
// This code is contributed by vt_m.
PHP
Javascript
输出:
Printing first few Kaprekar Numbers using iskaprekar()
1 9 45 55 99 297 703 999 2223 2728 4879 4950 5050 5292 7272 7777 9999