给定两个整数N和K ,任务是检查N被除以[1,K]范围内的所有整数时是否仅留下不同的余数。如果是这样,请打印“是” 。否则,打印No。
例子:
Input: N = 5, K = 3
Output: Yes
Explanation:
(5 % 1) == 0
(5 % 2) == 1
(5 % 3) == 2
Since all the remainders {0, 1, 2} are distinct.
Input: N = 5, K = 4
Output: No
Explanation:
(5 % 1) == 0
(5 % 2) == 1
(5 % 3) == 2
(5 % 4) == 1, which is not distinct.
方法:
请按照以下步骤解决问题:
- 初始化集合S
- 迭代范围[1,K] 。
- 在每次迭代中,检查Set S中是否已经存在N%i 。
- 如果不存在,则将N%i插入集合S中
- 否则,打印否并终止。
下面是上述方法的实现:
C++
// C++ Program to check if all
// remainders are distinct or not
#include
using namespace std;
// Function to check and return
// if all remainders are distinct
bool is_distinct(long long n, long long k)
{
// Stores the remainder
unordered_set s;
for (int i = 1; i <= k; i++) {
// Calculate the remainder
long long tmp = n % i;
// If remainder already occurred
if (s.find(tmp) != s.end()) {
return false;
}
// Insert into the set
s.insert(tmp);
}
return true;
}
// Driver Code
int main()
{
long long N = 5, K = 3;
if (is_distinct(N, K))
cout << "Yes";
else
cout << "No";
return 0;
}
Java
// Java program to check if all
// remainders are distinct or not
import java.util.*;
class GFG{
// Function to check and return
// if all remainders are distinct
static boolean is_distinct(long n, long k)
{
// Stores the remainder
HashSet s = new HashSet();
for(int i = 1; i <= k; i++)
{
// Calculate the remainder
long tmp = n % i;
// If remainder already occurred
if (s.contains(tmp))
{
return false;
}
// Insert into the set
s.add(tmp);
}
return true;
}
// Driver Code
public static void main(String[] args)
{
long N = 5, K = 3;
if (is_distinct(N, K))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by gauravrajput1
Python3
# Python3 program to check if all
# remainders are distinct or not
# Function to check and return
# if all remainders are distinct
def is_distinct(n, k):
# Stores the remainder
s = set()
for i in range(1, k + 1):
# Calculate the remainder
tmp = n % i
# If remainder already occurred
if (tmp in s):
return False
# Insert into the set
s.add(tmp)
return True
# Driver Code
if __name__ == '__main__':
N = 5
K = 3
if (is_distinct(N, K)):
print("Yes")
else:
print("No")
# This code is contributed by Shivam Singh
C#
// C# program to check if all
// remainders are distinct or not
using System;
using System.Collections.Generic;
class GFG{
// Function to check and return
// if all remainders are distinct
static bool is_distinct(long n, long k)
{
// Stores the remainder
HashSet s = new HashSet();
for(int i = 1; i <= k; i++)
{
// Calculate the remainder
long tmp = n % i;
// If remainder already occurred
if (s.Contains(tmp))
{
return false;
}
// Insert into the set
s.Add(tmp);
}
return true;
}
// Driver Code
public static void Main(String[] args)
{
long N = 5, K = 3;
if (is_distinct(N, K))
Console.Write("Yes");
else
Console.Write("No");
}
}
// This code is contributed by gauravrajput1
输出:
Yes
时间复杂度: O(K)
辅助空间: O(K)