通过反复从一堆中取出2个硬币和从另一堆中取出1个硬币来检查是否可以清空两堆硬币

给定两堆由N和M数量的硬币组成的硬币，任务是检查是否可以通过反复从一堆中取出2个硬币和从另一堆中取出1个硬币来同时清空两堆硬币。如果两堆都可以放空，则打印“是” 。否则，打印“否” 。

例子：

Input: N = 1, M = 2
Output: Yes
Explanation:
Remove 1 coin from 1^st pile and 2 coins from the other pile. Therefore, the number of coins in both the piles is 0.

Input: N = 2, M = 2
Output: No

方法：可以根据以下观察结果解决给定问题：

• 有两种方法可以从桩除去硬币，即，无论是从桩2移除桩1 2枚硬币和从桩2 1枚硬币或从桩1 1枚硬币和2枚硬币。
• 令X为第一次移出的移动次数， Y为第二次移出的移动次数，则两堆硬币的剩余数量分别为(N – 2 * X – Y)和(M – 2 * Y – X)分别。
• 执行(X + Y)移动后，必须清空桩，即

(N – 2*X – Y) = 0 and (M – 2*Y – X) = 0

Rearranging terms in the above equations generates the equations:

N = 2*X + Y and M = 2*Y + X

• 两堆中的硬币总数为(N + M) = (2 * X + Y)+(X + 2 * Y)= 3(X + Y) 。
• 因此，要使两个桩都变空，请满足以下条件：
  • 两堆硬币的总和应为3的倍数。
  • N和M最大必须小于最小的N和M的两倍一个一大堆将成为空和一些硬币仍然会在另外一个不留。因此，较大桩的尺寸不应大于较小桩的尺寸的两倍。

因此，该想法是检查硬币总数的总和是否为3的倍数，并且最大硬币数目最多为最小硬币数目的两倍，然后打印“是” 。否则，打印“否” 。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to check if two given piles
// can be emptied by repeatedly removing
// 2 coins from a pile and 1 coin from the other
void canBeEmptied(int A, int B)
{
    // If maximum of A & B exceeds
    // the twice of minimum of A & B
    if (max(A, B) > 2 * min(A, B)) {
 
        // Not possible to
        // empty the piles
        cout << "No";
        return;
    }
 
    // If sum of both the coins is
    // divisible by 3, then print Yes
    if ((A + B) % 3 == 0)
        cout << "Yes";
 
    // Otherwise, print "No"
    else
        cout << "No";
}
 
// Driver Code
int main()
{
    int A = 1, B = 2;
    canBeEmptied(A, B);
 
    return 0;
}

Java

// Java program for above approach
import java.util.*;
 
class GFG{
 
// Function to check if two given piles
// can be emptied by repeatedly removing
// 2 coins from a pile and 1 coin from the other
static void canBeEmptied(int A, int B)
{
     
    // If maximum of A & B exceeds
    // the twice of minimum of A & B
    if (Math.max(A, B) > 2 * Math.min(A, B))
    {
         
        // Not possible to
        // empty the piles
        System.out.println("No");
        return;
    }
 
    // If sum of both the coins is
    // divisible by 3, then print Yes
    if ((A + B) % 3 == 0)
        System.out.println("Yes");
 
    // Otherwise, print "No"
    else
        System.out.println("No");
}
 
// Driver Code
public static void main (String[] args)
{
    int A = 1, B = 2;
     
    canBeEmptied(A, B);
}
}
 
// This code is contributed by sanjoy_62

Python3

# Python3 program for the above approach
 
# Function to check if two given piles
# can be emptied by repeatedly removing
# 2 coins from a pile and 1 coin from the other
def canBeEmptied(A, B):
   
    # If maximum of A & B exceeds
    # the twice of minimum of A & B
    if (max(A, B) > 2 * min(A, B)):
       
        # Not possible to
        # empty the piles
        print("No")
        return
 
    # If sum of both the coins is
    # divisible by 3, then print Yes
    if ((A + B) % 3 == 0):
        print("Yes")
 
    # Otherwise, print "No"
    else:
        print("No")
 
# Driver Code
if __name__ == '__main__':
    A = 1
    B = 2
    canBeEmptied(A, B)
 
    # This code is contributed by bgangwar59.

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to check if two given piles
// can be emptied by repeatedly removing
// 2 coins from a pile and 1 coin from the other
static void canBeEmptied(int A, int B)
{
     
    // If maximum of A & B exceeds
    // the twice of minimum of A & B
    if (Math.Max(A, B) > 2 * Math.Min(A, B))
    {
         
        // Not possible to
        // empty the piles
        Console.WriteLine("No");
        return;
    }
 
    // If sum of both the coins is
    // divisible by 3, then print Yes
    if ((A + B) % 3 == 0)
        Console.WriteLine("Yes");
 
    // Otherwise, print "No"
    else
        Console.WriteLine("No");
}
 
// Driver Code
public static void Main ()
{
    int A = 1, B = 2;
     
    canBeEmptied(A, B);
}
}
 
// This code is contributed by mohit kumar 29

Javascript

 
// Javascript program for the above approach
 
// Function to check if two given piles
// can be emptied by repeatedly removing
// 2 coins from a pile and 1 coin from the other
function canBeEmptied(A, B)
{
     
    // If maximum of A & B exceeds
    // the twice of minimum of A & B
    if (Math.max(A, B) > 2 * Math.min(A, B))
    {
 
        // Not possible to
        // empty the piles
        document.write("No");
        return;
    }
 
    // If sum of both the coins is
    // divisible by 3, then print Yes
    if ((A + B) % 3 == 0)
        document.write("Yes");
 
    // Otherwise, print "No"
    else
        document.write("No");
}
 
// Driver Code
let A = 1, B = 2;
 
canBeEmptied(A, B);
 
// This code is contributed by subhammahato348
 

输出：

Yes

时间复杂度： O(1)
辅助空间： O(1)