给定一个二进制数组arr[] cof size N ,任务是通过以下两个操作将数组缩减为单个元素:
- 连续的0或1的三元组保持不变。
- 由两个 0 和单个 1组成的连续数组元素的三元组可以转换为更频繁的元素,反之亦然。
例子:
Input: arr[] = {0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1}
Output: No
Explanation:
Following are the operations performed on the array:
{0, 1, 1} -> 1 modifies the array to {1, 1, 1, 0, 0, 1, 1, 1, 1}
{1, 0, 0} -> 0 modifies the array to {1, 1, 0, 1, 1, 1, 1}
{1, 0, 1} -> 1 modifies the array to {1, 1, 1, 1, 1}
Since, all the remaining elements are 1, they remain unchanged.
Therefore, the array cannot be reduced to a single element.
Input: arr[] = {1, 0, 0, 0, 1, 1, 1}
Output: Yes
Explanation:
Following are the operations performed on the array:
{1, 0, 0} -> 0 {0, 0, 1, 1, 1}
{0, 0, 1} -> 0 {0, 1, 1}
{0, 1, 1} -> 1 {1}
方法:
请按照以下步骤解决问题:
- 计算0和1的频率。
- 计算它们各自计数的绝对差。
- 如果差为 1,则数组只能减少为 1。因此,打印 Yes。
- 否则,打印编号。
下面是上述方法的实现:
C++
// C++ program to implement
// the above approach
#include
using namespace std;
// Function to check if it is possible to
// reduce the array to a single element
void solve(int arr[], int n)
{
// Stores frequency of 0's
int countzeroes = 0;
// Stores frequency of 1's
int countones = 0;
for (int i = 0; i < n; i++) {
if (arr[i] == 0)
countzeroes++;
else
countones++;
}
// Condition for array to be reduced
if (abs(countzeroes - countones) == 1)
cout << "Yes";
// Otherwise
else
cout << "No";
}
// Driver Code
int main()
{
int arr[] = { 0, 1, 0, 0, 1, 1, 1 };
int n = sizeof(arr) / sizeof(arr[0]);
solve(arr, n);
return 0;
}
Java
// Java program to implement
// the above approach
class GFG{
// Function to check if it is possible to
// reduce the array to a single element
static void solve(int arr[], int n)
{
// Stores frequency of 0's
int countzeroes = 0;
// Stores frequency of 1's
int countones = 0;
for(int i = 0; i < n; i++)
{
if (arr[i] == 0)
countzeroes++;
else
countones++;
}
// Condition for array to be reduced
if (Math.abs(countzeroes - countones) == 1)
System.out.print("Yes");
// Otherwise
else
System.out.print("No");
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 0, 1, 0, 0, 1, 1, 1 };
int n = arr.length;
solve(arr, n);
}
}
// This code is contributed by 29AjayKumar
Python3
# Python3 program to implement
# the above approach
# Function to check if it is possible to
# reduce the array to a single element
def solve(arr, n):
# Stores frequency of 0's
countzeroes = 0;
# Stores frequency of 1's
countones = 0;
for i in range(n):
if (arr[i] == 0):
countzeroes += 1;
else:
countones += 1;
# Condition for array to be reduced
if (abs(countzeroes - countones) == 1):
print("Yes");
# Otherwise
else:
print("No");
# Driver Code
if __name__ == '__main__':
arr = [ 0, 1, 0, 0, 1, 1, 1 ];
n = len(arr);
solve(arr, n);
# This code is contributed by Amit Katiyar
C#
// C# program to implement
// the above approach
using System;
class GFG{
// Function to check if it is possible to
// reduce the array to a single element
static void solve(int []arr, int n)
{
// Stores frequency of 0's
int countzeroes = 0;
// Stores frequency of 1's
int countones = 0;
for(int i = 0; i < n; i++)
{
if (arr[i] == 0)
countzeroes++;
else
countones++;
}
// Condition for array to be reduced
if (Math.Abs(countzeroes - countones) == 1)
Console.Write("Yes");
// Otherwise
else
Console.Write("No");
}
// Driver Code
public static void Main(String[] args)
{
int []arr = { 0, 1, 0, 0, 1, 1, 1 };
int n = arr.Length;
solve(arr, n);
}
}
// This code is contributed by 29AjayKumar
Javascript
Yes
时间复杂度: O(N)
辅助空间: O(1)