给定大小为N的数组arr [] ,任务是打印给定数组可以通过执行以下操作而减小到的最小大小:
- 删除任意两个相邻的元素,例如arr [i]和arr [i + 1],并在数组中的该位置插入单个元素arr [i] * arr [i + 1] 。
- 如果所有数组元素都相等,则打印数组的大小。
例子:
Input: arr[] = {1, 7, 7, 1, 7, 1}
Output: 1
Explanation:
Pick arr[0] and arr[1] and replace with arr[0]*arr[1], arr[] = {7, 7, 1, 7, 1}
Pick arr[0] and arr[1] and replace with arr[0]*arr[1], arr[] = {49, 1, 7, 1}
Pick arr[0] and arr[1] and replace with arr[0]*arr[1], arr[] = {49, 7, 1}
Pick arr[0] and arr[1] and replace with arr[0]*arr[1], arr[] = {343, 1}
Pick arr[0] and arr[1] and replace with arr[0]*arr[1], arr[] = {343}
Input: arr[] = {2, 2, 2, 2}
Output: 4
方法:该方法基于以下想法:如果所有数组元素都相同,则无法在给定数组上执行给定的操作。否则,在每种情况下,都可以将数组大小减小为1。以下是步骤:
- 遍历给定数组arr [] 。
- 如果数组的所有元素都相同,则将N打印为所需答案。
- 否则,请始终选择能够提供最大乘积以将arr []的大小减小为1的相邻元素。因此,最小可能的大小将为1 。
下面是上述方法的实现:
C++
// C++ implementation of the above approach
#include
using namespace std;
// Function to minimize the size of
// array by performing given operations
int minLength(int arr[], int N)
{
for (int i = 1; i < N; i++) {
// If all array elements
// are not same
if (arr[0] != arr[i]) {
return 1;
}
}
// If all array elements
// are same
return N;
}
// Driver Code
int main()
{
int arr[] = { 2, 1, 3, 1 };
int N = sizeof(arr) / sizeof(arr[0]);
// Function Call
cout << minLength(arr, N);
return 0;
}
Java
// Java implementation of the above approach
import java.io.*;
class GFG{
// Function to minimize the size of
// array by performing given operations
static int minLength(int arr[], int N)
{
for(int i = 1; i < N; i++)
{
// If all array elements
// are not same
if (arr[0] != arr[i])
{
return 1;
}
}
// If all array elements
// are same
return N;
}
// Driver Code
public static void main(String[] args)
{
int[] arr = { 2, 1, 3, 1 };
int N = arr.length;
// Function call
System.out.print(minLength(arr, N));
}
}
// This code is contributed by akhilsaini
Python3
# Python3 implementation of the above approach
# Function to minimize the size of
# array by performing given operations
def minLength(arr, N):
for i in range(1, N):
# If all array elements
# are not same
if (arr[0] != arr[i]):
return 1
# If all array elements
# are same
return N
# Driver Code
if __name__ == "__main__":
arr = [ 2, 1, 3, 1 ]
N = len(arr)
# Function call
print(minLength(arr, N))
# This code is contributed by akhilsaini
C#
// C# implementation of the above approach
using System;
class GFG{
// Function to minimize the size of
// array by performing given operations
static int minLength(int[] arr, int N)
{
for(int i = 1; i < N; i++)
{
// If all array elements
// are not same
if (arr[0] != arr[i])
{
return 1;
}
}
// If all array elements
// are same
return N;
}
// Driver Code
public static void Main()
{
int[] arr = { 2, 1, 3, 1 };
int N = arr.Length;
// Function call
Console.Write(minLength(arr, N));
}
}
// This code is contributed by akhilsaini
输出:
1
时间复杂度: O(N)
辅助空间: O(1)