给定大小为N的数组arr [] ，任务是通过执行以下操作最少次数来使所有数组元素相等：
- 将任何后缀数组的所有数组元素增加1。
- 将任何后缀数组的所有元素减少1。
- 替换任何数组元素。
例子：
Input: arr[] = {99, 96, 97, 95}
Output: 3
Explanation:
Operation 1: Replace a1 by a2, i.e. 99 → 96. The array arr[] modifies to {96, 96, 97, 95}.
Operation 2: Increment the suffix { a4} by 2, i.e., 95 → 97. The array arr[] modifies to {96, 96, 97, 97}.
Operation 3: Decrement the suffix { a3 } by 1, i.e., 97 → 96. The array arr[] modifies to {96, 96, 96, 96}.
Hence, the total number of operations required is 3.
Input: arr[] = {1, -1, 0, 1, 1}
Output: 2
方法：这个想法是找到实际总和与所有元素相等的数组之和之间的差，然后选择要执行的运算，从而导致最少的运算数。请按照以下步骤解决问题：
- 初始化一个变量，例如totOps ，以存储使所有数组元素相等所需的实际操作。
- 遍历数组并存储所有成对的连续元素之间的差，并将它们的和存储在totOps中。
- 初始化一个变量，例如maxOps ，以存储所需的最大操作数。
- 现在，找到在更改元素时发生的最大更改，并将其存储在maxOps变量中。有以下三种情况：
- 对于第一个元素，即arr [1] ，更改arr [1]的最佳方法是使其变为arr [2] 。
- 对于最后一个元素，即arr [N] ，更改arr [N]的最佳方法是使其变为arr [N-1] 。
- 对于元素的其余部分，更改arr [i]会同时影响arr [i-1]和arr [i + 1] ，因此，最大更改为abs(arr [i] – arr [i + 1])+ abs(arr [i] – arr [i-1])– abs(arr [i-1] – arr [i + 1)。
- 因此，所需的最小操作数等于totOps和maxOps之间的差。
下面是上述方法的实现：
C++
// C++ Program for the above approach
#include
using namespace std;
// Function to calculate the minimum
// operations of given type required
// to make the array elements equal
void minOperation(int a[], int N)
{
// Stores the total count of operations
int totOps = 0;
// Traverse the array
for (int i = 0; i < N - 1; i++) {
// Update difference between
// pairs of adjacent elements
totOps += abs(a[i] - a[i + 1]);
}
// Store the maximum count of operations
int maxOps
= max(abs(a[0] - a[1]),
abs(a[N - 1] - a[N - 2]));
for (int i = 1; i < N - 1; i++) {
// Rest of the elements
maxOps
= max(maxOps, abs(a[i] - a[i - 1])
+ abs(a[i] - a[i + 1])
- abs(a[i - 1] - a[i + 1]));
}
// Total Operation - Maximum Operation
cout << totOps - maxOps << endl;
}
// Driver Code
int main()
{
// Given array
int arr[] = { 1, -1, 0, 1, 1 };
// Size of the array
int N = sizeof(arr) / sizeof(arr[0]);
minOperation(arr, N);
return 0;
} Java
// Java Program for the above approach
import java.io.*;
class GFG
{
// Function to calculate the minimum
// operations of given type required
// to make the array elements equal
static void minOperation(int a[], int N)
{
// Stores the total count of operations
int totOps = 0;
// Traverse the array
for (int i = 0; i < N - 1; i++)
{
// Update difference between
// pairs of adjacent elements
totOps += Math.abs(a[i] - a[i + 1]);
}
// Store the maximum count of operations
int maxOps
= Math.max(Math.abs(a[0] - a[1]),
Math.abs(a[N - 1] - a[N - 2]));
for (int i = 1; i < N - 1; i++)
{
// Rest of the elements
maxOps = Math.max(
maxOps,
Math.abs(a[i] - a[i - 1])
+ Math.abs(a[i] - a[i + 1])
- Math.abs(a[i - 1] - a[i + 1]));
}
// Total Operation - Maximum Operation
System.out.println(totOps - maxOps);
}
// Driver Code
public static void main(String[] args)
{
// Given array
int[] arr = { 1, -1, 0, 1, 1 };
// Size of the array
int N = arr.length;
minOperation(arr, N);
}
}
// This code is contributed by Dharanendra L VPython3
# Python3 Program for the above approach
# Function to calculate the minimum
# operations of given type required
# to make the array elements equal
def minOperation(a, N):
# Stores the total count of operations
totOps = 0
# Traverse the array
for i in range(N - 1):
# Update difference between
# pairs of adjacent elements
totOps += abs(a[i] - a[i + 1])
# Store the maximum count of operations
maxOps = max(abs(a[0] - a[1]), abs(a[N - 1] - a[N - 2]))
for i in range(1, N - 1):
# Rest of the elements
maxOps = max(maxOps, abs(a[i] - a[i - 1]) +
abs(a[i] - a[i + 1])- abs(a[i - 1] - a[i + 1]))
# Total Operation - Maximum Operation
print (totOps - maxOps)
# Driver Code
if __name__ == '__main__':
# Given array
arr = [1, -1, 0, 1, 1]
# Size of the array
N = len(arr)
minOperation(arr, N)
# This code is contributed by mohit kumar 29.C#
// C# Program for the above approach
using System;
public class GFG {
// Function to calculate the minimum
// operations of given type required
// to make the array elements equal
static void minOperation(int[] a, int N)
{
// Stores the total count of operations
int totOps = 0;
// Traverse the array
for (int i = 0; i < N - 1; i++)
{
// Update difference between
// pairs of adjacent elements
totOps += Math.Abs(a[i] - a[i + 1]);
}
// Store the maximum count of operations
int maxOps
= Math.Max(Math.Abs(a[0] - a[1]),
Math.Abs(a[N - 1] - a[N - 2]));
for (int i = 1; i < N - 1; i++)
{
// Rest of the elements
maxOps = Math.Max(
maxOps,
Math.Abs(a[i] - a[i - 1])
+ Math.Abs(a[i] - a[i + 1])
- Math.Abs(a[i - 1] - a[i + 1]));
}
// Total Operation - Maximum Operation
Console.WriteLine(totOps - maxOps);
}
// Driver Code
static public void Main()
{
// Given array
int[] arr = { 1, -1, 0, 1, 1 };
// Size of the array
int N = arr.Length;
minOperation(arr, N);
}
}
// This code is contributed by Dharanendra L VJavascript
输出：
2时间复杂度： O(N)
辅助空间： O(1)