在 K 个否定后最大化数组总和 |设置 1

给定一个大小为 n 的数组和一个数字 k。我们必须修改数组 K 次。这里修改数组意味着在每个操作中我们可以用-arr[i]替换任何数组元素arr[i]。我们需要以这样的方式执行此操作，即经过K次操作后，数组的总和必须最大？

例子 ：

Input : arr[] = {-2, 0, 5, -1, 2} 
        K = 4
Output: 10
Explanation:
1. Replace (-2) by -(-2), array becomes {2, 0, 5, -1, 2}
2. Replace (-1) by -(-1), array becomes {2, 0, 5, 1, 2}
3. Replace (0) by -(0), array becomes {2, 0, 5, 1, 2}
4. Replace (0) by -(0), array becomes {2, 0, 5, 1, 2}

Input : arr[] = {9, 8, 8, 5} 
        K = 3
Output: 20

这个问题有一个非常简单的解决方案，我们只需要将数组中的最小元素 arr[i] 替换为 -arr[i] 以进行当前操作。这样我们就可以在 K 次操作后使数组的总和最大。一个有趣的例子是，一旦最小元素变为 0，我们就不需要再做任何更改了。

C++

// C++ program to maximize array sum after
// k operations.
#include 
using namespace std;
 
// This function does k operations on array
// in a way that maximize the array sum.
// index --> stores the index of current minimum
// element for j'th operation
int maximumSum(int arr[], int n, int k)
{
    // Modify array K number of times
    for (int i = 1; i <= k; i++)
    {
        int min = INT_MAX;
        int index = -1;
 
        // Find minimum element in array for
        // current operation and modify it
        // i.e; arr[j] --> -arr[j]
        for (int j = 0; j < n; j++)
        {
            if (arr[j] < min) {
                min = arr[j];
                index = j;
            }
        }
 
        // this the condition if we find 0 as
        // minimum element, so it will useless to
        // replace 0 by -(0) for remaining operations
        if (min == 0)
            break;
 
        // Modify element of array
        arr[index] = -arr[index];
    }
 
    // Calculate sum of array
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += arr[i];
    return sum;
}
 
// Driver code
int main()
{
    int arr[] = { -2, 0, 5, -1, 2 };
    int k = 4;
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << maximumSum(arr, n, k);
    return 0;
}

Java

// Java program to maximize array
// sum after k operations.
 
class GFG {
    // This function does k operations
    // on array in a way that maximize
    // the array sum. index --> stores
    // the index of current minimum
    // element for j'th operation
    static int maximumSum(int arr[], int n, int k)
    {
        // Modify array K number of times
        for (int i = 1; i <= k; i++)
        {
            int min = [phone];
            int index = -1;
 
            // Find minimum element in array for
            // current operation and modify it
            // i.e; arr[j] --> -arr[j]
            for (int j = 0; j < n; j++)
            {
                if (arr[j] < min)
                {
                    min = arr[j];
                    index = j;
                }
            }
 
            // this the condition if we find 0 as
            // minimum element, so it will useless to
            // replace 0 by -(0) for remaining operations
            if (min == 0)
                break;
 
            // Modify element of array
            arr[index] = -arr[index];
        }
 
        // Calculate sum of array
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += arr[i];
        return sum;
    }
 
    // Driver code
    public static void main(String arg[])
    {
        int arr[] = { -2, 0, 5, -1, 2 };
        int k = 4;
        int n = arr.length;
        System.out.print(maximumSum(arr, n, k));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python3 program to maximize
# array sum after k operations.
 
# This function does k operations on array
# in a way that maximize the array sum.
# index --> stores the index of current
# minimum element for j'th operation
 
 
def maximumSum(arr, n, k):
 
    # Modify array K number of times
    for i in range(1, k + 1):
 
        min = [phone]
        index = -1
 
        # Find minimum element in array for
        # current operation and modify it
        # i.e; arr[j] --> -arr[j]
        for j in range(n):
 
            if (arr[j] < min):
 
                min = arr[j]
                index = j
 
        # this the condition if we find 0 as
        # minimum element, so it will useless to
        # replace 0 by -(0) for remaining operations
        if (min == 0):
            break
 
        # Modify element of array
        arr[index] = -arr[index]
 
    # Calculate sum of array
    sum = 0
    for i in range(n):
        sum += arr[i]
    return sum
 
 
# Driver code
arr = [-2, 0, 5, -1, 2]
k = 4
n = len(arr)
print(maximumSum(arr, n, k))
 
# This code is contributed by Anant Agarwal.

C#

// C# program to maximize array
// sum after k operations.
using System;
 
class GFG {
 
    // This function does k operations
    // on array in a way that maximize
    // the array sum. index --> stores
    // the index of current minimum
    // element for j'th operation
    static int maximumSum(int[] arr, int n, int k)
    {
 
        // Modify array K number of times
        for (int i = 1; i <= k; i++)
        {
            int min = [phone];
            int index = -1;
 
            // Find minimum element in array for
            // current operation and modify it
            // i.e; arr[j] --> -arr[j]
            for (int j = 0; j < n; j++)
            {
                if (arr[j] < min)
                {
                    min = arr[j];
                    index = j;
                }
            }
 
            // this the condition if we find
            // 0 as minimum element, so it
            // will useless to replace 0 by -(0)
            // for remaining operations
            if (min == 0)
                break;
 
            // Modify element of array
            arr[index] = -arr[index];
        }
 
        // Calculate sum of array
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += arr[i];
        return sum;
    }
 
    // Driver code
    public static void Main()
    {
        int[] arr = { -2, 0, 5, -1, 2 };
        int k = 4;
        int n = arr.Length;
        Console.Write(maximumSum(arr, n, k));
    }
}
 
// This code is contributed by Nitin Mittal.

PHP

 stores
// the index of current minimum
// element for j'th operation
function maximumSum($arr, $n, $k)
{
    $INT_MAX = 0;
    // Modify array K
    // number of times
    for ($i = 1; $i <= $k; $i++)
    {
        $min = $INT_MAX;
        $index = -1;
 
        // Find minimum element in
        // array for current operation
        // and modify it i.e;
        // arr[j] --> -arr[j]
        for ($j = 0; $j < $n; $j++)
        {
            if ($arr[$j] < $min)
            {
                $min = $arr[$j];
                $index = $j;
            }
        }
 
        // this the condition if we
        // find 0 as minimum element, so
        // it will useless to replace 0
        // by -(0) for remaining operations
        if ($min == 0)
            break;
 
        // Modify element of array
        $arr[$index] = -$arr[$index];
    }
 
    // Calculate sum of array
    $sum = 0;
    for ($i = 0; $i < $n; $i++)
        $sum += $arr[$i];
    return $sum;
}
 
// Driver Code
$arr = array(-2, 0, 5, -1, 2);
$k = 4;
$n = sizeof($arr) / sizeof($arr[0]);
echo maximumSum($arr, $n, $k);
     
// This code is contributed
// by nitin mittal.
?>

Javascript

     
// Javascript program to maximize array
// sum after k operations.
 
// This function does k operations
// on array in a way that maximize
// the array sum. index --> stores
// the index of current minimum
// element for j'th operation
function maximumSum(arr, n, k)
{
     
    // Modify array K number of times
    for(let i = 1; i <= k; i++)
    {
        let min = [phone];
        let index = -1;
 
        // Find minimum element in array for
        // current operation and modify it
        // i.e; arr[j] --> -arr[j]
        for(let j = 0; j < n; j++)
        {
            if (arr[j] < min)
            {
                min = arr[j];
                index = j;
            }
        }
 
        // This the condition if we find 0 as
        // minimum element, so it will useless to
        // replace 0 by -(0) for remaining operations
        if (min == 0)
            break;
 
        // Modify element of array
        arr[index] = -arr[index];
    }
 
    // Calculate sum of array
    let sum = 0;
    for(let i = 0; i < n; i++)
        sum += arr[i];
         
    return sum;
}
     
// Driver code
let arr = [ -2, 0, 5, -1, 2 ];
let k = 4;
let n = arr.length;
 
document.write(maximumSum(arr, n, k));
 
// This code is contributed by code_hunt
 

输出

10

时间复杂度： O(k*n)
辅助空间： O(1)

1. 方法 2（使用排序）：
   这种方法比上面讨论的方法要好一些。在这种方法中，我们将首先使用Java内置的排序函数对给定的数组进行排序，该函数具有 O(nlogn) 的最差运行时间复杂度。
2. 然后对于给定的 k 值，我们将继续遍历数组，直到 k 保持大于 0，如果任何索引处的数组值小于 0，我们将更改其符号并将 k 减 1。
3. 如果我们在数组中找到 0，我们将立即设置 k 等于 0 以最大化我们的结果。
4. 在某些情况下，如果数组中的所有值都大于 0，我们将更改正值的符号，因为我们的数组已经排序，我们将更改数组中存在的较低值的符号，这最终将最大化我们的总和。

下面是上述方法的实现：

C++

// C++ program to find maximum array sum
// after at most k negations.
#include 
 
using namespace std;
 
int sol(int arr[], int n, int k)
{
    int sum = 0;
    int i = 0;
   
    // Sorting given array using in-built
    // sort function
    sort(arr, arr + n);
    while (k > 0)
    {
        // If we find a 0 in our
        // sorted array, we stop
        if (arr[i] >= 0)
            k = 0;
        else
        {
            arr[i] = (-1) * arr[i];
            k = k - 1;
        }
        i++;
        
    }
 
    // Calculating sum
    for(int j = 0; j < n; j++)
    {
        sum += arr[j];
    }
    return sum;
}
 
// Driver code
int main()
{
    int arr[] = { -2, 0, 5, -1, 2 };
 
    int n = sizeof(arr) / sizeof(arr[0]);
     
    cout << sol(arr, n, 4) << endl;
 
    return 0;
}
 
// This code is contributed by pratham76

Java

// Java program to find maximum array sum
// after at most k negations.
import java.util.Arrays;
 
public class GFG {
 
    static int sol(int arr[], int k)
    {
        // Sorting given array using in-built
        // java sort function
        Arrays.sort(arr);
        int sum = 0;
 
        int i = 0;
        while (k > 0)
        {
            // If we find a 0 in our
            // sorted array, we stop
            if (arr[i] >= 0)
                k = 0;
 
            else
            {
                arr[i] = (-1) * arr[i];
                k = k - 1;
            }
 
            i++;
        }
 
        // Calculating sum
        for (int j = 0; j < arr.length; j++)
        {
            sum += arr[j];
        }
        return sum;
    }
   
    // Driver Code
    public static void main(String[] args)
    {
        int arr[] = { -2, 0, 5, -1, 2 };
        System.out.println(sol(arr, 4));
    }
}

蟒蛇3

# Python3 program to find maximum array
# sum after at most k negations
 
 
def sol(arr, k):
 
    # Sorting given array using
    # in-built java sort function
    arr.sort()
 
    Sum = 0
    i = 0
 
    while (k > 0):
 
        # If we find a 0 in our
        # sorted array, we stop
        if (arr[i] >= 0):
            k = 0
        else:
            arr[i] = (-1) * arr[i]
            k = k - 1
 
        i += 1
 
    # Calculating sum
    for j in range(len(arr)):
        Sum += arr[j]
 
    return Sum
 
 
# Driver code
arr = [-2, 0, 5, -1, 2]
 
print(sol(arr, 4))
 
# This code is contributed by avanitrachhadiya2155

C＃

// C# program to find maximum array sum
// after at most k negations.
using System;
  
class GFG{
  
static int sol(int []arr, int k)
{
     
    // Sorting given array using
    // in-built java sort function
    Array.Sort(arr);
     
    int sum = 0;
    int i = 0;
     
    while (k > 0)
    {
         
        // If we find a 0 in our
        // sorted array, we stop
        if (arr[i] >= 0)
            k = 0;
 
        else
        {
            arr[i] = (-1) * arr[i];
            k = k - 1;
        }
        i++;
    }
     
    // Calculating sum
    for(int j = 0; j < arr.Length; j++)
    {
        sum += arr[j];
    }
    return sum;
}
 
// Driver code
public static void Main(string[] args)
{
    int []arr = { -2, 0, 5, -1, 2 };
     
    Console.Write(sol(arr, 4));
}
}
 
// This code is contributed by rutvik_56

Javascript

 
// JavaScript program to find maximum array sum
// after at most k negations.
 
    function sol(arr, k)
    {
     
        // Sorting given array using in-built
        // java sort function
        arr.sort();
        let sum = 0;
  
        let i = 0;
        while (k > 0)
        {
         
            // If we find a 0 in our
            // sorted array, we stop
            if (arr[i] >= 0)
                k = 0;
  
            else
            {
                arr[i] = (-1) * arr[i];
                k = k - 1;
            }
  
            i++;
        }
  
        // Calculating sum
        for (let j = 0; j < arr.length; j++)
        {
            sum += arr[j];
        }
        return sum;
    }
 
// Driver code
    let arr = [ -2, 0, 5, -1, 2 ];
    document.write(sol(arr, 4));
 
// This code is contributed by souravghosh0416.                            

输出

10

时间复杂度： O(n*logn)
辅助空间： O(1)

方法3（使用排序）：

当需要否定至多 k 个元素时，上述方法 2 是最佳的。为了解决当恰好有 k 个否定时，下面给出了算法。

1. 按升序对数组进行排序。初始化 i = 0。
2. 递增 i 并将所有负元素乘以 -1，直到 k 成为或达到正元素。
3. 检查数组是否已结束。如果为真，则转到第 (n-1) 个元素。
4. 如果 k ==0 或 k 为偶数，则返回所有元素的总和。否则将第 i 个或第 (i-1) 个元素的最小值的绝对值乘以 -1。
5. 返回数组的总和。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
#include 
using namespace std;
 
// Function to calculate sum of the array
long long int sumArray(long long int* arr, int n)
{
    long long int sum = 0;
 
    // Iterate from 0 to n - 1
    for (int i = 0; i < n; i++) {
        sum += arr[i];
    }
    return sum;
}
 
// Function to maximize sum
long long int maximizeSum(long long int arr[], int n, int k)
{
    sort(arr, arr + n);
    int i = 0;
 
    // Iterate from 0 to n - 1
    for (i = 0; i < n; i++) {
        if (k && arr[i] < 0) {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
 
    if (k == 0 || k % 2 == 0) {
        return sumArray(arr, n);
    }
 
    if (i != 0 && abs(arr[i]) >= abs(arr[i - 1])) {
        i--;
    }
 
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
int main()
{
    int n = 5;
    int k = 4;
    long long int arr[5] = { -3, -2, -1, 5, 6 };
 
    // Function Call
    cout << maximizeSum(arr, n, k) << endl;
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to calculate sum of the array
static int sumArray( int[] arr, int n)
{
    int sum = 0;
    
    // Iterate from 0 to n - 1
    for(int i = 0; i < n; i++)
    {
        sum += arr[i];
    }
    return sum;
}
  
// Function to maximize sum
static int maximizeSum(int arr[], int n, int k)
{
    Arrays.sort(arr);
    int i = 0;
    
    // Iterate from 0 to n - 1
    for(i = 0; i < n; i++)
    {
        if (k != 0 && arr[i] < 0)
        {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
  
    if (k == 0 || k % 2 == 0)
    {
        return sumArray(arr, n);
    }
  
    if (i != 0 && Math.abs(arr[i]) >=
        Math.abs(arr[i - 1]))
    {
        i--;
    }
  
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
public static void main(String args[])
{
    int n = 5;
    int k = 4;
    int arr[] = { -3, -2, -1, 5, 6 };
    
    // Function Call
    System.out.print(maximizeSum(arr, n, k));
}
}
 
// This code is contributed by sanjoy_62

蟒蛇3

# Python3 program for the above approach
 
# Function to calculate sum of the array
def sumArray(arr, n):
    sum = 0
     
    # Iterate from 0 to n - 1
    for i in range(n):
        sum += arr[i]
         
    return sum
 
# Function to maximize sum
def maximizeSum(arr, n, k):
     
    arr.sort()
    i = 0
   
    # Iterate from 0 to n - 1
    for i in range(n):
        if (k and arr[i] < 0):
            arr[i] *= -1
            k -= 1
            continue
         
        break
     
    if (i == n):
        i -= 1
 
    if (k == 0 or k % 2 == 0):
        return sumArray(arr, n)
 
    if (i != 0 and abs(arr[i]) >= abs(arr[i - 1])):
        i -= 1
 
    arr[i] *= -1
    return sumArray(arr, n)
 
# Driver Code
n = 5
k = 4
arr = [ -3, -2, -1, 5, 6 ]
   
# Function Call
print(maximizeSum(arr, n, k))
 
# This code is contributed by rohitsingh07052

C＃

// C# program for the above approach
using System;
 
class GFG{
     
// Function to calculate sum of the array
static int sumArray( int[] arr, int n)
{
    int sum = 0;
    
    // Iterate from 0 to n - 1
    for(int i = 0; i < n; i++)
    {
        sum += arr[i];
    }
    return sum;
}
  
// Function to maximize sum
static int maximizeSum(int[] arr, int n, int k)
{
    Array.Sort(arr);
    int i = 0;
    
    // Iterate from 0 to n - 1
    for(i = 0; i < n; i++)
    {
        if (k != 0 && arr[i] < 0)
        {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
  
    if (k == 0 || k % 2 == 0)
    {
        return sumArray(arr, n);
    }
  
    if (i != 0 && Math.Abs(arr[i]) >=
                  Math.Abs(arr[i - 1]))
    {
        i--;
    }
  
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
static public void Main()
{
    int n = 5;
    int k = 4;
    int[] arr = { -3, -2, -1, 5, 6 };
    
    // Function Call
    Console.Write(maximizeSum(arr, n, k));
}
}
 
// This code is contributed by shubhamsingh10

Javascript

// Javascript program for the above approach
 
// Function to calculate sum of the array
function  sumArray(arr,n)
{
    let sum = 0;
     
    // Iterate from 0 to n - 1
    for(let i = 0; i < n; i++)
    {
        sum += arr[i];
    }
    return sum;
}
 
// Function to maximize sum
function maximizeSum(arr,n,k)
{
    (arr).sort(function(a,b){return a-b;});
    let i = 0;
     
    // Iterate from 0 to n - 1
    for(i = 0; i < n; i++)
    {
        if (k != 0 && arr[i] < 0)
        {
            arr[i] *= -1;
            k--;
            continue;
        }
        break;
    }
    if (i == n)
        i--;
   
    if (k == 0 || k % 2 == 0)
    {
        return sumArray(arr, n);
    }
   
    if (i != 0 && Math.abs(arr[i]) >=
        Math.abs(arr[i - 1]))
    {
        i--;
    }
   
    arr[i] *= -1;
    return sumArray(arr, n);
}
 
// Driver Code
let n = 5;
let k = 4;   
let arr=[-3, -2, -1, 5, 6 ];
 
// Function Call
document.write(maximizeSum(arr, n, k));
 
// This code is contributed by ab2127

输出

15

时间复杂度： O(n*logn)

辅助空间： O(1)

在 K 个否定后最大化数组总和 | 2套

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