通过用其上一个或下一个元素的最近幂替换元素来修改数组

给定一个由N 个正整数组成的圆形数组arr[] ，任务是通过用其前一个或下一个数组元素的最近幂替换每个数组元素来修改数组。

例子：

Input: arr[] = {2, 3, 4, 1, 2}
Output: {2, 4, 3, 1, 2}
Explanation:
For arr[0](= 2): The previous and the next array elements are 2 and 3 respectively. Therefore, nearest power is 2¹.
For arr[1](= 3): The previous and the next elements are 2 and 4 respectively. Therefore, the nearest power is 4¹.
For arr[2](= 4): The previous and the next elements are 3 and 1 respectively. Therefore, the nearest power is 3¹.
For arr[3](= 1): The previous and the next elements are 4, and 2. Therefore, the nearest power is 4⁰.
For arr[4](= 2): The previous and the next elements are 1, and 2. Therefore, the nearest power of 1 is 2¹.

Input: arr[] = {21, 3, 54, 78, 9}
Output: {27, 1, 78, 81, 1}

方法：思想是遍历数组，用其上一个元素或下一个数组元素的最近幂替换每个数组元素。
请按照以下步骤解决此问题：

• 遍历数组arr[]并执行以下步骤：
  • 找出X ^K最接近Y的K值。
  • 计算K 时，取log _x (Y) 的下限值。
  • 因此， K和K + 1将是最近幂最接近的两个整数。
  • 计算Y ^K和Y ^{(K + 1)}并检查哪个最接近X并使用最接近的值更新数组元素arr[i] 。
• 完成上述步骤后，将数组arr[]打印为修改后的数组。

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 power
// of y which is nearest to x
int nearestPow(int x, int y)
{
     
    // Base Case
    if (y == 1)
        return 1;
 
    // Stores the logarithmic
    // value of x with base y
    int k = log10(x) / log10(y);
 
    if (abs(pow(y, k) - x) <
        abs(pow(y, (k + 1)) - x))
        return pow(y, k);
 
    return pow(y, (k + 1));
}
 
// Function to replace each array
// element by the nearest power of
// its previous or next element
void replacebyNearestPower(vector arr)
{
 
    // Stores the previous
    // and next element
    int prev = arr[arr.size() - 1];
    int lastNext = arr[0];
    int next = 0;
 
    // Traverse the array
    for(int i = 0; i < arr.size(); i++)
    {
        int temp = arr[i];
        if (i == arr.size() - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.size()];
 
        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);
 
        // Replacing the array values
        if (abs(arr[i] - prevPow) <
            abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;
 
        prev = temp;
    }
 
    // Print the updated array
    for(int i = 0; i < arr.size(); i++)
        cout << arr[i] << " ";
}
 
// Driver Code
int main()
{
     
    // Given array
    vector arr{ 2, 3, 4, 1, 2 };
 
    replacebyNearestPower(arr);
}
     
// This code is contributed by ipg2016107

Java

// Java program for the above approach
class GFG{
 
// Function to calculate the power
// of y which is nearest to x
static int nearestPow(int x, int y)
{
     
    // Base Case
    if (y == 1)
        return 1;
 
    // Stores the logarithmic
    // value of x with base y
    int k = (int)(Math.log10(x) /
                  Math.log10(y));
 
    if (Math.abs(Math.pow(y, k) - x) <
        Math.abs(Math.pow(y, (k + 1)) - x))
        return (int)(Math.pow(y, k));
 
    return (int)(Math.pow(y, (k + 1)));
}
 
// Function to replace each array
// element by the nearest power of
// its previous or next element
static void replacebyNearestPower(int[] arr)
{
 
    // Stores the previous
    // and next element
    int prev = arr[arr.length - 1];
    int lastNext = arr[0];
    int next = 0;
 
    // Traverse the array
    for(int i = 0; i < arr.length; i++)
    {
        int temp = arr[i];
        if (i == arr.length - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.length];
 
        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);
 
        // Replacing the array values
        if (Math.abs(arr[i] - prevPow) <
            Math.abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;
 
        prev = temp;
    }
 
    // Print the updated array
    for(int i = 0; i < arr.length; i++)
        System.out.print(arr[i] + " ");
}
 
// Driver Code
public static void main(String args[])
{
     
    // Given array
    int[] arr = { 2, 3, 4, 1, 2 };
 
    replacebyNearestPower(arr);
}
}
 
// This code is contributed by abhinavjain194

Python3

# Python3 program for the above approach
 
import math
 
# Function to calculate the power
# of y which is nearest to x
def nearestPow(x, y):
   
    # Base Case
    if y == 1:
        return 1
 
    # Stores the logarithmic
    # value of x with base y
    k = int(math.log(x, y))
 
    if abs(y**k - x) < abs(y**(k + 1) - x):
        return y**k
 
    return y**(k + 1)
 
# Function to replace each array
# element by the nearest power of
# its previous or next element
def replacebyNearestPower(arr):
   
    # Stores the previous
    # and next element
    prev = arr[-1]
    
    lastNext = arr[0]
     
    # Traverse the array
    for i in range(len(arr)):
 
        temp = arr[i]
        if i == len(arr)-1:
            next = lastNext
        else:
            next = arr[(i + 1) % len(arr)]
 
        # Calculate nearest power for
        # previous and next elements
        prevPow = nearestPow(arr[i], prev)
        nextPow = nearestPow(arr[i], next)
 
        # Replacing the array values
        if abs(arr[i]-prevPow) < abs(arr[i]-nextPow):
            arr[i] = prevPow
        else:
            arr[i] = nextPow
        prev = temp
 
    # Print the updated array
    print(arr)
 
# Driver Code
 
# Given array
arr = [2, 3, 4, 1, 2]
 
replacebyNearestPower(arr)

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to calculate the power
// of y which is nearest to x
static int nearestPow(int x, int y)
{
     
    // Base Case
    if (y == 1)
        return 1;
 
    // Stores the logarithmic
    // value of x with base y
    int k = (int)(Math.Log(x, y));
 
    if (Math.Abs(Math.Pow(y, k) - x) <
        Math.Abs(Math.Pow(y, (k + 1)) - x))
        return (int)(Math.Pow(y, k));
 
    return (int)(Math.Pow(y, (k + 1)));
}
 
// Function to replace each array
// element by the nearest power of
// its previous or next element
static void replacebyNearestPower(int[] arr)
{
 
    // Stores the previous
    // and next element
    int prev = arr[arr.Length - 1];
    int lastNext = arr[0];
    int next = 0;
 
    // Traverse the array
    for(int i = 0; i < arr.Length; i++)
    {
        int temp = arr[i];
        if (i == arr.Length - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.Length];
 
        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);
 
        // Replacing the array values
        if (Math.Abs(arr[i] - prevPow) <
            Math.Abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;
             
        prev = temp;
    }
     
    // Print the updated array
    for(int i = 0; i < arr.Length; i++)
        Console.Write(arr[i] + " ");
}
 
// Driver Code
public static void Main()
{
     
    // Given array
    int[] arr = { 2, 3, 4, 1, 2 };
 
    replacebyNearestPower(arr);
}
}
 
// This code is contributed by ukasp

Javascript

 
// JavaScript program for the above approach
 
// Function to calculate the power
// of y which is nearest to x
function nearestPow(x, y) {
   
    // Base Case
    if (y == 1)
        return 1
 
    // Stores the logarithmic
    // value of x with base y
    var k = Math.floor(Math.log(x) / Math.log(y))
 
    if (Math.abs(Math.pow(y,k) - x) <
        Math.abs(Math.pow(y,(k + 1)) - x))
        return Math.pow(y,k)
 
    return Math.pow(y,(k + 1))
}
 
// Function to replace each array
// element by the nearest power of
// its previous or next element
function replacebyNearestPower(arr) {
   
    // Stores the previous
    // and next element
    var prev = arr[arr.length -1]
    
    var lastNext = arr[0]
     
    // Traverse the array
    for (var i = 0; i < arr.length; i++){
 
        var temp = arr[i]
        if (i == arr.length -1)
            var next = lastNext
        else
            var next = arr[(i + 1) % arr.length]
 
        // Calculate nearest power for
        // previous and next elements
        var prevPow = nearestPow(arr[i], prev)
        var nextPow = nearestPow(arr[i], next)
 
        // Replacing the array values
        if (Math.abs(arr[i]-prevPow) <
            Math.abs(arr[i]-nextPow))
            arr[i] = prevPow
        else
            arr[i] = nextPow
             
        prev = temp
    }
 
    // Print the updated array
    document.write(arr)
}
// Driver Code
// Given array
var arr = [2, 3, 4, 1, 2]
 
replacebyNearestPower(arr)
 
// This code is contributed by AnkThon
 

输出：

[2, 4, 3, 1, 2]

时间复杂度： O(N)
辅助空间： O(1)

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