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📜  使用所有相邻元素的异或值查找原始数组

📅  最后修改于: 2021-09-02 06:28:01             🧑  作者: Mango

给定一个由N-1 个元素组成的序列arr[] ,它是数组中所有相邻对的异或,任务是从arr[] 中找到原始数组
注意:假设 N 总是奇数并且 arr[] 包含 N 个自然数的排列。
例子:

方法:

  1. 思路是求1到N的所有元素的异或和给定数组相邻元素的异或,求出期望数组的最后一个元素。
  2. 由于相邻元素的 XOR 将包含除最后一个元素之外的所有元素,因此 this 与从 1 到 N 的所有数字的 XOR 将给出预期排列的最后一个元素。
    例如:
Let's the expected array be - {a, b, c, d, e}
Then the XOR array for this array will be - 
{a^b, b^c, c^d, d^e}

Now XOR of all the element from 1 to N -
xor_all => a ^ b ^ c ^ d ^ e

XOR of the adjacent elements -
xor_adjacent => ((a ^ b) ^ (c ^ d))

Now the XOR of the both the array will be the 
last element of the expected permutation 
=> (a ^ b ^ c ^ d ^ e) ^ ((a ^ b) ^ (c ^ d))
=> As all elements are in pair except the last element.
=> (a ^ a ^ b ^ b ^ c ^ c ^ d ^ d ^ e)
=> (0 ^ 0 ^ 0 ^ 0 ^ e)
=> e
  1. 现在对于元素的其余部分,连续地,在最后一个元素的异或上,我们将获得最后一个第二个元素,即d
  2. 反复更新最后一个元素,最终得到第一个元素,即a

下面是上述方法的实现:

C++
// C++ implementation to find the
// Array from the XOR array
// of the adjacent elements of array
 
#include 
using namespace std;
 
// XOR of all elements from 1 to N
int xor_all_elements(int n)
{
 
    switch (n & 3) {
 
    case 0:
        return n;
    case 1:
        return 1;
    case 2:
        return n + 1;
    case 3:
        return 0;
    }
}
 
// Function to find the Array
// from the XOR Array
vector findArray(int xorr[], int n)
{
    // Take a vector to store
    // the permutation
    vector arr;
 
    // XOR of N natural numbers
    int xor_all = xor_all_elements(n);
    int xor_adjacent = 0;
 
    // Loop to find the XOR of
    // adjacent elements of the XOR Array
    for (int i = 0; i < n - 1; i += 2) {
        xor_adjacent = xor_adjacent ^ xorr[i];
    }
    int last_element = xor_all ^ xor_adjacent;
    arr.push_back(last_element);
 
    // Loop to find the other
    // elements of the permutation
    for (int i = n - 2; i >= 0; i--) {
        // Finding the next and next elements
        last_element = xorr[i] ^ last_element;
        arr.push_back(last_element);
    }
 
    return arr;
}
 
// Driver Code
int main()
{
    vector arr;
 
    int xorr[] = { 7, 5, 3, 7 };
    int n = 5;
 
    arr = findArray(xorr, n);
 
    // Required Permutation
    for (int i = n - 1; i >= 0; i--) {
        cout << arr[i] << " ";
    }
}


Java
// Java implementation to find the
// Array from the XOR array
// of the adjacent elements of array
import java.util.*;
 
class GFG{
 
// XOR of all elements from 1 to N
static int xor_all_elements(int n)
{
 
    switch (n & 3) {
 
    case 0:
        return n;
    case 1:
        return 1;
    case 2:
        return n + 1;
    }
    return 0;
}
 
// Function to find the Array
// from the XOR Array
static Vector findArray(int xorr[], int n)
{
    // Take a vector to store
    // the permutation
    Vector arr = new Vector();
 
    // XOR of N natural numbers
    int xor_all = xor_all_elements(n);
    int xor_adjacent = 0;
 
    // Loop to find the XOR of
    // adjacent elements of the XOR Array
    for (int i = 0; i < n - 1; i += 2) {
        xor_adjacent = xor_adjacent ^ xorr[i];
    }
    int last_element = xor_all ^ xor_adjacent;
    arr.add(last_element);
 
    // Loop to find the other
    // elements of the permutation
    for (int i = n - 2; i >= 0; i--)
    {
        // Finding the next and next elements
        last_element = xorr[i] ^ last_element;
        arr.add(last_element);
    }
 
    return arr;
}
 
// Driver Code
public static void main(String[] args)
{
    Vector arr = new Vector();
 
    int xorr[] = { 7, 5, 3, 7 };
    int n = 5;
 
    arr = findArray(xorr, n);
 
    // Required Permutation
    for (int i = n - 1; i >= 0; i--)
    {
        System.out.print(arr.get(i)+ " ");
    }
}
}
 
// This code is contributed by PrinciRaj1992


Python3
# Python3 implementation to find the
# Array from the XOR array
# of the adjacent elements of array
 
# XOR of all elements from 1 to N
def xor_all_elements(n):
 
    if n & 3 == 0:
        return n
    elif n & 3 == 1:
        return 1
    elif n & 3 == 2:
        return n + 1
    else:
        return 0
 
# Function to find the Array
# from the XOR Array
def findArray(xorr, n):
     
    # Take a vector to store
    # the permutation
    arr = []
 
    # XOR of N natural numbers
    xor_all = xor_all_elements(n)
    xor_adjacent = 0
 
    # Loop to find the XOR of
    # adjacent elements of the XOR Array
    for i in range(0, n - 1, 2):
        xor_adjacent = xor_adjacent ^ xorr[i]
 
    last_element = xor_all ^ xor_adjacent
    arr.append(last_element)
 
    # Loop to find the other
    # elements of the permutation
    for i in range(n - 2, -1, -1):
         
        # Finding the next and next elements
        last_element = xorr[i] ^ last_element
        arr.append(last_element)
 
    return arr
 
# Driver Code
xorr = [7, 5, 3, 7]
n = 5
 
arr = findArray(xorr, n)
 
# Required Permutation
for i in range(n - 1, -1, -1):
    print(arr[i], end=" ")
     
# This code is contributed by mohit kumar 29


C#
// C# implementation to find the
// Array from the XOR array
// of the adjacent elements of array
using System;
using System.Collections.Generic;
 
class GFG{
  
// XOR of all elements from 1 to N
static int xor_all_elements(int n)
{
  
    switch (n & 3) {
  
    case 0:
        return n;
    case 1:
        return 1;
    case 2:
        return n + 1;
    }
    return 0;
}
  
// Function to find the Array
// from the XOR Array
static List findArray(int []xorr, int n)
{
    // Take a vector to store
    // the permutation
    List arr = new List();
  
    // XOR of N natural numbers
    int xor_all = xor_all_elements(n);
    int xor_adjacent = 0;
  
    // Loop to find the XOR of
    // adjacent elements of the XOR Array
    for (int i = 0; i < n - 1; i += 2) {
        xor_adjacent = xor_adjacent ^ xorr[i];
    }
    int last_element = xor_all ^ xor_adjacent;
    arr.Add(last_element);
  
    // Loop to find the other
    // elements of the permutation
    for (int i = n - 2; i >= 0; i--)
    {
        // Finding the next and next elements
        last_element = xorr[i] ^ last_element;
        arr.Add(last_element);
    }
  
    return arr;
}
  
// Driver Code
public static void Main(String[] args)
{
    List arr = new List();
  
    int []xorr = { 7, 5, 3, 7 };
    int n = 5;
  
    arr = findArray(xorr, n);
  
    // Required Permutation
    for (int i = n - 1; i >= 0; i--)
    {
        Console.Write(arr[i]+ " ");
    }
}
}
 
// This code contributed by Rajput-Ji


Javascript


输出:
3 4 1 2 5

性能分析:

  • 时间复杂度:在上面的方法中,我们遍历整个异或数组以找到相邻元素的异或,那么最坏情况下的复杂度将是O(N)
  • 空间复杂度:在上面的方法中,有一个向量数组用于存储从 1 到 N 的数字的排列,那么空间复杂度将为O(N)