给定一个包含N 个正整数的数组arr ，任务是检查给定的数组是否可以分解为两个排列，并在可能的情况下打印排列。如果M 个整数的序列包含从1 到 M 的所有整数恰好一次，则称为置换。
例子：
Input: arr[] = { 1, 2, 5, 3, 4, 1, 2 }, N = 7
Output: {1 2 5 3 4}, {1 2}
Input: arr[] = {2, 1, 1, 3}, N = 4
Output: Not possible
方法：
- 首先，我们需要检查数组是否是两个排列的串联。在这篇文章中有解释。
- 如果是这样，找到数组的最大元素，比如x 。
- 如果索引[0, x-1]和[x, n-1]处的元素形成两个有效排列，则打印它们。
- 否则，将索引[0, n -1 – x]和[n – x, n – 1]处的元素打印为两个有效排列。
下面是上述方法的实现：
C++
// C++ program to print two
// permutations from a given sequence
#include
using namespace std;
// Function to check if the sequence is
// concatenation of two permutations or not
bool checkPermutation(int arr[], int n)
{
// Computing the sum of all the
// elements in the array
long long sum = 0;
for (int i = 0; i < n; i++)
sum += arr[i];
// Computing the prefix sum
// for all the elements in the array
long long prefix[n + 1] = { 0 };
prefix[0] = arr[0];
for (int i = 1; i < n; i++)
prefix[i] = prefix[i - 1] + arr[i];
// Iterating through the i
// from lengths 1 to n-1
for (int i = 0; i < n - 1; i++) {
// Sum of first i+1 elements
long long lsum = prefix[i];
// Sum of remaining n-i-1 elements
long long rsum = sum - prefix[i];
// Lengths of the 2 permutations
long long l_len = i + 1,
r_len = n - i - 1;
// Checking if the sums
// satisfy the formula or not
if (((2 * lsum)
== (l_len * (l_len + 1)))
&& ((2 * rsum)
== (r_len * (r_len + 1))))
return true;
}
return false;
}
// Function to print the
// two permutations
void printPermutations(int arr[], int n,
int l1, int l2)
{
// Print the first permutation
for (int i = 0; i < l1; i++) {
cout << arr[i] << " ";
}
cout << endl;
// Print the second permutation
for (int i = l1; i < n; i++) {
cout << arr[i] << " ";
}
}
// Function to find the two permutations
// from the given sequence
void findPermutations(int arr[], int n)
{
// If the sequence is not a
// concatenation of two permutations
if (!checkPermutation(arr, n)) {
cout << "Not Possible";
return;
}
int l1 = 0, l2 = 0;
// Find the largest element in the
// array and set the lengths of the
// permutations accordingly
l1 = *max_element(arr, arr + n);
l2 = n - l1;
set s1, s2;
for (int i = 0; i < l1; i++)
s1.insert(arr[i]);
for (int i = l1; i < n; i++)
s2.insert(arr[i]);
if (s1.size() == l1 && s2.size() == l2)
printPermutations(arr, n, l1, l2);
else {
swap(l1, l2);
printPermutations(arr, n, l1, l2);
}
}
// Driver code
int main()
{
int arr[] = { 2, 1, 3, 4, 5,
6, 7, 8, 9, 1,
10, 2 };
int n = sizeof(arr) / sizeof(int);
findPermutations(arr, n);
return 0;
} Java
// Java program to print two
// permutations from a given sequence
import java.util.*;
class GFG{
// Function to check if the sequence is
// concatenation of two permutations or not
static boolean checkPermutation(int arr[], int n)
{
// Computing the sum of all the
// elements in the array
long sum = 0;
for (int i = 0; i < n; i++)
sum += arr[i];
// Computing the prefix sum
// for all the elements in the array
int []prefix = new int[n + 1];
prefix[0] = arr[0];
for (int i = 1; i < n; i++)
prefix[i] = prefix[i - 1] + arr[i];
// Iterating through the i
// from lengths 1 to n-1
for (int i = 0; i < n - 1; i++) {
// Sum of first i+1 elements
long lsum = prefix[i];
// Sum of remaining n-i-1 elements
long rsum = sum - prefix[i];
// Lengths of the 2 permutations
long l_len = i + 1,
r_len = n - i - 1;
// Checking if the sums
// satisfy the formula or not
if (((2 * lsum)
== (l_len * (l_len + 1)))
&& ((2 * rsum)
== (r_len * (r_len + 1))))
return true;
}
return false;
}
// Function to print the
// two permutations
static void printPermutations(int arr[], int n,
int l1, int l2)
{
// Print the first permutation
for (int i = 0; i < l1; i++) {
System.out.print(arr[i]+ " ");
}
System.out.println();
// Print the second permutation
for (int i = l1; i < n; i++) {
System.out.print(arr[i]+ " ");
}
}
// Function to find the two permutations
// from the given sequence
static void findPermutations(int arr[], int n)
{
// If the sequence is not a
// concatenation of two permutations
if (!checkPermutation(arr, n)) {
System.out.print("Not Possible");
return;
}
int l1 = 0, l2 = 0;
// Find the largest element in the
// array and set the lengths of the
// permutations accordingly
l1 = Arrays.stream(arr).max().getAsInt();
l2 = n - l1;
HashSet s1 = new HashSet(),
s2 = new HashSet();
for (int i = 0; i < l1; i++)
s1.add(arr[i]);
for (int i = l1; i < n; i++)
s2.add(arr[i]);
if (s1.size() == l1 && s2.size() == l2)
printPermutations(arr, n, l1, l2);
else {
l1 = l1+l2;
l2 = l1-l2;
l1 = l1-l2;
printPermutations(arr, n, l1, l2);
}
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 2, 1, 3, 4, 5,
6, 7, 8, 9, 1,
10, 2 };
int n = arr.length;
findPermutations(arr, n);
}
}
// This code is contributed by 29AjayKumar Python3
# Python3 program to print two
# permutations from a given sequence
# Function to check if the sequence is
# concatenation of two permutations or not
def checkPermutation(arr, n):
# Computing the sum of all the
# elements in the array
sum = 0
for i in range(n):
sum += arr[i]
# Computing the prefix sum
# for all the elements in the array
prefix = [0 for i in range(n+1)]
prefix[0] = arr[0]
for i in range(1,n):
prefix[i] = prefix[i - 1] + arr[i]
# Iterating through the i
# from lengths 1 to n-1
for i in range(n - 1):
# Sum of first i+1 elements
lsum = prefix[i]
# Sum of remaining n-i-1 elements
rsum = sum - prefix[i]
# Lengths of the 2 permutations
l_len = i + 1
r_len = n - i - 1
# Checking if the sums
# satisfy the formula or not
if (((2 * lsum) == (l_len * (l_len + 1))) and
((2 * rsum) == (r_len * (r_len + 1)))):
return True
return False
# Function to print the
# two permutations
def printPermutations(arr,n,l1,l2):
# Print the first permutation
for i in range(l1):
print(arr[i],end = " ")
print("\n",end = "");
# Print the second permutation
for i in range(l1, n, 1):
print(arr[i], end = " ")
# Function to find the two permutations
# from the given sequence
def findPermutations(arr,n):
# If the sequence is not a
# concatenation of two permutations
if (checkPermutation(arr, n) == False):
print("Not Possible")
return
l1 = 0
l2 = 0
# Find the largest element in the
# array and set the lengths of the
# permutations accordingly
l1 = max(arr)
l2 = n - l1
s1 = set()
s2 = set()
for i in range(l1):
s1.add(arr[i])
for i in range(l1,n):
s2.add(arr[i])
if (len(s1) == l1 and len(s2) == l2):
printPermutations(arr, n, l1, l2)
else:
temp = l1
l1 = l2
l2 = temp
printPermutations(arr, n, l1, l2)
# Driver code
if __name__ == '__main__':
arr = [2, 1, 3, 4, 5,6, 7, 8, 9, 1,10, 2]
n = len(arr)
findPermutations(arr, n)
# This code is contributed by Surendra_GangwarC#
// C# program to print two
// permutations from a given sequence
using System;
using System.Linq;
using System.Collections.Generic;
class GFG{
// Function to check if the sequence is
// concatenation of two permutations or not
static bool checkPermutation(int []arr, int n)
{
// Computing the sum of all the
// elements in the array
long sum = 0;
for (int i = 0; i < n; i++)
sum += arr[i];
// Computing the prefix sum
// for all the elements in the array
int []prefix = new int[n + 1];
prefix[0] = arr[0];
for (int i = 1; i < n; i++)
prefix[i] = prefix[i - 1] + arr[i];
// Iterating through the i
// from lengths 1 to n-1
for (int i = 0; i < n - 1; i++) {
// Sum of first i+1 elements
long lsum = prefix[i];
// Sum of remaining n-i-1 elements
long rsum = sum - prefix[i];
// Lengths of the 2 permutations
long l_len = i + 1,
r_len = n - i - 1;
// Checking if the sums
// satisfy the formula or not
if (((2 * lsum)
== (l_len * (l_len + 1)))
&& ((2 * rsum)
== (r_len * (r_len + 1))))
return true;
}
return false;
}
// Function to print the
// two permutations
static void printPermutations(int []arr, int n,
int l1, int l2)
{
// Print the first permutation
for (int i = 0; i < l1; i++) {
Console.Write(arr[i]+ " ");
}
Console.WriteLine();
// Print the second permutation
for (int i = l1; i < n; i++) {
Console.Write(arr[i]+ " ");
}
}
// Function to find the two permutations
// from the given sequence
static void findPermutations(int []arr, int n)
{
// If the sequence is not a
// concatenation of two permutations
if (!checkPermutation(arr, n)) {
Console.Write("Not Possible");
return;
}
int l1 = 0, l2 = 0;
// Find the largest element in the
// array and set the lengths of the
// permutations accordingly
l1 = arr.Max();
l2 = n - l1;
HashSet s1 = new HashSet(),
s2 = new HashSet();
for (int i = 0; i < l1; i++)
s1.Add(arr[i]);
for (int i = l1; i < n; i++)
s2.Add(arr[i]);
if (s1.Count == l1 && s2.Count == l2)
printPermutations(arr, n, l1, l2);
else {
l1 = l1+l2;
l2 = l1-l2;
l1 = l1-l2;
printPermutations(arr, n, l1, l2);
}
}
// Driver code
public static void Main(String[] args)
{
int []arr = { 2, 1, 3, 4, 5,
6, 7, 8, 9, 1,
10, 2 };
int n = arr.Length;
findPermutations(arr, n);
}
}
// This code contributed by Rajput-Ji 输出：
2 1
3 4 5 6 7 8 9 1 10 2
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