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📜  检查给定矩阵是否可以通过行列交换转换为另一个给定矩阵

📅  最后修改于: 2021-09-07 02:12:21             🧑  作者: Mango

给定一个矩阵startMatrix和另一个矩阵finalMatrix ，任务是检查startMatrix 是否可以通过列交换和行交换转换为finalMatrix 。

例子：

方法：
为了解决这个问题，我们只需要检查startMatrix中所有行和列的元素是否都保留在finalMatrix矩阵中，而不管它们的顺序。任何违反此条件的行为都将确保无法获得finalMatrix矩阵。通过每一行遍历一个循环，并检查是否在startMatrix该行的所有元素存在于finalMatrix单行。然后转置startMatrix和finalMatrix并重复相同的验证。

下面的代码是上述方法的实现：

C++
// CPP program to check if a
// given matrix can be converted
// to another given matrix by row
// and column exchanges
#include 
using namespace std;
 
// Function to get transpose of a matrix
vector> getTranspose(vector> matrix)
{
  int n = matrix.size();
  vector> transpose(n, vector(n));
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      transpose[j][i] = matrix[i][j];
    }
  }
  return transpose;
}
 
// Function to check for row preservation
bool rowEquality(vector> s,
                 vector> f)
{
  vector> sets, setf;
  unordered_map map;
 
  // Creating sets from the initial matrix
  for (int i = 0; i < s.size(); i++)
  {
 
    // Create set for corresponding row
    set sett;
 
    // Add first element to the set
    sett.insert(s[i][0]);
    sets.push_back(sett);
 
    // Store the row number in map
    map[s[i][0]] = i;
 
    // Add remaining elements to the set
    for (int j = 1; j < s.size(); j++)
    {
      sett.insert(s[i][j]);
    }
  }
 
  // Create sets for final matrix
  // and check with the initial matrix
  int rowIndex = -1;
  for (int i = 0; i < f.size(); i++)
  {
    rowIndex = -1;
    set sett;
 
    for (int j = 0; j < f.size(); j++)
    {
      sett.insert(f[i][j]);
      if (map.find(f[i][j]) != map.end())
      {
        rowIndex = map[f[i][j]];
      }
    }
 
    setf.push_back(sett);
    if (setf[i] != sets[rowIndex])
      return true;
  }
 
  return false;
}
 
// Driver code
int main()
{
  vector> startMatrix = {
      {1, 2, 3, 4},
      {5, 6, 7, 8},
      {9, 10, 11, 12},
      {13, 14, 15, 16}
  };
  vector> finalMatrix = {
      {3, 4, 1, 2},
      {15, 16, 13, 14},
      {7, 8, 5, 6},
      {11, 12, 9, 10}
  };
 
  vector> startTranspose = getTranspose(startMatrix);
  vector> finalTranspose = getTranspose(finalMatrix);
 
  if (rowEquality(startMatrix, finalMatrix) &&
      rowEquality(startTranspose, finalTranspose))
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
 
// This code is contributed by sanjeev2552

Java
// Java program to check if a
// given matrix can be converted
// to another given matrix by row
// and column exchanges
 
import java.util.*;
public class Solution{
 
    // Function to get transpose of a matrix
    static int[][] getTranspose(int[][] matrix){
        int n = matrix.length;
        int[][] transpose = new int[n][n];
        for(int i=0; i> sets = new ArrayList<>();
        ArrayList> setf = new ArrayList<>();
        HashMap map = new HashMap<>();
         
        // Creating sets from the initial matrix
        for(int i=0; i set = new HashSet();
            // Add first element to the set
            set.add(s[i][0]);
            sets.add(set);
            // Store the row number in map
            map.put(s[i][0], i);
            // Add remaining elements to the set
            for(int j=1; j set = new HashSet();
             
            for(int j=0; j

Python3
# Python3 program to check if a
# given matrix can be converted
# to another given matrix by row
# and column exchanges
 
# Function to get transpose of a matrix
def getTranspose(matrix):
    n = len(matrix)
    transpose = [[0 for i in range(n)] for j in range(n)]
    for i in range(n):
        for j in range(n):
            transpose[j][i] = matrix[i][j]
    return transpose
 
# Function to check for row preservation
def rowEquality(s, f):
    sets = []
    setf = []
    mp = {i : 0 for i in range(100)}
     
    # Creating sets from the initial matrix
    for i in range(len(s)):
         
        # Create set for corresponding row
        st = set()
         
        # Add first element to the set
        st.add(s[i][0])
        sets.append(st)
         
        # Store the row number in mp
        mp[s[i][0]] = i
         
        # Add remaining elements to the set
        for j in range(1, len(s)):
            st.add(s[i][j])
     
    # Create sets for final matrix
    # and check with the initial matrix
    rowIndex = -1
    for i in range(len(f)):
        rowIndex = -1;
        st1 = set()
         
        for j in range(len(f)):
            st1.add(f[i][j])
            if(f[i][j] in mp):
                rowIndex = mp[f[i][j]]
         
        setf.append(st1)
        if(rowIndex != -1 and setf[i] !=
           sets[rowIndex]):
            return True
     
    return False
     
#Driver code
if __name__ == '__main__':
    startMatrix = [[ 1, 2, 3, 4 ],
                    [ 5, 6, 7, 8 ],
                    [ 9, 10, 11, 12 ],
                    [ 13, 14, 15, 16 ]]
    finalMatrix = [[ 3, 4, 1, 2],
                        [ 15, 16, 13, 14 ],
                        [ 7, 8, 5, 6 ],
                        [ 11, 12, 9, 10 ]]
     
    startTranspose = getTranspose(startMatrix)
    finalTranspose = getTranspose(finalMatrix)
 
    if(rowEquality(startMatrix, finalMatrix) and
       rowEquality(startTranspose, finalTranspose)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by Samarth

C#
// C# program to check if a
// given matrix can be converted
// to another given matrix by row
// and column exchanges
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to get transpose of a matrix
static int[,] getTranspose(int[,] matrix)
{
    int n = matrix.GetLength(0);
    int[,] transpose = new int[n, n];
     
    for(int i = 0; i < n; i++)
    {
        for(int j = 0; j < n; j++)
        {
            transpose[j, i] = matrix[i, j];
        }
    }
    return transpose;
}
 
// Function to check for row preservation
static bool rowEquality(int[,] s, int[,] f)
{
    List> sets = new List>();
    List> setf = new List>();
     
    Dictionary map = new Dictionary();
     
    // Creating sets from the initial matrix
    for(int i = 0; i < s.GetLength(0); i++)
    {
         
        // Create set for corresponding row
        HashSet set = new HashSet();
         
        // Add first element to the set
        set.Add(s[i, 0]);
        sets.Add(set);
         
        // Store the row number in map
        map.Add(s[i, 0], i);
         
        // Add remaining elements to the set
        for(int j = 1; j < s.GetLength(1); j++)
        {
            set.Add(s[i, j]);
        }
    }
     
    // Create sets for readonly matrix
    // and check with the initial matrix
    int rowIndex = -1;
     
    for(int i = 0; i < f.GetLength(0); i++)
    {
        rowIndex = -1;
        HashSet set = new HashSet();
         
        for(int j = 0; j < f.GetLength(1); j++)
        {
            set.Add(f[i, j]);
            if (map.ContainsKey(f[i, j]))
            {
                rowIndex = map[f[i, j]];
            }
        }
         
        setf.Add(set);
        if (rowIndex != -1 &&
           !setf[i].Equals(sets[rowIndex]))
            return true;
    }
    return false;
     
}
 
// Driver code
public static void Main(String []args)
{
    int[,] startMatrix = { { 1, 2, 3, 4 },
                           { 5, 6, 7, 8 },
                           { 9, 10, 11, 12 },
                           { 13, 14, 15, 16 } };
    int[,] finalMatrix = { { 3, 4, 1, 2 },
                           { 15, 16, 13, 14 },
                           { 7, 8, 5, 6 },
                           { 11, 12, 9, 10 } };
     
    int[,] startTranspose = getTranspose(startMatrix);
    int[,] finalTranspose = getTranspose(finalMatrix);
 
    if (rowEquality(startMatrix,finalMatrix) &&
        rowEquality(startTranspose,finalTranspose))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by Princi Singh

输出： 
Yes

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