检查是否可以通过仅交换相应值来使两个矩阵严格递增

给定两个n * m矩阵A[][]和B[][] ，任务是仅通过交换不同矩阵中的两个元素（如果它们位于相应位置）使两个矩阵严格递增（行和列）即A[i][j]只能与B[i][j]交换。如果可能，则打印Yes否则， No 。
例子：

Input: 
A[][] = {{2, 10},      B[][] = {{9, 4},  
         {11, 5}}               {3, 12}}
Output: Yes
Swap 2 with 9 and 5 with 12 then the resulting 
matrices will be strictly increasing.

Input: 
A[][] = {{1, 3},       B[][] = {{3, 1}, 
         {2, 4},                {3, 6}, 
         {5, 10}}               {4, 8}}
Output: No

方法：我们可以使用贪心技术来解决这个问题。如果A[i][j] > B[i][j]将 A[i][j]与B[i][j]交换。最后，对于每个i和j ，我们有A[i][j] ≤ B[i][j] 。
如果结果矩阵严格增加，则打印Yes否则，打印No 。
下面是上述方法的实现：

C++

#include
using namespace std;
  
// Function to check whether the matrices 
// can be made strictly increasing 
// with the given operation
string Check(int a[][2], int b[][2], int n, int m)
{
  
    // Swap only when a[i][j] > b[i][j]
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (a[i][j] > b[i][j])
                swap(a[i][j], b[i][j]);
  
    // Check if rows are strictly increasing
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m - 1; j++)
            if(a[i][j] >= a[i][j + 1] || b[i][j] >= b[i][j + 1])
                return "No";
  
    // Check if columns are strictly increasing
    for (int i = 0; i < n - 1; i++)
        for (int j = 0; j < m ;j++)
            if (a[i][j] >= a[i + 1][j] || b[i][j] >= b[i + 1][j])
                return "No";
  
    return "Yes";
}
  
// Driver code
int main()
{ 
    int n = 2, m = 2;
    int a[][2] = {{2, 10}, {11, 5}};
    int b[][2] = {{9, 4}, {3, 12}};
    cout << (Check(a, b,n,m));
}
  
// This code is contributed by chitranayal

Java

class GFG{
      
// Function to check whether the matrices 
// can be made strictly increasing 
// with the given operation
public static String Check(int a[][], int b[][],
                           int n, int m)
{
      
    // Swap only when a[i][j] > b[i][j]
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m; j++)
            if (a[i][j] > b[i][j])
            {
                int temp = a[i][j];
                a[i][j] = b[i][j];
                b[i][j] = temp;
            }
   
    // Check if rows are strictly increasing
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m - 1; j++)
            if (a[i][j] >= a[i][j + 1] ||
                b[i][j] >= b[i][j + 1])
                return "No";
   
    // Check if columns are strictly increasing
    for(int i = 0; i < n - 1; i++)
        for(int j = 0; j < m ;j++)
            if (a[i][j] >= a[i + 1][j] ||
                b[i][j] >= b[i + 1][j])
                return "No";
   
    return "Yes";
}   
  
// Driver code
public static void main(String[] args)
{
    int n = 2, m = 2;
    int a[][] = { { 2, 10 }, { 11, 5 } };
    int b[][] = { { 9, 4 }, { 3, 12 } };
      
    System.out.print(Check(a, b, n, m));
}
}
  
// This code is contributed by divyeshrabadiya07

Python3

# Function to check whether the matrices 
# can be made strictly increasing 
# with the given operation
def Check(a, b):
  
    # Swap only when a[i][j] > b[i][j]
    for i in range(n):
        for j in range(m):
            if a[i][j]>b[i][j]:
                a[i][j], b[i][j]= b[i][j], a[i][j]
  
    # Check if rows are strictly increasing
    for i in range(n):
        for j in range(m-1):
            if(a[i][j]>= a[i][j + 1] or b[i][j]>= b[i][j + 1]):
                return "No"
  
    # Check if columns are strictly increasing
    for i in range(n-1):
        for j in range(m):
            if (a[i][j]>= a[i + 1][j] or b[i][j]>= b[i + 1][j]):
                return "No"
  
    return "Yes"
  
# Driver code
if __name__=="__main__":
      
    n, m = 2, 2
    a =[[2, 10], [11, 5]]
    b =[[9, 4], [3, 12]]
    print(Check(a, b))

C#

// C# implementation of the 
// above approach 
using System;
using System.Collections;
class GfG{
       
// Function to check 
// whether the matrices 
// can be made strictly 
// increasing with the 
// given operation
static string Check(int [,]a, int [,]b, 
                    int n, int m)
{
  // Swap only when 
  // a[i][j] > b[i][j]
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
      if (a[i, j] > b[i, j])
      {
        int tmp = a[i, j];
        a[i, j] = b[i, j];
        b[i, j] = tmp;
      }
  
  // Check if rows are 
  // strictly increasing
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m - 1; j++)
      if(a[i, j] >= a[i, j + 1] || 
         b[i, j] >= b[i, j + 1])
        return "No";
  
  // Check if columns are 
  // strictly increasing
  for (int i = 0; i < n - 1; i++)
    for (int j = 0; j < m ; j++)
      if (a[i, j] >= a[i + 1, j] || 
          b[i, j] >= b[i + 1, j])
        return "No";
  
  return "Yes";
}
       
// Driver Code
public static void Main(string []arg)
{
  int n = 2, m = 2;
  int [,]a = {{2, 10}, {11, 5}};
  int [,]b = {{9, 4}, {3, 12}};
  Console.Write(Check(a, b, n, m));
}
}
  
// This code is contributed by Rutvik_56

PHP

 b[i][j] 
    for ($i = 0; $i < $n; $i++)
    { 
        for ($j= 0; $j < $n; $j++)
        { 
            if ($a[$i][$j] > $b[$i][$j]) 
            {
                $temp = $a[$i][$j];
                $a[$i][$j] = $b[$i][$j];
                $b[$i][$j] = $temp;
            }
        }
    }
              
  
    // Check if rows are strictly increasing 
    for ($i = 0; $i < $n; $i++)
    { 
        for ($j= 0;$j < $m-1 ; $j++)
        { 
            if($a[$i][$j] >= $a[$i][$j + 1] or 
               $b[$i][$j] >= $b[$i][$j + 1])
                return "No";
        }
    }
  
    // Check if columns are strictly increasing 
    for ($i = 0; $i < $n - 1; $i++)
    {
        for ($j = 0; $j < $m; $j++)
        { 
            if ($a[$i][$j] >= $a[$i + 1][$j] or 
                $b[$i][$j] >= $b[$i + 1][$j])
                return "No";
        }
    }
    return "Yes";
}
  
// Driver code 
$n = 2; $m = 2;
$a = array(array(2, 10), array(11, 5)); 
$b = array(array(9, 4), array(3, 12)); 
print(Check($a, $b, $n, $m));
  
// This code is contributed by AnkitRai01
?>

Javascript

输出：

Yes