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행렬에서 정렬된 모든 행 수 계산

m*n 크기의 행렬이 주어지면 작업은 엄밀한 오름차순 또는 엄밀한 내림차순으로 정렬된 행렬의 모든 행을 계산하는 것입니다.

예:  

Input : m = 4 n = 5  
mat[m][n] = 1 2 3 4 5
4 3 1 2 6
8 7 6 5 4
5 7 8 9 10
Output: 3

아이디어는 간단하며 두 번의 행렬 순회가 포함됩니다. 



  1. 행렬의 왼쪽부터 탐색하여 다음에 있는 모든 행의 개수를 계산합니다. 엄격하게 증가하는 순서  
  2. 행렬의 오른쪽부터 탐색하여 다음에 있는 모든 행의 개수를 계산합니다. 엄격하게 감소하는 순서

아래는 위의 아이디어를 구현한 것입니다. 

C++
// C++ program to find number of sorted rows #include    #define MAX 100 using namespace std; // Function to count all sorted rows in a matrix int sortedCount(int mat[][MAX] int r int c) {  int result = 0; // Initialize result  // Start from left side of matrix to  // count increasing order rows  for (int i=0; i<r; i++)  {  // Check if there is any pair of element  // that are not in increasing order.  int j;  for (j=0; j<c-1; j++)  if (mat[i][j+1] <= mat[i][j])  break;  // If the loop didn't break (All elements  // of current row were in increasing order)  if (j == c-1)  result++;  }  // Start from right side of matrix to  // count increasing order rows ( reference  // to left these are in decreasing order )  for (int i=0; i<r; i++)  {  // Check if there is any pair of element  // that are not in decreasing order.  int j;  for (j=c-1; j>0; j--)  if (mat[i][j-1] <= mat[i][j])  break;  // Note c > 1 condition is required to make  // sure that a single column row is not counted  // twice (Note that a single column row is sorted  // both in increasing and decreasing order)   if (c > 1 && j == 0)  result++;  }  return result; } // Driver program to run the case int main() {  int m = 4 n = 5;  int mat[][MAX] = {{1 2 3 4 5}  {4 3 1 2 6}  {8 7 6 5 4}  {5 7 8 9 10}};  cout << sortedCount(mat m n);  return 0; } 
Java
// Java program to find number of sorted rows class GFG {    static int MAX = 100;  // Function to count all sorted rows in a matrix  static int sortedCount(int mat[][] int r int c)  {  int result = 0; // Initialize result  // Start from left side of matrix to  // count increasing order rows  for (int i = 0; i < r; i++) {    // Check if there is any pair of element  // that are not in increasing order.  int j;  for (j = 0; j < c - 1; j++)  if (mat[i][j + 1] <= mat[i][j])  break;  // If the loop didn't break (All elements  // of current row were in increasing order)  if (j == c - 1)  result++;  }  // Start from right side of matrix to  // count increasing order rows ( reference  // to left these are in decreasing order )  for (int i = 0; i < r; i++) {    // Check if there is any pair of element  // that are not in decreasing order.  int j;  for (j = c - 1; j > 0; j--)  if (mat[i][j - 1] <= mat[i][j])  break;  // Note c > 1 condition is required to make  // sure that a single column row is not counted  // twice (Note that a single column row is sorted  // both in increasing and decreasing order)  if (c > 1 && j == 0)  result++;  }  return result;  }    // Driver code  public static void main(String arg[])  {  int m = 4 n = 5;  int mat[][] = { { 1 2 3 4 5 }  { 4 3 1 2 6 }  { 8 7 6 5 4 }  { 5 7 8 9 10 } };  System.out.print(sortedCount(mat m n));  } } // This code is contributed by Anant Agarwal. 
Python
# Python3 program to find number  # of sorted rows def sortedCount(mat r c): result = 0 # Start from left side of matrix to  # count increasing order rows  for i in range(r): # Check if there is any pair of element  # that are not in increasing order. j = 0 for j in range(c - 1): if mat[i][j + 1] <= mat[i][j]: break # If the loop didn't break (All elements  # of current row were in increasing order) if j == c - 2: result += 1 # Start from right side of matrix to  # count increasing order rows ( reference  # to left these are in decreasing order ) for i in range(0 r): # Check if there is any pair of element  # that are not in decreasing order. j = 0 for j in range(c - 1 0 -1): if mat[i][j - 1] <= mat[i][j]: break # Note c > 1 condition is required to  # make sure that a single column row  # is not counted twice (Note that a  # single column row is sorted both  # in increasing and decreasing order) if c > 1 and j == 1: result += 1 return result # Driver code m n = 4 5 mat = [[1 2 3 4 5] [4 3 1 2 6] [8 7 6 5 4] [5 7 8 9 10]] print(sortedCount(mat m n)) # This code is contributed by # Mohit kumar 29 (IIIT gwalior) 
C#
// C# program to find number of sorted rows using System; class GFG {   // static int MAX = 100;  // Function to count all sorted rows in   // a matrix  static int sortedCount(int []mat int r  int c)  {  int result = 0; // Initialize result  // Start from left side of matrix to  // count increasing order rows  for (int i = 0; i < r; i++) {    // Check if there is any pair of  // element that are not in  // increasing order.  int j;  for (j = 0; j < c - 1; j++)  if (mat[ij + 1] <= mat[ij])  break;  // If the loop didn't break (All  // elements of current row were   // in increasing order)  if (j == c - 1)  result++;  }  // Start from right side of matrix   // to count increasing order rows   // ( reference to left these are in   // decreasing order )  for (int i = 0; i < r; i++) {    // Check if there is any pair   // of element that are not in  // decreasing order.  int j;  for (j = c - 1; j > 0; j--)  if (mat[ij - 1] <= mat[ij])  break;  // Note c > 1 condition is   // required to make sure that a   // single column row is not   // counted twice (Note that a   // single column row is sorted  // both in increasing and  // decreasing order)  if (c > 1 && j == 0)  result++;  }  return result;  }    // Driver code  public static void Main()  {  int m = 4 n = 5;  int []mat = { { 1 2 3 4 5 }  { 4 3 1 2 6 }  { 8 7 6 5 4 }  { 5 7 8 9 10 } };    Console.WriteLine(  sortedCount(mat m n));  } } // This code is contributed by anuj_67. 
JavaScript
<script> // Javascript program to find number of sorted rows    let MAX = 100;    // Function to count all sorted rows in a matrix  function sortedCount(matrc)  {  let result = 0; // Initialize result    // Start from left side of matrix to  // count increasing order rows  for (let i = 0; i < r; i++) {    // Check if there is any pair of element  // that are not in increasing order.  let j;  for (j = 0; j < c - 1; j++)  if (mat[i][j + 1] <= mat[i][j])  break;    // If the loop didn't break (All elements  // of current row were in increasing order)  if (j == c - 1)  result++;  }    // Start from right side of matrix to  // count increasing order rows ( reference  // to left these are in decreasing order )  for (let i = 0; i < r; i++) {    // Check if there is any pair of element  // that are not in decreasing order.  let j;  for (j = c - 1; j > 0; j--)  if (mat[i][j - 1] <= mat[i][j])  break;    // Note c > 1 condition is required to make  // sure that a single column row is not counted  // twice (Note that a single column row is sorted  // both in increasing and decreasing order)  if (c > 1 && j == 0)  result++;  }  return result;  }  // Driver code   let m = 4 n = 5;    let mat = [[1 2 3 4 5]  [4 3 1 2 6]  [8 7 6 5 4]  [5 7 8 9 10]]  document.write(sortedCount(mat m n))    // This code is contributed by unknown2108 </script> 
PHP
 // PHP program to find  // number of sorted rows $MAX = 100; // Function to count all  // sorted rows in a matrix function sortedCount($mat $r $c) { // Initialize result $result = 0; // Start from left side of // matrix to count increasing  // order rows for ( $i = 0; $i < $r; $i++) { // Check if there is any  // pair of element that  // are not in increasing order. $j; for ($j = 0; $j < $c - 1; $j++) if ($mat[$i][$j + 1] <= $mat[$i][$j]) break; // If the loop didn't break  // (All elements of current  // row were in increasing order) if ($j == $c - 1) $result++; } // Start from right side of  // matrix to count increasing  // order rows ( reference to left // these are in decreasing order ) for ($i = 0; $i < $r; $i++) { // Check if there is any pair  // of element that are not // in decreasing order. $j; for ($j = $c - 1; $j > 0; $j--) if ($mat[$i][$j - 1] <= $mat[$i][$j]) break; // Note c > 1 condition is  // required to make sure that  // a single column row is not  // counted twice (Note that a  // single column row is sorted // both in increasing and  // decreasing order)  if ($c > 1 && $j == 0) $result++; } return $result; } // Driver Code $m = 4; $n = 5; $mat = array(array(1 2 3 4 5) array(4 3 1 2 6) array(8 7 6 5 4) array(5 7 8 9 10)); echo sortedCount($mat $m $n); // This code is contributed by anuj_67. ?> 

산출
3

시간복잡도 : O(m*n) 
보조 공간 : 오(1)

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