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Cel mai mare produs dintr-un subgrup de mărimea k

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Având în vedere un tablou format din n numere întregi pozitive și un întreg k. Găsiți cel mai mare subgrup de produse de dimensiunea k, adică găsiți producția maximă de k elemente învecinate în tabloul în care k<= n.
Exemple:  

    Input:    arr[] = {1 5 9 8 2 4  
1 8 1 2}
k = 6
Output: 4608
The subarray is {9 8 2 4 1 8}
Input: arr[] = {1 5 9 8 2 4 1 8 1 2}
k = 4
Output: 720
The subarray is {5 9 8 2}
Input: arr[] = {2 5 8 1 1 3};
k = 3
Output: 80
The subarray is {2 5 8}
Recommended Practice Cel mai mare produs Încearcă!

Abordarea forței brute:



c număr aleator

Iterăm peste toate subbaryurile de dimensiunea k utilizând două bucle imbricate. Bucla exterioară merge de la 0 la n-k, iar bucla interioară de la i la i+k-1. Calculăm produsul fiecărui subbary și actualizăm produsul maxim găsit până acum. În sfârșit returnăm produsul maxim.

Iată pașii pentru abordarea de mai sus:

  1. Inițializați o variabilă maxProduct la INT_MIN care reprezintă cea mai mică valoare întreagă posibilă.
  2. Iterați peste toate sub-tabele de dimensiunea k folosind două bucle imbricate.
  3. Bucla exterioară merge de la 0 la n-k.
  4. Bucla interioară se desfășoară de la i la i+k-1 unde i este indicele de pornire al subbarajului.
  5. Calculați produsul subbarajului curent folosind bucla interioară.
  6. Dacă produsul este mai mare decât maxProduct, actualizați maxProduct la produsul curent.
  7. Returnează maxProduct ca rezultat.

Mai jos este codul abordării de mai sus:



C++
// C++ program to find the maximum product of a subarray // of size k. #include    using namespace std; // This function returns maximum product of a subarray // of size k in given array arr[0..n-1]. This function // assumes that k is smaller than or equal to n. int findMaxProduct(int arr[] int n int k) {  int maxProduct = INT_MIN;  for (int i = 0; i <= n - k; i++) {  int product = 1;  for (int j = i; j < i + k; j++) {  product *= arr[j];  }  maxProduct = max(maxProduct product);  }  return maxProduct; } // Driver code int main() {  int arr1[] = {1 5 9 8 2 4 1 8 1 2};  int k = 6;  int n = sizeof(arr1)/sizeof(arr1[0]);  cout << findMaxProduct(arr1 n k) << endl;  k = 4;  cout << findMaxProduct(arr1 n k) << endl;  int arr2[] = {2 5 8 1 1 3};  k = 3;  n = sizeof(arr2)/sizeof(arr2[0]);  cout << findMaxProduct(arr2 n k);  return 0; } 
Java
import java.util.Arrays; public class Main {  // This function returns the maximum product of a subarray of size k in the given array  // It assumes that k is smaller than or equal to the length of the array.  static int findMaxProduct(int[] arr int n int k) {  int maxProduct = Integer.MIN_VALUE;  for (int i = 0; i <= n - k; i++) {  int product = 1;  for (int j = i; j < i + k; j++) {  product *= arr[j];  }  maxProduct = Math.max(maxProduct product);  }  return maxProduct;  }  // Driver code  public static void main(String[] args) {  int[] arr1 = {1 5 9 8 2 4 1 8 1 2};  int k = 6;  int n = arr1.length;  System.out.println(findMaxProduct(arr1 n k));  k = 4;  System.out.println(findMaxProduct(arr1 n k));  int[] arr2 = {2 5 8 1 1 3};  k = 3;  n = arr2.length;  System.out.println(findMaxProduct(arr2 n k));  } } 
Python3
# Python Code def find_max_product(arr k): max_product = float('-inf') # Initialize max_product to negative infinity n = len(arr) # Get the length of the input array # Iterate through the array with a window of size k for i in range(n - k + 1): product = 1 # Initialize product to 1 for each subarray for j in range(i i + k): product *= arr[j] # Calculate the product of the subarray max_product = max(max_product product) # Update max_product if necessary return max_product # Return the maximum product of a subarray of size k # Driver code if __name__ == '__main__': arr1 = [1 5 9 8 2 4 1 8 1 2] k = 6 print(find_max_product(arr1 k)) # Output 25920 k = 4 print(find_max_product(arr1 k)) # Output 1728 arr2 = [2 5 8 1 1 3] k = 3 print(find_max_product(arr2 k)) # Output 80 # This code is contributed by guptapratik 
C#
using System; public class GFG {  // This function returns the maximum product of a subarray of size k in the given array  // It assumes that k is smaller than or equal to the length of the array.  static int FindMaxProduct(int[] arr int n int k)  {  int maxProduct = int.MinValue;  for (int i = 0; i <= n - k; i++)  {  int product = 1;  for (int j = i; j < i + k; j++)  {  product *= arr[j];  }  maxProduct = Math.Max(maxProduct product);  }  return maxProduct;  }  // Driver code  public static void Main(string[] args)  {  int[] arr1 = { 1 5 9 8 2 4 1 8 1 2 };  int k = 6;  int n = arr1.Length;  Console.WriteLine(FindMaxProduct(arr1 n k));  k = 4;  Console.WriteLine(FindMaxProduct(arr1 n k));  int[] arr2 = { 2 5 8 1 1 3 };  k = 3;  n = arr2.Length;  Console.WriteLine(FindMaxProduct(arr2 n k));  } } 
JavaScript
// This function returns the maximum product of a subarray of size k in the given array // It assumes that k is smaller than or equal to the length of the array. function findMaxProduct(arr k) {  let maxProduct = Number.MIN_VALUE;  const n = arr.length;  for (let i = 0; i <= n - k; i++) {  let product = 1;  for (let j = i; j < i + k; j++) {  product *= arr[j];  }  maxProduct = Math.max(maxProduct product);  }  return maxProduct; } // Driver code const arr1 = [1 5 9 8 2 4 1 8 1 2]; let k = 6; console.log(findMaxProduct(arr1 k)); k = 4; console.log(findMaxProduct(arr1 k)); const arr2 = [2 5 8 1 1 3]; k = 3; console.log(findMaxProduct(arr2 k)); 

Ieșire
4608 720 80

Complexitatea timpului: O(n*k) unde n este lungimea matricei de intrare și k este dimensiunea sub-tabelului pentru care găsim produsul maxim.
Spațiu auxiliar: O(1) pentru că folosim doar o cantitate constantă de spațiu suplimentar pentru a stoca produsul maxim și produsul subgrupului curent.

dependență parțială

Metoda 2 (Eficient: O(n))  
O putem rezolva în O(n) utilizând faptul că produsul unui subgrup de dimensiunea k poate fi calculat în timp O(1) dacă avem la dispoziție produsul subseriei anterioare. 
 

obiect la jsonobject java
curr_product = (prev_product / arr[i-1]) * arr[i + k -1]  
prev_product : Product of subarray of size k beginning
with arr[i-1]
curr_product : Product of subarray of size k beginning
with arr[i]


În acest fel, putem calcula produsul subbary de dimensiune k maximă într-o singură traversare. Mai jos este implementarea C++ a ideii.



C++
// C++ program to find the maximum product of a subarray // of size k. #include    using namespace std; // This function returns maximum product of a subarray // of size k in given array arr[0..n-1]. This function // assumes that k is smaller than or equal to n. int findMaxProduct(int arr[] int n int k) {  // Initialize the MaxProduct to 1 as all elements  // in the array are positive  int MaxProduct = 1;  for (int i=0; i<k; i++)  MaxProduct *= arr[i];  int prev_product = MaxProduct;  // Consider every product beginning with arr[i]  // where i varies from 1 to n-k-1  for (int i=1; i<=n-k; i++)  {  int curr_product = (prev_product/arr[i-1]) *  arr[i+k-1];  MaxProduct = max(MaxProduct curr_product);  prev_product = curr_product;  }  // Return the maximum product found  return MaxProduct; } // Driver code int main() {  int arr1[] = {1 5 9 8 2 4 1 8 1 2};  int k = 6;  int n = sizeof(arr1)/sizeof(arr1[0]);  cout << findMaxProduct(arr1 n k) << endl;  k = 4;  cout << findMaxProduct(arr1 n k) << endl;  int arr2[] = {2 5 8 1 1 3};  k = 3;  n = sizeof(arr2)/sizeof(arr2[0]);  cout << findMaxProduct(arr2 n k);  return 0; } 
Java
// Java program to find the maximum product of a subarray // of size k import java.io.*; import java.util.*; class GFG  {  // Function returns maximum product of a subarray  // of size k in given array arr[0..n-1]. This function  // assumes that k is smaller than or equal to n.  static int findMaxProduct(int arr[] int n int k)  {  // Initialize the MaxProduct to 1 as all elements  // in the array are positive  int MaxProduct = 1;  for (int i=0; i<k; i++)  MaxProduct *= arr[i];    int prev_product = MaxProduct;    // Consider every product beginning with arr[i]  // where i varies from 1 to n-k-1  for (int i=1; i<=n-k; i++)  {  int curr_product = (prev_product/arr[i-1]) *  arr[i+k-1];  MaxProduct = Math.max(MaxProduct curr_product);  prev_product = curr_product;  }    // Return the maximum product found  return MaxProduct;  }    // driver program  public static void main (String[] args)   {  int arr1[] = {1 5 9 8 2 4 1 8 1 2};  int k = 6;  int n = arr1.length;  System.out.println(findMaxProduct(arr1 n k));    k = 4;  System.out.println(findMaxProduct(arr1 n k));    int arr2[] = {2 5 8 1 1 3};  k = 3;  n = arr2.length;  System.out.println(findMaxProduct(arr2 n k));  } } // This code is contributed by Pramod Kumar 
Python3
# Python 3 program to find the maximum  # product of a subarray of size k. # This function returns maximum product  # of a subarray of size k in given array # arr[0..n-1]. This function assumes  # that k is smaller than or equal to n. def findMaxProduct(arr n k) : # Initialize the MaxProduct to 1  # as all elements in the array  # are positive MaxProduct = 1 for i in range(0 k) : MaxProduct = MaxProduct * arr[i] prev_product = MaxProduct # Consider every product beginning # with arr[i] where i varies from # 1 to n-k-1 for i in range(1 n - k + 1) : curr_product = (prev_product // arr[i-1]) * arr[i+k-1] MaxProduct = max(MaxProduct curr_product) prev_product = curr_product # Return the maximum product found return MaxProduct # Driver code arr1 = [1 5 9 8 2 4 1 8 1 2] k = 6 n = len(arr1) print (findMaxProduct(arr1 n k) ) k = 4 print (findMaxProduct(arr1 n k)) arr2 = [2 5 8 1 1 3] k = 3 n = len(arr2) print(findMaxProduct(arr2 n k)) # This code is contributed by Nikita Tiwari. 
C#
// C# program to find the maximum  // product of a subarray of size k using System; class GFG  {  // Function returns maximum   // product of a subarray of   // size k in given array   // arr[0..n-1]. This function   // assumes that k is smaller   // than or equal to n.  static int findMaxProduct(int []arr   int n int k)  {  // Initialize the MaxProduct   // to 1 as all elements  // in the array are positive  int MaxProduct = 1;  for (int i = 0; i < k; i++)  MaxProduct *= arr[i];  int prev_product = MaxProduct;  // Consider every product beginning   // with arr[i] where i varies from   // 1 to n-k-1  for (int i = 1; i <= n - k; i++)  {  int curr_product = (prev_product /   arr[i - 1]) *   arr[i + k - 1];  MaxProduct = Math.Max(MaxProduct   curr_product);  prev_product = curr_product;  }  // Return the maximum  // product found  return MaxProduct;  }    // Driver Code  public static void Main ()   {  int []arr1 = {1 5 9 8 2   4 1 8 1 2};  int k = 6;  int n = arr1.Length;  Console.WriteLine(findMaxProduct(arr1 n k));  k = 4;  Console.WriteLine(findMaxProduct(arr1 n k));  int []arr2 = {2 5 8 1 1 3};  k = 3;  n = arr2.Length;  Console.WriteLine(findMaxProduct(arr2 n k));  } } // This code is contributed by anuj_67. 
JavaScript
<script>  // JavaScript program to find the maximum   // product of a subarray of size k    // Function returns maximum   // product of a subarray of   // size k in given array   // arr[0..n-1]. This function   // assumes that k is smaller   // than or equal to n.  function findMaxProduct(arr n k)  {  // Initialize the MaxProduct   // to 1 as all elements  // in the array are positive  let MaxProduct = 1;  for (let i = 0; i < k; i++)  MaxProduct *= arr[i];    let prev_product = MaxProduct;    // Consider every product beginning   // with arr[i] where i varies from   // 1 to n-k-1  for (let i = 1; i <= n - k; i++)  {  let curr_product =   (prev_product / arr[i - 1]) * arr[i + k - 1];  MaxProduct = Math.max(MaxProduct curr_product);  prev_product = curr_product;  }    // Return the maximum  // product found  return MaxProduct;  }    let arr1 = [1 5 9 8 2 4 1 8 1 2];  let k = 6;  let n = arr1.length;  document.write(findMaxProduct(arr1 n k) + '
'
); k = 4; document.write(findMaxProduct(arr1 n k) + '
'
); let arr2 = [2 5 8 1 1 3]; k = 3; n = arr2.length; document.write(findMaxProduct(arr2 n k) + '
'
); </script>
PHP
 // PHP program to find the maximum  // product of a subarray of size k. // This function returns maximum  // product of a subarray of size  // k in given array arr[0..n-1]. // This function assumes that k  // is smaller than or equal to n. function findMaxProduct( $arr $n $k) { // Initialize the MaxProduct to // 1 as all elements // in the array are positive $MaxProduct = 1; for($i = 0; $i < $k; $i++) $MaxProduct *= $arr[$i]; $prev_product = $MaxProduct; // Consider every product // beginning with arr[i] // where i varies from 1  // to n-k-1 for($i = 1; $i < $n - $k; $i++) { $curr_product = ($prev_product / $arr[$i - 1]) * $arr[$i + $k - 1]; $MaxProduct = max($MaxProduct $curr_product); $prev_product = $curr_product; } // Return the maximum // product found return $MaxProduct; } // Driver code $arr1 = array(1 5 9 8 2 4 1 8 1 2); $k = 6; $n = count($arr1); echo findMaxProduct($arr1 $n $k)'n' ; $k = 4; echo findMaxProduct($arr1 $n $k)'n'; $arr2 = array(2 5 8 1 1 3); $k = 3; $n = count($arr2); echo findMaxProduct($arr2 $n $k); // This code is contributed by anuj_67. ?> 

Ieșire
4608 720 80

Spațiu auxiliar: O(1) deoarece nu este folosit spațiu suplimentar.
Acest articol este contribuit de Ashutosh Kumar .