Dadas dos arrays ordenadas de tamaño m y n de elementos distintos. Dado un valor x . El problema es contar todos los pares de ambas arrays cuya suma sea igual a x .
Nota: El par tiene un elemento de cada array.
Ejemplos:
Input : arr1[] = {1, 3, 5, 7} arr2[] = {2, 3, 5, 8} x = 10 Output : 2 The pairs are: (5, 5) and (7, 3) Input : arr1[] = {1, 2, 3, 4, 5, 7, 11} arr2[] = {2, 3, 4, 5, 6, 8, 12} x = 9 Output : 5
Método 1 (enfoque ingenuo): utilizando dos bucles, seleccione elementos de ambas arrays y verifique si la suma del par es igual ax o no.
C++
// C++ implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value #include <bits/stdc++.h> using namespace std; // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; // generating pairs from // both the arrays for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) // if sum of pair is equal // to 'x' increment count if ((arr1[i] + arr2[j]) == x) count++; // required count of pairs return count; } // Driver Code int main() { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = sizeof(arr1) / sizeof(arr1[0]); int n = sizeof(arr2) / sizeof(arr2[0]); int x = 10; cout << "Count = " << countPairs(arr1, arr2, m, n, x); return 0; }
Java
// Java implementation to count pairs from // both sorted arrays whose sum is equal // to a given value import java.io.*; class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int []arr1, int []arr2, int m, int n, int x) { int count = 0; // generating pairs from // both the arrays for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) // if sum of pair is equal // to 'x' increment count if ((arr1[i] + arr2[j]) == x) count++; // required count of pairs return count; } // Driver Code public static void main (String[] args) { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = arr1.length; int n = arr2.length; int x = 10; System.out.println( "Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
Python3
# python implementation to count # pairs from both sorted arrays # whose sum is equal to a given # value # function to count all pairs from # both the sorted arrays whose sum # is equal to a given value def countPairs(arr1, arr2, m, n, x): count = 0 # generating pairs from both # the arrays for i in range(m): for j in range(n): # if sum of pair is equal # to 'x' increment count if arr1[i] + arr2[j] == x: count = count + 1 # required count of pairs return count # Driver Program arr1 = [1, 3, 5, 7] arr2 = [2, 3, 5, 8] m = len(arr1) n = len(arr2) x = 10 print("Count = ", countPairs(arr1, arr2, m, n, x)) # This code is contributed by Shrikant13.
C#
// C# implementation to count pairs from // both sorted arrays whose sum is equal // to a given value using System; class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int []arr1, int []arr2, int m, int n, int x) { int count = 0; // generating pairs from // both the arrays for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) // if sum of pair is equal // to 'x' increment count if ((arr1[i] + arr2[j]) == x) count++; // required count of pairs return count; } // Driver Code public static void Main () { int []arr1 = {1, 3, 5, 7}; int []arr2 = {2, 3, 5, 8}; int m = arr1.Length; int n = arr2.Length; int x = 10; Console.WriteLine( "Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
PHP
<?php // PHP implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs( $arr1, $arr2, $m, $n, $x) { $count = 0; // generating pairs from // both the arrays for ( $i = 0; $i < $m; $i++) for ( $j = 0; $j < $n; $j++) // if sum of pair is equal // to 'x' increment count if (($arr1[$i] + $arr2[$j]) == $x) $count++; // required count of pairs return $count; } // Driver Code $arr1 = array(1, 3, 5, 7); $arr2 = array(2, 3, 5, 8); $m = count($arr1); $n = count($arr2); $x = 10; echo "Count = ", countPairs($arr1, $arr2, $m,$n, $x); // This code is contributed by anuj_67. ?>
Javascript
<script> // JavaScript implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs(arr1, arr2, m, n, x) { let count = 0; // generating pairs from // both the arrays for (let i = 0; i < m; i++) for (let j = 0; j < n; j++) // if sum of pair is equal // to 'x' increment count if ((arr1[i] + arr2[j]) == x) count++; // required count of pairs return count; } // Driver Code let arr1 = [1, 3, 5, 7]; let arr2 = [2, 3, 5, 8]; let m = arr1.length; let n = arr2.length; let x = 10; document.write("Count = " + countPairs(arr1, arr2, m, n, x)); // This code is contributed by Surbhi Tyagi. </script>
Producción :
Count = 2
Complejidad de tiempo: O(mn)
Espacio auxiliar: O(1)
Método 2 (Búsqueda binaria): Para cada elemento arr1[i] , donde 1 <= i <= m , busque el valor (x – arr1[i]) en arr2[] . Si la búsqueda es exitosa, incremente el conteo .
C++
// C++ implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value #include <bits/stdc++.h> using namespace std; // function to search 'value' // in the given array 'arr[]' // it uses binary search technique // as 'arr[]' is sorted bool isPresent(int arr[], int low, int high, int value) { while (low <= high) { int mid = (low + high) / 2; // value found if (arr[mid] == value) return true; else if (arr[mid] > value) high = mid - 1; else low = mid + 1; } // value not found return false; } // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; for (int i = 0; i < m; i++) { // for each arr1[i] int value = x - arr1[i]; // check if the 'value' // is present in 'arr2[]' if (isPresent(arr2, 0, n - 1, value)) count++; } // required count of pairs return count; } // Driver Code int main() { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = sizeof(arr1) / sizeof(arr1[0]); int n = sizeof(arr2) / sizeof(arr2[0]); int x = 10; cout << "Count = " << countPairs(arr1, arr2, m, n, x); return 0; }
Java
// Java implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value import java.io.*; class GFG { // function to search 'value' // in the given array 'arr[]' // it uses binary search technique // as 'arr[]' is sorted static boolean isPresent(int arr[], int low, int high, int value) { while (low <= high) { int mid = (low + high) / 2; // value found if (arr[mid] == value) return true; else if (arr[mid] > value) high = mid - 1; else low = mid + 1; } // value not found return false; } // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; for (int i = 0; i < m; i++) { // for each arr1[i] int value = x - arr1[i]; // check if the 'value' // is present in 'arr2[]' if (isPresent(arr2, 0, n - 1, value)) count++; } // required count of pairs return count; } // Driver Code public static void main (String[] args) { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = arr1.length; int n = arr2.length; int x = 10; System.out.println("Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
Python 3
# Python 3 implementation to count # pairs from both sorted arrays # whose sum is equal to a given # value # function to search 'value' # in the given array 'arr[]' # it uses binary search technique # as 'arr[]' is sorted def isPresent(arr, low, high, value): while (low <= high): mid = (low + high) // 2 # value found if (arr[mid] == value): return True elif (arr[mid] > value) : high = mid - 1 else: low = mid + 1 # value not found return False # function to count all pairs # from both the sorted arrays # whose sum is equal to a given # value def countPairs(arr1, arr2, m, n, x): count = 0 for i in range(m): # for each arr1[i] value = x - arr1[i] # check if the 'value' # is present in 'arr2[]' if (isPresent(arr2, 0, n - 1, value)): count += 1 # required count of pairs return count # Driver Code if __name__ == "__main__": arr1 = [1, 3, 5, 7] arr2 = [2, 3, 5, 8] m = len(arr1) n = len(arr2) x = 10 print("Count = ", countPairs(arr1, arr2, m, n, x)) # This code is contributed # by ChitraNayal
C#
// C# implementation to count pairs from both // sorted arrays whose sum is equal to a given // value using System; class GFG { // function to search 'value' in the given // array 'arr[]' it uses binary search // technique as 'arr[]' is sorted static bool isPresent(int []arr, int low, int high, int value) { while (low <= high) { int mid = (low + high) / 2; // value found if (arr[mid] == value) return true; else if (arr[mid] > value) high = mid - 1; else low = mid + 1; } // value not found return false; } // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int []arr1, int []arr2, int m, int n, int x) { int count = 0; for (int i = 0; i < m; i++) { // for each arr1[i] int value = x - arr1[i]; // check if the 'value' // is present in 'arr2[]' if (isPresent(arr2, 0, n - 1, value)) count++; } // required count of pairs return count; } // Driver Code public static void Main () { int []arr1 = {1, 3, 5, 7}; int []arr2 = {2, 3, 5, 8}; int m = arr1.Length; int n = arr2.Length; int x = 10; Console.WriteLine("Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
PHP
<?php // PHP implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to search 'value' // in the given array 'arr[]' // it uses binary search technique // as 'arr[]' is sorted function isPresent($arr, $low, $high, $value) { while ($low <= $high) { $mid = ($low + $high) / 2; // value found if ($arr[$mid] == $value) return true; else if ($arr[$mid] > $value) $high = $mid - 1; else $low = $mid + 1; } // value not found return false; } // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs($arr1, $arr2, $m, $n, $x) { $count = 0; for ($i = 0; $i < $m; $i++) { // for each arr1[i] $value = $x - $arr1[$i]; // check if the 'value' // is present in 'arr2[]' if (isPresent($arr2, 0, $n - 1, $value)) $count++; } // required count of pairs return $count; } // Driver Code $arr1 = array(1, 3, 5, 7); $arr2 = array(2, 3, 5, 8); $m = count($arr1); $n = count($arr2); $x = 10; echo "Count = " , countPairs($arr1, $arr2, $m, $n, $x); // This code is contributed by anuj_67. ?>
Javascript
<script> // Javascript implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to search 'value' // in the given array 'arr[]' // it uses binary search technique // as 'arr[]' is sorted function isPresent(arr,low,high,value) { while (low <= high) { let mid = Math.floor((low + high) / 2); // value found if (arr[mid] == value) return true; else if (arr[mid] > value) high = mid - 1; else low = mid + 1; } // value not found return false; } // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value1 function countPairs(arr1,arr2,m,n,x) { let count = 0; for (let i = 0; i < m; i++) { // for each arr1[i] let value = x - arr1[i]; // check if the 'value' // is present in 'arr2[]' if (isPresent(arr2, 0, n - 1, value)) count++; } // required count of pairs return count; } // Driver Code let arr1=[1, 3, 5, 7]; let arr2=[2, 3, 5, 8]; let m=arr1.length; let n = arr2.length; let x = 10; document.write("Count = " + countPairs(arr1, arr2, m, n, x)); // This code is contributed by avanitrachhadiya2155 </script>
Producción :
Count = 2
Complejidad de tiempo: O(mlogn), la búsqueda debe aplicarse en la array que es de mayor tamaño para reducir la complejidad de tiempo.
Espacio auxiliar: O(1)
Método 3 (hashing): la tabla hash se implementa usando unordered_set en C++ . Almacenamos todos los primeros elementos de la array en la tabla hash. Para los elementos de la segunda array, restamos cada elemento de x y verificamos el resultado en la tabla hash. Si el resultado está presente, incrementamos el conteo .
C++
// C++ implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value #include <bits/stdc++.h> using namespace std; // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; unordered_set<int> us; // insert all the elements // of 1st array in the hash // table(unordered_set 'us') for (int i = 0; i < m; i++) us.insert(arr1[i]); // for each element of 'arr2[] for (int j = 0; j < n; j++) // find (x - arr2[j]) in 'us' if (us.find(x - arr2[j]) != us.end()) count++; // required count of pairs return count; } // Driver Code int main() { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = sizeof(arr1) / sizeof(arr1[0]); int n = sizeof(arr2) / sizeof(arr2[0]); int x = 10; cout << "Count = " << countPairs(arr1, arr2, m, n, x); return 0; }
Java
import java.util.*; // Java implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; HashSet<Integer> us = new HashSet<Integer>(); // insert all the elements // of 1st array in the hash // table(unordered_set 'us') for (int i = 0; i < m; i++) us.add(arr1[i]); // for each element of 'arr2[] for (int j = 0; j < n; j++) // find (x - arr2[j]) in 'us' if (us.contains(x - arr2[j])) count++; // required count of pairs return count; } // Driver Code public static void main(String[] args) { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = arr1.length; int n = arr2.length; int x = 10; System.out.print("Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code has been contributed by 29AjayKumar
Python3
# Python3 implementation to count # pairs from both sorted arrays # whose sum is equal to a given value # function to count all pairs from # both the sorted arrays whose sum # is equal to a given value def countPairs(arr1, arr2, m, n, x): count = 0 us = set() # insert all the elements # of 1st array in the hash # table(unordered_set 'us') for i in range(m): us.add(arr1[i]) # or each element of 'arr2[] for j in range(n): # find (x - arr2[j]) in 'us' if x - arr2[j] in us: count += 1 # required count of pairs return count # Driver code arr1 = [1, 3, 5, 7] arr2 = [2, 3, 5, 8] m = len(arr1) n = len(arr2) x = 10 print("Count =", countPairs(arr1, arr2, m, n, x)) # This code is contributed by Shrikant13
C#
// C# implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value using System; using System.Collections.Generic; class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int []arr1, int []arr2, int m, int n, int x) { int count = 0; HashSet<int> us = new HashSet<int>(); // insert all the elements // of 1st array in the hash // table(unordered_set 'us') for (int i = 0; i < m; i++) us.Add(arr1[i]); // for each element of 'arr2[] for (int j = 0; j < n; j++) // find (x - arr2[j]) in 'us' if(us.Contains(x - arr2[j])) count++; // required count of pairs return count; } // Driver Code public static void Main(String[] args) { int []arr1 = {1, 3, 5, 7}; int []arr2 = {2, 3, 5, 8}; int m = arr1.Length; int n = arr2.Length; int x = 10; Console.Write("Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code contributed by Rajput-Ji
Javascript
<script> // Javascript implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs(arr1, arr2, m, n, x) { let count = 0; let us = new Set(); // insert all the elements // of 1st array in the hash // table(unordered_set 'us') for (let i = 0; i < m; i++) us.add(arr1[i]); // for each element of 'arr2[] for (let j = 0; j < n; j++) // find (x - arr2[j]) in 'us' if (us.has(x - arr2[j])) count++; // required count of pairs return count; } // Driver Code let arr1=[1, 3, 5, 7]; let arr2=[2, 3, 5, 8]; let m = arr1.length; let n = arr2.length; let x = 10; document.write("Count = " + countPairs(arr1, arr2, m, n, x)); // This code is contributed by rag2127 </script>
Producción :
Count = 2
Complejidad de tiempo: O (m + n)
Espacio auxiliar: O (m), la tabla hash debe crearse de la array que tiene un tamaño más pequeño para reducir la complejidad del espacio.
Método 4 (Enfoque eficiente): este enfoque utiliza el concepto de dos punteros, uno para recorrer el primer arreglo de izquierda a derecha y otro para recorrer el segundo arreglo de derecha a izquierda.
Algoritmo:
countPairs(arr1, arr2, m, n, x) Initialize l = 0, r = n - 1 Initialize count = 0 loop while l = 0 if (arr1[l] + arr2[r]) == x l++, r-- count++ else if (arr1[l] + arr2[r]) < x l++ else r-- return count
C++
// C++ implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value #include <bits/stdc++.h> using namespace std; // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; int l = 0, r = n - 1; // traverse 'arr1[]' from // left to right // traverse 'arr2[]' from // right to left while (l < m && r >= 0) { // if this sum is equal // to 'x', then increment 'l', // decrement 'r' and // increment 'count' if ((arr1[l] + arr2[r]) == x) { l++; r--; count++; } // if this sum is less // than x, then increment l else if ((arr1[l] + arr2[r]) < x) l++; // else decrement 'r' else r--; } // required count of pairs return count; } // Driver Code int main() { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = sizeof(arr1) / sizeof(arr1[0]); int n = sizeof(arr2) / sizeof(arr2[0]); int x = 10; cout << "Count = " << countPairs(arr1, arr2, m, n, x); return 0; }
Java
// Java implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value import java.io.*; class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int arr1[], int arr2[], int m, int n, int x) { int count = 0; int l = 0, r = n - 1; // traverse 'arr1[]' from // left to right // traverse 'arr2[]' from // right to left while (l < m && r >= 0) { // if this sum is equal // to 'x', then increment 'l', // decrement 'r' and // increment 'count' if ((arr1[l] + arr2[r]) == x) { l++; r--; count++; } // if this sum is less // than x, then increment l else if ((arr1[l] + arr2[r]) < x) l++; // else decrement 'r' else r--; } // required count of pairs return count; } // Driver Code public static void main (String[] args) { int arr1[] = {1, 3, 5, 7}; int arr2[] = {2, 3, 5, 8}; int m = arr1.length; int n = arr2.length; int x = 10; System.out.println( "Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
Python3
# Python 3 implementation to count # pairs from both sorted arrays # whose sum is equal to a given # value # function to count all pairs # from both the sorted arrays # whose sum is equal to a given # value def countPairs(arr1, arr2, m, n, x): count, l, r = 0, 0, n - 1 # traverse 'arr1[]' from # left to right # traverse 'arr2[]' from # right to left while (l < m and r >= 0): # if this sum is equal # to 'x', then increment 'l', # decrement 'r' and # increment 'count' if ((arr1[l] + arr2[r]) == x): l += 1 r -= 1 count += 1 # if this sum is less # than x, then increment l elif ((arr1[l] + arr2[r]) < x): l += 1 # else decrement 'r' else: r -= 1 # required count of pairs return count # Driver Code if __name__ == '__main__': arr1 = [1, 3, 5, 7] arr2 = [2, 3, 5, 8] m = len(arr1) n = len(arr2) x = 10 print("Count =", countPairs(arr1, arr2, m, n, x)) # This code is contributed # by PrinciRaj19992
C#
// C# implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value using System; class GFG { // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value static int countPairs(int []arr1, int []arr2, int m, int n, int x) { int count = 0; int l = 0, r = n - 1; // traverse 'arr1[]' from // left to right // traverse 'arr2[]' from // right to left while (l < m && r >= 0) { // if this sum is equal // to 'x', then increment 'l', // decrement 'r' and // increment 'count' if ((arr1[l] + arr2[r]) == x) { l++; r--; count++; } // if this sum is less // than x, then increment l else if ((arr1[l] + arr2[r]) < x) l++; // else decrement 'r' else r--; } // required count of pairs return count; } // Driver Code public static void Main () { int []arr1 = {1, 3, 5, 7}; int []arr2 = {2, 3, 5, 8}; int m = arr1.Length; int n = arr2.Length; int x = 10; Console.WriteLine( "Count = " + countPairs(arr1, arr2, m, n, x)); } } // This code is contributed by anuj_67.
PHP
<?php // PHP implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs( $arr1, $arr2, $m, $n, $x) { $count = 0; $l = 0; $r = $n - 1; // traverse 'arr1[]' from // left to right // traverse 'arr2[]' from // right to left while ($l < $m and $r >= 0) { // if this sum is equal // to 'x', then increment 'l', // decrement 'r' and // increment 'count' if (($arr1[$l] + $arr2[$r]) == $x) { $l++; $r--; $count++; } // if this sum is less // than x, then increment l else if (($arr1[$l] + $arr2[$r]) < $x) $l++; // else decrement 'r' else $r--; } // required count of pairs return $count; } // Driver Code $arr1 = array(1, 3, 5, 7); $arr2 = array(2, 3, 5, 8); $m = count($arr1); $n = count($arr2); $x = 10; echo "Count = " , countPairs($arr1, $arr2, $m, $n, $x); // This code is contributed by anuj_67 ?>
Javascript
<script> // Javascript implementation to count // pairs from both sorted arrays // whose sum is equal to a given // value // function to count all pairs // from both the sorted arrays // whose sum is equal to a given // value function countPairs(arr1, arr2, m, n, x) { let count = 0; let l = 0, r = n - 1; // traverse 'arr1[]' from // left to right // traverse 'arr2[]' from // right to left while (l < m && r >= 0) { // if this sum is equal // to 'x', then increment 'l', // decrement 'r' and // increment 'count' if ((arr1[l] + arr2[r]) == x) { l++; r--; count++; } // if this sum is less // than x, then increment l else if ((arr1[l] + arr2[r]) < x) l++; // else decrement 'r' else r--; } // required count of pairs return count; } let arr1 = [1, 3, 5, 7]; let arr2 = [2, 3, 5, 8]; let m = arr1.length; let n = arr2.length; let x = 10; document.write("Count = " + countPairs(arr1, arr2, m, n, x)); </script>
Producción :
Count = 2
Complejidad de tiempo: O(m + n)
Espacio auxiliar: O(1)
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA