Given an array arr[]and an integer K, the task is to find the sum of all K length subsequences from the given array.
Example:
Input: arr[] = {2, 3, 4}, K = 2
Output: 18
Explanation:
There are 3 possible subsequences of length 2 which are {2, 3}, {2, 4} and {3, 4}
The sum of all 2 length subsequences is 5 + 6 + 7 = 18Input: arr[] = {7, 8, 9, 2}, K = 2
Output: 78
Explanation:
There are 6 subsequences of length 2 which are {7, 8}, {7, 9}, {7, 2}, {8, 9}, {8, 2} and {9, 2}.
The sum of all 2 length sub sequences is 15 + 16 + 9 + 17 + 10 + 11 = 78
Approach:
To solve the problem mentioned above we have to consider all K length subsequence that is “n choose k”, i.e. .
- The count of total element in all K length subsequences is
, possibility of appearing of each element is same.
- So each element appears
times and it contributes
in the result.
- Hence, the sum of all K length subsequence is
Below is the implementation of the above mentioned approach:
C++
// C++ implementation to find sum // of all subsequences of length K #include <bits/stdc++.h> using namespace std; int fact( int n); // Function to find nCr int nCr( int n, int r) { return fact(n) / (fact(r) * fact(n - r)); } // Function that returns // factorial of n int fact( int n) { int res = 1; for ( int i = 2; i <= n; i++) res = res * i; return res; } // Function for finding sum // of all K length subsequences int sumSubsequences( int arr[], int n, int k) { int sum = 0; // Calculate the sum of array for ( int i = 0; i < n; i++) { sum += arr[i]; } int kLengthSubSequence; // Calculate nCk kLengthSubSequence = nCr(n, k); int ans = sum * ((k * kLengthSubSequence) / n); // Return the final result return ans; } // Driver code int main() { int arr[] = { 7, 8, 9, 2 }; int K = 2; int n = sizeof (arr) / sizeof (arr[0]); cout << sumSubsequences(arr, n, K); return 0; } |
Java
// Java implementation to find sum // of all subsequences of length K class GFG{ // Function to find nCr static int nCr( int n, int r) { return fact(n) / (fact(r) * fact(n - r)); } // Function that returns // factorial of n static int fact( int n) { int res = 1 ; for ( int i = 2 ; i <= n; i++) res = res * i; return res; } // Function for finding sum // of all K length subsequences static int sumSubsequences( int arr[], int n, int k) { int sum = 0 ; // Calculate the sum of array for ( int i = 0 ; i < n; i++) { sum += arr[i]; } int kLengthSubSequence; // Calculate nCk kLengthSubSequence = nCr(n, k); int ans = sum * ((k * kLengthSubSequence) / n); // Return the final result return ans; } // Driver code public static void main(String[] args) { int arr[] = { 7 , 8 , 9 , 2 }; int K = 2 ; int n = arr.length; System.out.print(sumSubsequences(arr, n, K)); } } // This code contributed by Rajput-Ji |
Python3
# Python3 implementation to find sum # of all subsequences of length K # Function to find nCr def nCr(n, r): return fact(n) / (fact(r) * fact(n - r)) # Function that returns # factorial of n def fact(n): res = 1 for i in range ( 2 , n + 1 ): res = res * i return res # Function for finding sum # of all K length subsequences def sumSubsequences(arr, n, k): sum = 0 # Calculate the sum of array for i in range ( 0 , n): sum = sum + arr[i] # Calculate nCk kLengthSubSequence = nCr(n, k) ans = sum * ((k * kLengthSubSequence) / n); # Return the final result return ans # Driver Code arr = [ 7 , 8 , 9 , 2 ] k = 2 n = len (arr) print (sumSubsequences(arr, n, k)) # This code is contributed by skylags |
C#
// C# implementation to find sum // of all subsequences of length K using System; class GFG{ // Function to find nCr static int nCr( int n, int r) { return fact(n) / (fact(r) * fact(n - r)); } // Function that returns // factorial of n static int fact( int n) { int res = 1; for ( int i = 2; i <= n; i++) res = res * i; return res; } // Function for finding sum // of all K length subsequences static int sumSubsequences( int [] arr, int n, int k) { int sum = 0; // Calculate the sum of array for ( int i = 0; i < n; i++) { sum += arr[i]; } int kLengthSubSequence; // Calculate nCk kLengthSubSequence = nCr(n, k); int ans = sum * ((k * kLengthSubSequence) / n); // Return the final result return ans; } // Driver code static void Main() { int [] arr = { 7, 8, 9, 2 }; int K = 2; int n = arr.Length; Console.Write(sumSubsequences(arr, n, K)); } } // This code is contributed by divyeshrabadiya07 |
78
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