Count of contiguous subarrays possible for every index by including the element at that index - GeeksforGeeks

24 Feb, 2022
Given a number N which represents the size of the array A[], the task is to find the number of contiguous subarrays that can be formed for every index of the array by including the element at that index in the original array.
Examples: 
Input: N = 4 Output: {4, 6, 6, 4} Explanation: Since the size of the array is given as 4. Let’s assume the array to be {1, 2, 3, 4}. The number of subarrays that contain 1 are: {{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}} The number of subarrays that contain 2 are: {{2}, {2, 3}, {2, 3, 4}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}} The number of subarrays that contain 3 are: {{3}, {2, 3}, {2, 3, 4}, {3, 4}, {1, 2, 3}, {1, 2, 3, 4}} The number of subarrays that contain 4 are: {{4}, {3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Input: 3 Output: {3, 4, 3} Explanation: Since the size of the array is given as 3. Lets assume the array to be {1, 2, 3}. The number of subarrays that contain 1 are: {{1}, {1, 2}, {1, 2, 3}} The number of subarrays that contain 2 are: {{2}, {1, 2}, {2, 3}, {1, 2, 3}} The number of subarrays that contain 3 are: {{3}, {2, 3}, {1, 2, 3}}  
Approach: The idea is to use the concept of permutation and combination. It can be observed that the number of subarrays possible including the element at the ith index is always equal to the number of subarrays possible including the element at the index (N – i) where N is the length of the array.  
Iterate through the first half of the array.
The number of subarrays including the element at the ith index is always equal to the number of subarrays including the element at the index N – i. Therefore, simultaneously update the count for both the indices.
To calculate the number of subarrays that include the element at the ith index, we simply subtract the number of subarrays not including the element at the ith index from the total number of ways.
Therefore, the formula to calculate the required value is:
Count of possible subarrays = N * (i + 1) - i * (i + 1)
where i is the current index.
Calculate and store the above values for every index.
Below is the implementation of the above approach: 
C++
Java
Python3
C#
Javascript
// C++ program to find the number of// contiguous subarrays including// the element at every index// of the array of size N #include <bits/stdc++.h>using namespace std; // Function to find the number of// subarrays including the element// at every index of the arrayvector<int> calculateWays(int N){    int x = 0;    vector<int> v;     // Creating an array of size N    for (int i = 0; i < N; i++)        v.push_back(0);     // The loop is iterated till half the    // length of the array    for (int i = 0; i <= N / 2; i++) {         // Condition to avoid overwriting        // the middle element for the        // array with even length.        if (N % 2 == 0 && i == N / 2)            break;         // Computing the number of subarrays        x = N * (i + 1) - (i + 1) * i;         // The ith element from the beginning        // and the ending have the same        // number of possible subarrays        v[i] = x;        v[N - i - 1] = x;    }    return v;} // Function to print the vectorvoid printArray(vector<int> v){    for (int i = 0; i < v.size(); i++)        cout << v[i] << " ";} // Driver codeint main(){    vector<int> v;    v = calculateWays(4);     printArray(v);     return 0;}
// Java program to find the number// of contiguous subarrays including// the element at every index// of the array of size Nimport java.util.Scanner; class contiguous_subarrays{     // Function to find the number of// subarrays including the element// at every index of the arraypublic static int[] calculateWays(int n){    int x = 0;             // Creating an array of size N    int[]v = new int[n];         for(int i = 0; i < n; i++)    v[i] = 0;             // The loop is iterated till half the    // length of the array    for(int i = 0; i < n / 2; i++)    {        // Condition to avoid overwriting        // the middle element for the        // array with even length.        if(n % 2 == 0 && i == n / 2)        break;                 // Computing the number of subarrays        x = n * (i + 1) - (i + 1) * i;                 // The ith element from the beginning        // and the ending have the same        // number of possible subarray        v[i] = x;        v[n - i - 1] = x;    }         return v;}     // Function to print the vectorpublic static void printArray(int[]v){    for(int i = 0; i < v.length; i++)    System.out.print(v[i] + " ");} // Driver codepublic static void main (String args[]){    int[]v;    v = calculateWays(4);         printArray(v);}} // This code is contributed by sayesha
# Python3 program to find the number of# contiguous subarrays including# the element at every index# of the array of size N # Function to find the number of# subarrays including the element# at every index of the arraydef calculateWays(N):    x = 0;    v = [];         # Creating an array of size N    for i in range(N):        v.append(0);     # The loop is iterated till half the    # length of the array    for i in range(N // 2 + 1):         # Condition to avoid overwriting        # the middle element for the        # array with even length.        if (N % 2 == 0 and i == N // 2):            break;         # Computing the number of subarrays        x = N * (i + 1) - (i + 1) * i;         # The ith element from the beginning        # and the ending have the same        # number of possible subarrays        v[i] = x;        v[N - i - 1] = x;         return v; # Function to print the vectordef printArray(v):         for i in range(len(v)):        print(v[i], end = " "); # Driver codeif __name__ == "__main__":     v = calculateWays(4);    printArray(v); # This code is contributed by AnkitRai01
// C# program to find the number// of contiguous subarrays including// the element at every index// of the array of size Nusing System; class GFG{     // Function to find the number of// subarrays including the element// at every index of the arraypublic static int[] calculateWays(int N){    int x = 0;             // Creating an array of size N    int[]v = new int[N];         for(int i = 0; i < N; i++)        v[i] = 0;             // The loop is iterated till half    // the length of the array    for(int i = 0; i < N / 2; i++)    {               // Condition to avoid overwriting       // the middle element for the       // array with even length.       if(N % 2 == 0 && i == N / 2)          break;               // Computing the number of subarrays       x = N * (i + 1) - (i + 1) * i;               // The ith element from the beginning       // and the ending have the same       // number of possible subarray       v[i] = x;       v[N - i - 1] = x;    }    return v;}     // Function to print the vectorpublic static void printArray(int []v){    for(int i = 0; i < v.Length; i++)    {       Console.Write(v[i] + " ");    }} // Driver codepublic static void Main (string []args){    int []v;    v = calculateWays(4);         printArray(v);}} // This code is contributed by rutvik_56
<script> // Javascript program to find the number// of contiguous subarrays including// the element at every index// of the array of size N // Function to find the number of// subarrays including the element// at every index of the arrayfunction calculateWays(n){    let x = 0;               // Creating an array of size N    let v = Array.from({length: n}, (_, i) => 0);           for(let i = 0; i < n; i++)        v[i] = 0;               // The loop is iterated till half the    // length of the array    for(let i = 0; i < n / 2; i++)    {                 // Condition to avoid overwriting        // the middle element for the        // array with even length.        if(n % 2 == 0 && i == n / 2)            break;                   // Computing the number of subarrays        x = n * (i + 1) - (i + 1) * i;                   // The ith element from the beginning        // and the ending have the same        // number of possible subarray        v[i] = x;        v[n - i - 1] = x;    }    return v;}       // Function to printt the vectorfunction printArray(v){    for(let i = 0; i < v.length; i++)        document.write(v[i] + " ");} // Driver Codelet v;v = calculateWays(4);   printArray(v); // This code is contributed by target_2 </script>
4 6 6 4
 
Time Complexity: O(n)
Auxiliary Space: O(n)
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