# LinkedIn

## Subarray Sum

Given a array of integers, find out the sum of all subarrays

Ex:\[1,2,3] -> \[1], \[2], \[3], \[1,2], \[2,3], \[1,2,3]

sum = 20

* Every element arr\[i] appears in two types of subsets:
  * In sybarrays beginning with arr\[i]. There are 

    (n-i) such subsets. For example \[2] appears

    in \[2] and \[2, 3].
  * In (n-i)\*i subarrays where this element is not

    first element. For example \[2] appears in 

    \[1, 2] and \[1, 2, 3].

`Sum = (n-i) + (n-i)*i = (n-i)(i+1)`

```java
public static long SubArraySum( int arr[] , int n )
{
    long result = 0;

    // computing sum of subarray using formula
    for (int i=0; i<n; i++)
        result += (arr[i] * (i+1) * (n-i));
    return result ;
}
```

## Duplicted number increase by 1

E.g.\
\[1,2,2,3,3] -> \[1,2,3,4,5]

```java
private static List<Integer> f(int[] A){
    List<Integer> list = new ArrayList<>();
    list.add(A[0]);
    int prev = A[0];
    for(int i=1; i<A.length; i++){
        if(A[i]<=prev) list.add(prev+1);
        else list.add(A[i]);
        prev = list.get(list.size()-1);
    }
    return list;
}
 public static void main(String []args){
     int[] A = new int[]{1,2,2,3,3};
    System.out.println(f(A));
 }
```


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