# Find Missing Element

{% hint style="info" %}
Array, Iterative approach
{% endhint %}

Given a sorted array of size `n`. Each element in the array is unique and lies from `1` to `n+1`. Find the missing element.

### Solutions

This algorithm uses the formula for the sum of an arithmetic series to calculate the sum of all numbers from `1` to `n+1`, and then subtracts the sum of the elements in the array to find the missing element.

#### Approach - Iterative Technique

Iterates over the array and for each element, it calculates the sum of the first `n+1` natural numbers (where `n` is the length of the array) using the formula `(n + 1) * (n + 2) / 2`. 

**Steps**

1. **Initialization**: The function `FindMissingElement` is defined with one parameter, `arr`, which is the input array. It calculates the length of the array `n` and initializes a variable `total` to the sum of the first `(n+1)` natural numbers, which is calculated using the formula `(n + 1) * (n + 2) / 2`. This is based on the assumption that the array contains all numbers from 1 to `n+1` with one missing number.
2. **Subtraction**: The function then iterates over each element in the array with `i` as the index. For each `i`, it subtracts `arr[i]` from `total`.
3. **Return Result**: After iterating over all elements, `total` will be equal to the missing number in the array, which is then returned by the function.

```csharp
public class Solution
{
    public static int FindMissingElement(int[] arr)
    {
        int n = arr.Length;
        int total = (n + 1) * (n + 2) / 2;
        for (int i = 0; i < n; i++)
            total -= arr[i];
        return total;
    }
}


```

> Complexity

* **Time complexity:** `O(N)`
* **Space complexity:** `O(1)`

##

```csharp
public class Solution
{
    public int MissingNumber(int[] arr, int n)
    {
        int[] temp = new int[n + 1];

        for (int i = 0; i < n - 1; i++)
        {
            temp[arr[i] - 1] = 1;
        }

        int ans = 0;
        for (int i = 0; i <= n; i++)
        {
            if (temp[i] == 0)
                return i + 1;
        }
        return ans;
    }
}
```


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