# 1354. Construct Target Array With Multiple Sums

### Description

Given an array of integers `target`. From a starting array, `A` consisting of all 1's, you may perform the following procedure :

* let `x` be the sum of all elements currently in your array.
* choose index `i`, such that `0 <= i < target.size` and set the value of `A` at index `i` to `x`.
* You may repeat this procedure as many times as needed.

Return True if it is possible to construct the `target` array from `A` otherwise return False.

### Constraints

* `N == target.length`
* `1 <= target.length <= 5 * 10^4`
* `1 <= target[i] <= 10^9`

### Approach

### Links

* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/construct-target-array-with-multiple-sums/)
* ProgramCreek
* YouTube

### **Examples**

{% tabs %}
{% tab title="Example 1" %}
**Input:** target = \[9,3,5]

**Output:** true

**Explanation:** Start with \[1, 1, 1]

\[1, 1, 1], sum = 3 choose index 1

\[1, 3, 1], sum = 5 choose index 2

\[1, 3, 5], sum = 9 choose index 0

\[9, 3, 5] Done
{% endtab %}

{% tab title="Example 2" %}
**Input:** target = \[1, 1, 1, 2]

**Output:** false

**Explanation:** Impossible to create target array from \[1, 1, 1, 1].
{% endtab %}

{% tab title="Example 3" %}
**Input:** target = \[8, 5]

**Output:** true
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    public boolean isPossible(int[] target) {
        if(target.length == 1) {
            return target[0] == 1;
        }
        
        PriorityQueue<Integer> pq = new PriorityQueue<>((a, b) -> b -a);
        
        int sum = 0;
        for(int n: target) {
            sum += n;
            pq.add(n);
        }
        
        while(pq.peek() != 1) {
            int num = pq.poll();
            sum -= num;
            if(sum < 1 || sum >= num) {
                return false;
            }
            num %= sum;
            sum += num;
            pq.add(num);
        }
        
        return true;
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*