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# Minimum Number of Increments on Subarrays to Form a Target Array

Given an array of positive integers `target` and an array `initial` of same size with all zeros.

Return the minimum number of operations to form a `target` array from `initial` if you are allowed to do the following operation:

* Choose **any** subarray from `initial` and increment each value by one.

The answer is guaranteed to fit within the range of a 32-bit signed integer.

**Example 1:**

```
Input: target = [1,2,3,2,1]
Output: 3
Explanation: We need at least 3 operations to form the target array from the initial array.
[0,0,0,0,0] increment 1 from index 0 to 4 (inclusive).
[1,1,1,1,1] increment 1 from index 1 to 3 (inclusive).
[1,2,2,2,1] increment 1 at index 2.
[1,2,3,2,1] target array is formed.
```

**Example 2:**

```
Input: target = [3,1,1,2]
Output: 4
Explanation: (initial)[0,0,0,0] -> [1,1,1,1] -> [1,1,1,2] -> [2,1,1,2] -> [3,1,1,2] (target).
```

**Example 3:**

```
Input: target = [3,1,5,4,2]
Output: 7
Explanation: (initial)[0,0,0,0,0] -> [1,1,1,1,1] -> [2,1,1,1,1] -> [3,1,1,1,1] 
                                  -> [3,1,2,2,2] -> [3,1,3,3,2] -> [3,1,4,4,2] -> [3,1,5,4,2] (target).
```

**Example 4:**

```
Input: target = [1,1,1,1]
Output: 1
```

**Constraints:**

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

```java
class Solution {
    public int minNumberOperations(int[] target) {
        // Each operation increments by 1
        int operationsUsed = target[0];
        int maxHeight = target[0];
        // Now we need to see upto where our current operations extend upto
        for (int i = 1; i < target.length; i++) {
            if (target[i] < maxHeight)
                maxHeight = target[i];
            // We need new operations for new local maximas
            else {
                operationsUsed += target[i] - maxHeight;
                maxHeight = target[i];
            }
        }
        return operationsUsed;
    }
}
```


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