# 1533. Find the Index of the Large Integer

We have an integer array `arr`, where all the integers in `arr` are equal except for one integer which is larger than the rest of the integers. You will not be given direct access to the array, instead, you will have an API `ArrayReader` which have the following functions:

• `int compareSub(int l, int r, int x, int y)`: where `0 <= l, r, x, y < ArrayReader.length()`, `l <= r and` `x <= y`. The function compares the sum of sub-array `arr[l..r]` with the sum of the sub-array `arr[x..y]` and returns:
• 1 if `arr[l]+arr[l+1]+...+arr[r] > arr[x]+arr[x+1]+...+arr[y]`.
• 0 if `arr[l]+arr[l+1]+...+arr[r] == arr[x]+arr[x+1]+...+arr[y]`.
• -1 if `arr[l]+arr[l+1]+...+arr[r] < arr[x]+arr[x+1]+...+arr[y]`.
• `int length()`: Returns the size of the array.

You are allowed to call `compareSub()` 20 times at most. You can assume both functions work in `O(1)` time.

Return the index of the array `arr` which has the largest integer.

Follow-up:

• What if there are two numbers in `arr` that are bigger than all other numbers?
• What if there is one number that is bigger than other numbers and one number that is smaller than other numbers?

Example 1:

```Input: arr = [7,7,7,7,10,7,7,7]
Output: 4
Explanation: The following calls to the API
reader.compareSub(0, 0, 1, 1) // returns 0 this is a query comparing the sub-array (0, 0) with the sub array (1, 1), (i.e. compares arr with arr).
Thus we know that arr and arr doesn't contain the largest element.
reader.compareSub(2, 2, 3, 3) // returns 0, we can exclude arr and arr.
reader.compareSub(4, 4, 5, 5) // returns 1, thus for sure arr is the largest element in the array.
Notice that we made only 3 calls, so the answer is valid.
```

Example 2:

```Input: nums = [6,6,12]
Output: 2
```

Constraints:

• `2 <= arr.length <= 5 * 10^5`
• `1 <= arr[i] <= 100`
• All elements of `arr` are equal except for one element which is larger than all other elements.

Medium

Prime

Unknown

### Solution(Chinese):

LEETCODE 1533. Find the Index of the Large Integer 解题思路分析