# Minimum Absolute Difference Queries Leetcode Solution

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## Minimum Absolute Difference Queries

The minimum absolute difference of an array `a` is defined as the minimum value of `|a[i] - a[j]|`, where `0 <= i < j < a.length` and `a[i] != a[j]`. If all elements of `a` are the same, the minimum absolute difference is `-1`.

• For example, the minimum absolute difference of the array `[5,2,3,7,2]` is `|2 - 3| = 1`. Note that it is not `0` because `a[i]` and `a[j]` must be different.

You are given an integer array `nums` and the array `queries` where `queries[i] = [li, ri]`. For each query `i`, compute the minimum absolute difference of the subarray `nums[li...ri]` containing the elements of `nums` between the 0-based indices `li` and `ri` (inclusive).

Return an array `ans` where `ans[i]` is the answer to the `ith` query.

subarray is a contiguous sequence of elements in an array.

The value of `|x|` is defined as:

• `x` if `x >= 0`.
• `-x` if `x < 0`.

Example 1:

```Input: nums = [1,3,4,8], queries = [[0,1],[1,2],[2,3],[0,3]]
Output: [2,1,4,1]
Explanation: The queries are processed as follows:
- queries[0] = [0,1]: The subarray is [1,3] and the minimum absolute difference is |1-3| = 2.
- queries[1] = [1,2]: The subarray is [3,4] and the minimum absolute difference is |3-4| = 1.
- queries[2] = [2,3]: The subarray is [4,8] and the minimum absolute difference is |4-8| = 4.
- queries[3] = [0,3]: The subarray is [1,3,4,8] and the minimum absolute difference is |3-4| = 1.
```

Example 2:

```Input: nums = [4,5,2,2,7,10], queries = [[2,3],[0,2],[0,5],[3,5]]
Output: [-1,1,1,3]
Explanation: The queries are processed as follows:
- queries[0] = [2,3]: The subarray is [2,2] and the minimum absolute difference is -1 because all the
elements are the same.
- queries[1] = [0,2]: The subarray is [4,5,2] and the minimum absolute difference is |4-5| = 1.
- queries[2] = [0,5]: The subarray is [4,5,2,2,7,10] and the minimum absolute difference is |4-5| = 1.
- queries[3] = [3,5]: The subarray is [2,7,10] and the minimum absolute difference is |7-10| = 3.
```

Constraints:

• `2 <= nums.length <= 105`
• `1 <= nums[i] <= 100`
• `1 <= queries.length <= 2 * 104`
• `0 <= li < ri < nums.length`

Program:

``````class Solution:
def minDifference(self, nums: List[int], queries: List[List[int]]) -> List[int]:
max_el, answer, counter = max(nums), [], [[0]*(max(nums)+1)]
set_of_nums = sorted(list(set(nums)))
for n in nums:
t = counter[-1][:]
t[n] += 1
counter.append(t)
def f(start, finish):
arr = [num for num in set_of_nums if counter[finish+1][num]-counter[start][num]>0]
if len(arr)==1:
return -1
return min([b-a for a,b in zip(arr, arr[1:])])

for q in queries: