arithmetic_subarrays.dart

/*

-* 1630. Arithmetic Subarrays *-


A sequence of numbers is called arithmetic if it consists of at least two elements, and the difference between every two consecutive elements is the same. More formally, a sequence s is arithmetic if and only if s[i+1] - s[i] == s[1] - s[0] for all valid i.

For example, these are arithmetic sequences:

1, 3, 5, 7, 9
7, 7, 7, 7
3, -1, -5, -9
The following sequence is not arithmetic:

1, 1, 2, 5, 7
You are given an array of n integers, nums, and two arrays of m integers each, l and r, representing the m range queries, where the ith query is the range [l[i], r[i]]. All the arrays are 0-indexed.

Return a list of boolean elements answer, where answer[i] is true if the subarray nums[l[i]], nums[l[i]+1], ... , nums[r[i]] can be rearranged to form an arithmetic sequence, and false otherwise.

 

Example 1:

Input: nums = [4,6,5,9,3,7], l = [0,0,2], r = [2,3,5]
Output: [true,false,true]
Explanation:
In the 0th query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence.
In the 1st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence.
In the 2nd query, the subarray is [5,9,3,7]. This can be rearranged as [3,5,7,9], which is an arithmetic sequence.
Example 2:

Input: nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10], l = [0,1,6,4,8,7], r = [4,4,9,7,9,10]
Output: [false,true,false,false,true,true]
 

Constraints:

n == nums.length
m == l.length
m == r.length
2 <= n <= 500
1 <= m <= 500
0 <= l[i] < r[i] < n
-105 <= nums[i] <= 105

*/

class Solution {
    bool isArithmetic(List<int> nums, int ll, int rr) {
      final int minN = nums.sublist(ll, rr + 1).reduce((a, b) => a < b ? a : b);
      final int maxN = nums.sublist(ll, rr + 1).reduce((a, b) => a > b ? a : b);
      final int diff = maxN - minN;
      if (diff == 0) return true;
      final int d = diff ~/ (rr - ll);
      if (diff % (rr - ll) != 0) return false;
      final List<bool> term = List.filled(rr - ll + 1, false);
      for (int i = ll; i <= rr; i++) {
        final int x = nums[i] - minN;
        if (x % d != 0) return false;
        final int j = x ~/ d;
        if (term[j])
          return false; // exact once
        else
          term[j] = true;
      }
      return true;
    }

    List<bool> checkArithmeticSubarrays(
        final List<int> nums, List<int> l, List<int> r) {
      // int n = nums.length;
      final int m = l.length;
      final List<bool> ans = List.filled(m, false);
      for (int i = 0; i < m; i++) {
        ans[i] = isArithmetic(nums, l[i], r[i]);
      }
      return ans;
    }
}