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package g1601_1700.s1630_arithmetic_subarrays;

// #Medium #Array #Sorting #Programming_Skills_II_Day_9
// #2022_04_19_Time_8_ms_(93.62%)_Space_54.4_MB_(59.83%)

import java.util.ArrayList;
import java.util.List;

/**
 * 1630 - Arithmetic Subarrays\.
 *
 * Medium
 *
 * 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 i^th 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 0^th query, the subarray is [4,6,5]. 
 *
 * This can be rearranged as [6,5,4], which is an arithmetic sequence. 
 *
 * In the 1^st query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence. 
 *
 * In the 2^nd 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
**/
public class Solution {
    public List checkArithmeticSubarrays(int[] nums, int[] l, int[] r) {
        List result = new ArrayList<>();
        int n = l.length;
        for (int i = 0; i < n; i++) {
            result.add(check(nums, l[i], r[i]));
        }
        return result;
    }

    private boolean check(int[] nums, int l, int r) {
        int n = r - l;
        if (n == 0) {
            return true;
        }
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for (int i = l; i <= r; i++) {
            max = Math.max(max, nums[i]);
            min = Math.min(min, nums[i]);
        }
        if ((max - min) % n != 0) {
            return false;
        }
        int diff = (max - min) / n;
        if (diff == 0) {
            return true;
        }
        boolean[] checked = new boolean[max - min + 1];
        for (int i = l; i <= r; i++) {
            int currentDiff = nums[i] - min;
            if (checked[currentDiff] || currentDiff % diff != 0) {
                return false;
            }
            checked[currentDiff] = true;
        }
        return true;
    }
}