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]. Thiscan 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.lengthm == l.lengthm == r.length2 <= n <= 5001 <= m <= 5000 <= l[i] < r[i] < n-105 <= nums[i] <= 105
class Solution:
def checkArithmeticSubarrays(self, nums: List[int], l: List[int], r: List[int]) -> List[bool]:
def check(nums, l, r):
if r - l < 2:
return True
s = set(nums[l: r + 1])
mx = max(nums[l: r + 1])
mi = min(nums[l: r + 1])
if (mx - mi) % (r - l) != 0:
return False
delta = (mx - mi) / (r - l)
for i in range(1, r - l + 1):
if (mi + delta * i) not in s:
return False
return True
return [check(nums, l[i], r[i]) for i in range(len(l))]class Solution {
public List<Boolean> checkArithmeticSubarrays(int[] nums, int[] l, int[] r) {
List<Boolean> res = new ArrayList<>();
for (int i = 0; i < l.length; ++i) {
res.add(check(nums, l[i], r[i]));
}
return res;
}
private boolean check(int[] nums, int l, int r) {
if (r - l < 2) {
return true;
}
Set<Integer> s = new HashSet<>();
int mx = Integer.MIN_VALUE;
int mi = Integer.MAX_VALUE;
for (int i = l; i <= r; ++i) {
s.add(nums[i]);
mx = Math.max(mx, nums[i]);
mi = Math.min(mi, nums[i]);
}
if ((mx - mi) % (r - l) != 0) {
return false;
}
int delta = (mx - mi) / (r - l);
for (int i = 1; i <= r - l; ++i) {
if (!s.contains(mi + delta * i)) {
return false;
}
}
return true;
}
}class Solution {
public:
vector<bool> checkArithmeticSubarrays(vector<int>& nums, vector<int>& l, vector<int>& r) {
vector<bool> res;
for (int i = 0; i < l.size(); ++i) {
res.push_back(check(nums, l[i], r[i]));
}
return res;
}
bool check(vector<int>& nums, int l, int r) {
if (r - l < 2) return true;
unordered_set<int> s;
int mx = -100010;
int mi = 100010;
for (int i = l; i <= r; ++i) {
s.insert(nums[i]);
mx = max(mx, nums[i]);
mi = min(mi, nums[i]);
}
if ((mx - mi) % (r - l) != 0) return false;
int delta = (mx - mi) / (r - l);
for (int i = 1; i <= r - l; ++i) {
if (!s.count(mi + delta * i)) return false;
}
return true;
}
};func checkArithmeticSubarrays(nums []int, l []int, r []int) []bool {
n := len(l)
var res []bool
for i := 0; i < n; i++ {
res = append(res, check(nums, l[i], r[i]))
}
return res
}
func check(nums []int, l, r int) bool {
if r-l < 2 {
return true
}
s := make(map[int]bool)
mx, mi := -100010, 100010
for i := l; i <= r; i++ {
s[nums[i]] = true
mx = max(mx, nums[i])
mi = min(mi, nums[i])
}
if (mx-mi)%(r-l) != 0 {
return false
}
delta := (mx - mi) / (r - l)
for i := 1; i <= r-l; i++ {
if !s[mi+delta*i] {
return false
}
}
return true
}
func max(a, b int) int {
if a > b {
return a
}
return b
}
func min(a, b int) int {
if a < b {
return a
}
return b
}