Arithmetic Sequence Permutation - Amazon Top Interview Questions


Problem Statement :


Given a list of integers nums, return whether you can rearrange the order of nums such that the difference between every consecutive two numbers is the same.

Constraints

n ≤ 100,000 where n is the length of nums


Example 1

Input
nums = [7, 1, 5, 3]

Output
True


Explanation
If we rearrange nums to [1, 3, 5, 7], then the difference between every two consecutive numbers is 2.



Example 2

Input
nums = [1, 5, 1, 5, 1, 5]

Output
False


Explanation
The difference between every consecutive two numbers alternates between 4 and -4.


Solution :



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                        Solution in C++ :

bool solve(vector<int>& nums) {
    // Finding Max and Min
    int max = nums[0], min = nums[0], max_i = -1, min_i = -1;
    for (int i = 1; i < nums.size(); i++) {
        if (nums[i] > max) {
            max = nums[i];
            max_i = i;
        }
        if (nums[i] < min) {
            min = nums[i];
            min_i = i;
        }
    }
    if (max - min == 0)  // All numbers same, diff=0
        return true;
    if ((max - min) % (nums.size() - 1) != 0)  // Case not possible
        return false;
    // Check for duplicates now
    vector<int> freqArr(max + 1, 0);
    for (int i = 0; i < nums.size(); i++) {
        freqArr[nums[i]] += 1;
        if (freqArr[nums[i]] > 1) return false;
    }
    int min_diff = (max - min) / (nums.size() - 1);
    for (int i = 0; i < nums.size(); i++) {
        if (i == min_i || i == max_i) continue;
        int d2 = nums[i] - min;
        if (d2 % min_diff != 0) {
            return false;
        }
    }
    return true;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public boolean solve(int[] nums) {
        Arrays.sort(nums);
        for (int i = 2; i < nums.length; i++) {
            if (nums[i] - nums[i - 1] != nums[i - 1] - nums[i - 2])
                return false;
        }
        return true;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):
        minima = min(nums)
        maxima = max(nums)

        d = (maxima - minima) / (len(nums) - 1)
        num = minima + d
        nums_set = set(nums)
        if d == 0:
            return True
        while num in nums_set:
            num += d

        if num > maxima:
            return True
        return False


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