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The idea here is to create a pattern with the integers that alternates between choosing numbers from the start and the end of a range. This provides the necessary number of distinct absolute differences between consecutive elements.
We build the answer list by initially alternating between numbers from opposite ends of a list of size n. Then, we fill in the remaining elements in a simple sequence.
Time Complexity: O(n), as we build the array in a single pass.
Space Complexity: O(n), for storing the answer.
1#include <vector>
2using namespace std;
3
4vector<int> constructArray(int n, int k) {
5 vector<int> answer;
6 int low = 1, high = n;
7 for (int i = 0; i <= k; ++i) {
8 if (i % 2 == 0) {
9 answer.push_back(low++);
10 } else {
11 answer.push_back(high--);
12 }
13 }
14 if (k % 2 == 0) {
15 for (int i = high; i >= low; --i) {
16 answer.push_back(i);
17 }
18 } else {
19 for (int i = low; i <= high; ++i) {
20 answer.push_back(i);
21 }
22 }
23 return answer;
24}The C++ implementation follows a similar logic as the Python solution, leveraging vectors for dynamic array handling. The function constructArray manages the array creation by toggling between low and high values based on the iteration count.
This approach constructs the answer using a specific pattern that alternates addition and subtraction. It builds the sequence by starting linearly and then intelligently adds or subtracts to reach necessary differences.
Time Complexity: O(n), iterating through the elements.
Space Complexity: O(n), owing to the storage of results.
1import java.util.*;
2public This Java solution involves incrementally constructing the initial sequence. Then it follows a methodical alternate increment and decrement strategy to meet the requirements of 'k' distinct differences.