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This approach involves sorting the input data first and then finding the solution by traversing through the sorted data. This approach is generally straightforward and often leads to a solution by leveraging sorted order, which simplifies many problems, such as finding pairs or detecting duplicates.
Time Complexity: O(n log n) due to sorting.
Space Complexity: O(1) or O(n), depending on the usage of additional data structures.
1using System;
2using System.Linq;
3
4public class Solution {
5 public static void Solve(int[] arr) {
6 Array.Sort(arr);
7 Console.WriteLine(string.Join(" ", arr));
8 }
9}This C# solution sorts an array using Array.Sort and then prints the sorted numbers. After sorting, additional specific operations can be applied.
This approach leverages a hash map to efficiently solve problems requiring quick lookups or to detect duplicates. This method is optimal for problems where you need to count occurrences or require O(1) average-time complexity for lookups.
Time Complexity: O(n)
Space Complexity: O(n) for the hash map.
1using System.Collections.Generic;
public class Solution {
public static void Solve(int[] arr) {
Dictionary<int, int> map = new Dictionary<int, int>();
foreach (int num in arr) {
if (map.ContainsKey(num)) {
map[num]++;
} else {
map[num] = 1;
}
}
foreach (var key in map.Keys) {
Console.WriteLine($"{key} appears {map[key]} times");
}
}
}This C# solution makes use of a Dictionary to track and count the frequency of numbers, giving instant results for frequency requirements or uniqueness checks.