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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.
1def solve(arr):
2 arr.sort()
3 print(' '.join(map(str, arr)))The Python solution sorts the list using the list sort method and prints the elements in a single line. After sorting, you can implement the specific logic for the problem.
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.
1#include <unordered_map>
#include <vector>
void solve(std::vector<int>& arr) {
std::unordered_map<int, int> hash;
for(int num : arr) {
hash[num]++;
}
for(const auto& entry : hash) {
std::cout << entry.first << " appears " << entry.second << " times\n";
}
}This C++ solution uses an unordered map to store and count the occurrences of each number, providing efficient insertions and lookups.