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This approach involves sorting the array of side lengths and then iterating through it to find the largest valid polygon, specifically checking sets of three sides. By sorting, we can easily make sure that when checking three sides, the largest is the last one, allowing a simple perimeter check.
Sort the array in non-decreasing order and start checking from the third last element using a sliding window of three elements to check if they form a valid polygon (triangle) using the property: if a <= b <= c, a triangle forms if a + b > c.
Time Complexity: O(n log n) due to the sorting step.
Space Complexity: O(1), as no extra space proportional to input size is used.
1import java.util.Arrays;
2
3public class Main {
4 public static int largestPerimeter(int[] nums) {
5The Java implementation sorts the array in ascending order using `Arrays.sort()`. It then iterates from the end of the array backwards, checking each set of three numbers to see if they can form a triangle according to the triangle inequality principle. If a set that forms a triangle is found, its perimeter is returned.
This approach involves checking each combination of three different side lengths from the list to see if they can form a valid polygon (triangle). For each valid combination found, we will calculate its perimeter, and keep track of the maximum perimeter obtained.
This naive method is straightforward but can be inefficient for larger lists due to its O(n^3) complexity. However, it can be insightful for understanding triangle properties in small datasets.
Time Complexity: O(n^3) due to triple nested loops.
Space Complexity: O(1), apart from input storage no extra space is required.
#include <algorithm>
int largestPerimeterBruteForce(std::vector<int>& nums) {
int max_perimeter = -1;
int n = nums.size();
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
for (int k = j + 1; k < n; ++k) {
if (nums[i] < nums[j] + nums[k] &&
nums[j] < nums[i] + nums[k] &&
nums[k] < nums[i] + nums[j]) {
max_perimeter = std::max(max_perimeter, nums[i] + nums[j] + nums[k]);
}
}
}
}
return max_perimeter;
}In C++, the use of triple nested loops allows us to assess all possible combinations of three numbers from the array to check if they can form a valid triangle. The largest found perimeter among possible triangles is kept track using `std::max()`.