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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.
1#include <stdio.h>
2#include <stdlib.h>
3
4int compare (const void * a, const void * b) {
Similar to the Python solution, the C implementation sorts the array in descending order using `qsort`. The function iterates over the possible triplets of side lengths to find a valid one. A triplet is considered valid if the sum of the two smaller numbers is greater than the largest number. If a valid triplet 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.
public int LargestPerimeterBruteForce(int[] nums) {
int maxPerimeter = -1;
for (int i = 0; i < nums.Length; i++) {
for (int j = i + 1; j < nums.Length; j++) {
for (int k = j + 1; k < nums.Length; k++) {
if (nums[i] < nums[j] + nums[k] &&
nums[j] < nums[i] + nums[k] &&
nums[k] < nums[i] + nums[j]) {
maxPerimeter = Math.Max(maxPerimeter, nums[i] + nums[j] + nums[k]);
}
}
}
}
return maxPerimeter;
}
}This C# implementation uses nested loops to check all sets of three numbers in the array for triangle formation, increasing the storage of the maximal perimeter of any valid set found.