Sum Triangle for given array1159

Summary

Given an array, we need to find the sum of all triangles that can be formed using the elements of the array. A triangle is considered valid if it has three sides and its area is non-negative.

Detailed Explanation

To solve this problem, we will use a brute force approach. First, we generate all possible combinations of three elements from the given array. Then, for each combination, we check if the sum of the three elements forms a valid triangle (i.e., the sum is positive). If it does, we add its area to our total sum.

Here's a step-by-step breakdown:

1. Initialize an empty set triangles to store the sum of all triangles.
2. Generate all possible combinations of three elements from the given array using a combination algorithm (e.g., recursive approach).
3. For each combination, calculate the sum of its elements and check if it forms a valid triangle by verifying the condition a + b > c, where a, b, and c are the sides of the triangle.
4. If the combination forms a valid triangle, add its area to the set triangles.
5. Finally, return the sum of all triangles in the set.

Time complexity: O(n^3), where n is the length of the input array. Space complexity: O(1), since we only need a constant amount of space to store the set triangles.

Optimized Solutions

Java

java
import java.util.*;

public class SumTriangle {
    public static int sumTriangle(int[] arr) {
        Set<Integer> triangles = new HashSet<>();
        for (int i = 0; i < arr.length; i++) {
            for (int j = i + 1; j < arr.length; j++) {
                for (int k = j + 1; k < arr.length; k++) {
                    int sum = arr[i] + arr[j] + arr[k];
                    if (sum > 0) {
                        triangles.add(sum);
                    }
                }
            }
        }
        return triangles.stream().mapToInt(Integer::intValue).sum();
    }
}

Python

python
def sum_triangle(arr):
    triangles = set()
    for i in range(len(arr)):
        for j in range(i + 1, len(arr)):
            for k in range(j + 1, len(arr)):
                sum_val = arr[i] + arr[j] + arr[k]
                if sum_val > 0:
                    triangles.add(sum_val)
    return sum(triangles)

C++

cpp
#include <iostream>
#include <set>

int sumTriangle(int* arr, int n) {
    std::set<int> triangles;
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                int sum = arr[i] + arr[j] + arr[k];
                if (sum > 0) {
                    triangles.insert(sum);
                }
            }
        }
    }
    int result = 0;
    for (auto it = triangles.begin(); it != triangles.end(); ++it) {
        result += *it;
    }
    return result;
}

JavaScript

javascript
function sumTriangle(arr) {
    const triangles = new Set();
    for (let i = 0; i < arr.length; i++) {
        for (let j = i + 1; j < arr.length; j++) {
            for (let k = j + 1; k < arr.length; k++) {
                const sum = arr[i] + arr[j] + arr[k];
                if (sum > 0) {
                    triangles.add(sum);
                }
            }
        }
    }
    return [...triangles].reduce((acc, cur) => acc + cur, 0);
}