Given an array of integers, we need to find out whether it is possible to construct at least one non-degenerate triangle using array values as its sides. In other words, we need to find out 3 such array indices which can become sides of a non-degenerate triangle.
Input : [4, 1, 2] Output : No No triangle is possible from given array values Input : [5, 4, 3, 1, 2] Output : Yes Sides of possible triangle are 2 3 4
For a non-degenerate triangle, its sides should follow these constraints,
A + B > C and B + C > A and C + A > B where A, B and C are length of sides of the triangle.
The task is to find any triplet from array that satisfies above condition.
A Simple Solution is to generate all triplets and for every triplet check if it forms a triangle or not by checking above three conditions.
An Efficient Solution is use sorting. First, we sort the array then we loop once and we will check three consecutive elements of this array if any triplet satisfies arr[i] + arr[i+1] > arr[i+2], then we will output that triplet as our final result.
Why checking only 3 consecutive elements will work instead of trying all possible triplets of sorted array?
Let we are at index i and 3 line segments are arr[i], arr[i + 1] and arr[i + 2] with relation arr[i] < arr[i+1] < arr[i+2], If they can't form a non-degenerate triangle, Line segments of lengths arr[i-1], arr[i+1] and arr[i+2] or arr[i], arr[i+1] and arr[i+3] can't form a non-degenerate triangle also because sum of arr[i-1] and arr[i+1] will be even less than sum of arr[i] and arr[i+1] in first case and sum of arr[i] and arr[i+1] must be less than arr[i+3] in second case, So we don't need to try all the combinations, we will try just 3 consecutive indices of array in sorted form.
The total complexity of below solution is O(n log n)
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Probability of cutting a rope into three pieces such that the sides form a triangle
- Number of possible pairs of Hypotenuse and Area to form right angled triangle
- Sum triangle from array
- Permutation of an array that has smaller values from another array
- Program to print Sum Triangle for a given array
- Maximum Perimeter Triangle from array
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Program to print a Hollow Triangle inside a Triangle
- Sort an array which contain 1 to n values
- Move all values equal to K to the end of the Array
- Sum of values of all possible non-empty subsets of the given array
- Sum of decomposition values of all suffixes of an Array
- Sum of even values and update queries on an array
- Number of subsets with same AND, OR and XOR values in an Array
- Print intermediate values in an array
- Product of values of all possible non-empty subsets of given Array
- Count minimum right flips to set all values in an array
- Pairs of Positive Negative values in an array
- Count the values greater than X in the modified array
- Maximum height of triangular arrangement of array values