Note that a polygon can be divided into triangles in more than one way. You need to print the minimum sum of triangle values of all the triangles created.
Given 'N' = 4, Array = [4, 3, 5, 2], the possible scores for these two triangle score are: (3 * 2 * 5) + (3 * 2 * 4) = 54 and (4 * 2 * 5) + (4 * 3 * 5) = 100. The minimum of these two triangle scores is 54. So you need to print 54.
The first line contains an integer ‘T’ which denotes the number of test cases. The first line of each test case contains a single integer ‘N’, denoting the vertices of the polygon. The next line contains ‘N’ space-separated integers denoting the value of the vertices of the polygon.
For each test case, you need to return the minimum triangle score possible from all triangles. Print the output of each test case in a separate line.
You don’t need to print anything; It has already been taken care of. Just implement the given function.
1 <= T <= 10 3 <= N <= 50 1 <= ARR[i] <= 100 Where 'ARR[i]' denotes the Array elements that represent the sides of the polygon. Time limit: 1 sec
We can solve this problem by dividing it into smaller subproblems using recursion. We can divide the polygon recursively into three parts - one triangle and two sub polygons and we have to find the optimal way to divide this so that we will get a minimum triangle score. Let us say the starting and ending index of the given array is ‘i’ and ‘j’ , and ‘k’ is any index between ‘i+1’ and ‘j-1’ then we can divide this polygon into two polygons A[ i…….k] + A[ k…….j] and a triangle formed by vertices i, j and k.
We will recursively divide all the polygons into sub polygons for all possible values of ‘ k ’ and return the minimum triangle score obtained.
The steps are as follows: