g1001_1100.s1039_minimum_score_triangulation_of_polygon

Class Solution

java.lang.Object

g1001_1100.s1039_minimum_score_triangulation_of_polygon.Solution

public class Solution
extends Object

1039 - Minimum Score Triangulation of Polygon.

Medium

You have a convex n-sided polygon where each vertex has an integer value. You are given an integer array values where values[i] is the value of the ith vertex (i.e., clockwise order ).

You will triangulate the polygon into n - 2 triangles. For each triangle, the value of that triangle is the product of the values of its vertices, and the total score of the triangulation is the sum of these values over all n - 2 triangles in the triangulation.

Return the smallest possible total score that you can achieve with some triangulation of the polygon.

Example 1:

Input: values = [1,2,3]

Output: 6

Explanation: The polygon is already triangulated, and the score of the only triangle is 6.

Example 2:

Input: values = [3,7,4,5]

Output: 144

Explanation: There are two triangulations, with possible scores: 3*7*5 + 4*5*7 = 245, or 3*4*5 + 3*4*7 = 144. The minimum score is 144.

Example 3:

Input: values = [1,3,1,4,1,5]

Output: 13

Explanation: The minimum score triangulation has score 1*1*3 + 1*1*4 + 1*1*5 + 1*1*1 = 13.

Constraints:

• n == values.length
• 3 <= n <= 50
• 1 <= values[i] <= 100

Constructor Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
int	minScoreTriangulation(int[] values)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

minScoreTriangulation

public int minScoreTriangulation(int[] values)