How hard is LeetCode 1039. Minimum Score Triangulation of Polygon?

LeetCode 1039. Minimum Score Triangulation of Polygon is rated Medium on LeetCode.

What is the time complexity of LeetCode 1039. Minimum Score Triangulation of Polygon?

The Python solution on this page runs in O(n^3).

What is the space complexity of LeetCode 1039. Minimum Score Triangulation of Polygon?

The Python solution on this page uses O(n^2), where n is the number of vertices in the polygon auxiliary space.

What topics does LeetCode 1039. Minimum Score Triangulation of Polygon cover?

LeetCode 1039. Minimum Score Triangulation of Polygon is tagged Array and Dynamic Programming on LeetCode.

Minimum Score Triangulation of Polygon — LeetCode 1039 Python Solution

MediumArrayDynamic Programming

Problem: #1039
Pattern: Dynamic Programming
Reading time: 2 min
Source: leetcode.com

The problem

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 in clockwise order.

Python solution

Python

class Solution:
    def minScoreTriangulation(self, values: List[int]) -> int:
        @cache
        def dfs(i: int, j: int) -> int:
            if i + 1 == j:
                return 0
            return min(
                dfs(i, k) + dfs(k, j) + values[i] * values[k] * values[j]
                for k in range(i + 1, j)
            )

        return dfs(0, len(values) - 1)

Complexity

Measure	Complexity
Time	O(n^3)
Space	O(n^2), where n is the number of vertices in the polygon auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1039. Minimum Score Triangulation of Polygon is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1039. Minimum Score Triangulation of Polygon?: LeetCode 1039. Minimum Score Triangulation of Polygon is rated Medium on LeetCode.
What is the time complexity of LeetCode 1039. Minimum Score Triangulation of Polygon?: The Python solution on this page runs in O(n^3).
What is the space complexity of LeetCode 1039. Minimum Score Triangulation of Polygon?: The Python solution on this page uses O(n^2), where n is the number of vertices in the polygon auxiliary space.
What topics does LeetCode 1039. Minimum Score Triangulation of Polygon cover?: LeetCode 1039. Minimum Score Triangulation of Polygon is tagged Array and Dynamic Programming on LeetCode.