Leetcode #1039: Minimum Score Triangulation of Polygon
In this guide, we solve Leetcode #1039 Minimum Score Triangulation of Polygon in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Python Solution
class Solution:
def minScoreTriangulation(self, values: List[int]) -> int:
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
The time complexity is , and the space complexity is , where is the number of vertices in the polygon. The space complexity is , where is the number of vertices in the polygon.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.