LeetCode 1039: Minimum Score Triangulation of Polygon Solution
Master LeetCode problem 1039 (Minimum Score Triangulation of Polygon), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.
1039. Minimum Score Triangulation of Polygon
Problem Explanation
Explanation:
To solve this problem, we can use dynamic programming. We will create a 2D dp array where dp[i][j] represents the minimum score of triangulating the polygon from vertex i to vertex j (inclusive). We will iterate over different lengths of diagonals to fill up the dp array, starting from smaller lengths and gradually building up the solution for larger lengths.
- Initialize the dp array with 0s.
- Iterate over different lengths of diagonals l starting from 2 to n. For each length, iterate over the range of possible starting vertices i and calculate the minimum score of triangulating the polygon from i to i+l.
- For each starting vertex i and diagonal length l, iterate over possible split points k to calculate the score of triangulating the polygon from i to i+l using split point k. Update dp[i][i+l] with the minimum score.
- The final answer will be stored in dp[0][n-1].
Time Complexity: O(n^3), where n is the number of vertices. Space Complexity: O(n^2)
:
Solution Code
class Solution {
public int minScoreTriangulation(int[] values) {
int n = values.length;
int[][] dp = new int[n][n];
for (int l = 2; l < n; l++) {
for (int i = 0; i < n - l; i++) {
int j = i + l;
dp[i][j] = Integer.MAX_VALUE;
for (int k = i + 1; k < j; k++) {
dp[i][j] = Math.min(dp[i][j], dp[i][k] + dp[k][j] + values[i] * values[j] * values[k]);
}
}
}
return dp[0][n - 1];
}
}Try It Yourself
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