1039-minimum-score-triangulation-of-polygon.js

/**
 * 1039. Minimum Score Triangulation of Polygon
 * https://leetcode.com/problems/minimum-score-triangulation-of-polygon/
 * Difficulty: 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 in clockwise order.
 *
 * Polygon triangulation is a process where you divide a polygon into a set of triangles and
 * the vertices of each triangle must also be vertices of the original polygon. Note that no
 * other shapes other than triangles are allowed in the division. This process will result
 * in n - 2 triangles.
 *
 * You will triangulate the polygon. For each triangle, the weight of that triangle is the
 * product of the values at its vertices. The total score of the triangulation is the sum of
 * these weights over all n - 2 triangles.
 *
 * Return the minimum possible score that you can achieve with some triangulation of the polygon.
 */

/**
 * @param {number[]} values
 * @return {number}
 */
var minScoreTriangulation = function(values) {
  const n = values.length;
  const dp = new Array(n).fill().map(() => new Array(n).fill(0));

  for (let len = 2; len < n; len++) {
    for (let start = 0; start + len < n; start++) {
      const end = start + len;
      dp[start][end] = Infinity;

      for (let mid = start + 1; mid < end; mid++) {
        const score = dp[start][mid] + dp[mid][end] + values[start] * values[mid] * values[end];
        dp[start][end] = Math.min(dp[start][end], score);
      }
    }
  }

  return dp[0][n - 1];
};