Create 02 - Bottom-Up | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/16 - Minimum Score Triangulation of Polygon/02 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the minimum score triangulation of the polygon using bottom-up DP
+    int solve(vector<int>& v) {
+        int n = v.size(); // Number of vertices in the polygon
+
+        // DP table where dp[i][j] represents the minimum score for triangulating the segment [i, j]
+        vector<vector<int>> dp(n, vector<int>(n, 0));
+
+        // Iterate over all possible starting indices in reverse (bottom-up DP)
+        for (int i = n - 1; i >= 0; i--) {
+            // Iterate over all possible ending indices for segments larger than 2 vertices
+            for (int j = i + 2; j < n; j++) {
+                int ans = INT_MAX; // Initialize the minimum score for the segment [i, j]
+
+                // Try every possible middle vertex k between i and j
+                for (int k = i + 1; k < j; k++) {
+                    // Calculate the score of forming a triangle (i, k, j) and add subproblem scores
+                    ans = min(ans, v[i] * v[j] * v[k] + dp[i][k] + dp[k][j]);
+                }
+
+                // Store the minimum score for the segment [i, j]
+                dp[i][j] = ans;
+            }
+        }
+
+        // The final result is stored in dp[0][n-1], which represents the entire polygon
+        return dp[0][n - 1];
+    }
+
+    // Main function to calculate the minimum score triangulation
+    int minScoreTriangulation(vector<int>& values) {
+        int n = values.size(); // Number of vertices in the polygon
+
+        // Call the DP function
+        return solve(values);
+    }
+};