Create 04 - Gap-Strategy | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/16 - Minimum Score Triangulation of Polygon/04 - Gap-Strategy | DP | Approach.cpp

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+class Solution {
+public:
+    // Gap Strategy Implementation for Minimum Score Triangulation
+    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));
+
+        // Outer loop controls the gap between i and j
+        // Gap of 2 means the segment [i, j] has at least 3 vertices, enough to form a triangle
+        for (int gap = 2; gap < n; gap++) {
+            // Inner loop iterates over all valid starting indices i for a given gap
+            for (int i = 0; i + gap < n; i++) {
+                int j = i + gap; // Calculate the ending index j based on the gap
+
+                dp[i][j] = INT_MAX; // Initialize dp[i][j] to the maximum value
+
+                // Iterate over all possible middle vertices (k) between i and j
+                for (int k = i + 1; k < j; k++) {
+                    // Calculate the score of forming a triangle (i, k, j)
+                    // Add the scores of solving the two subproblems [i, k] and [k, j]
+                    dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + v[i] * v[k] * v[j]);
+                }
+            }
+        }
+
+        // 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
+        return solve(values); // Call the gap strategy function
+    }
+};