Create MinCostPath.java

MinCostPath.java

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+/**
+ * DP based solution to find minimum cost to reach last cell of a weighted cost 
+ * matrix from its first cell
+ * 
+ * @author vavasing
+ */
+public class MinCostPath {
+    public static int minCost(int[][] costMatrix, int m, int n) {
+        // base case, matrix size 0.
+        if (n == 0 || m == 0) {
+            return Integer.MAX_VALUE;
+        }
+
+        // For 1x1 matrix return weight as is.
+        if (m == 1 && n == 1) {
+            return costMatrix[0][0];
+        }
+
+        // Add cost of current cell to recursive solution of minimum of
+        // path from adjacent left cell, adjacent top cell to cirrent cell.
+        return Integer.min(minCost(costMatrix, m - 1, n), minCost(costMatrix, m, n - 1))
+                + costMatrix[m - 1][n - 1];
+    }
+
+    // Tester method
+    public static void main(String[] args)
+    {
+        int[][] costMatrix =
+        {
+            { 3, 6, 8, 6, 5 },
+            { 6, 7, 3, 5, 2 },
+            { 3, 2, 1, 2, 4 },
+            { 7, 1, 7, 6, 7 },
+            { 2, 9, 2, 9, 3 }
+        };
+
+        System.out.print("The minimum cost : " + 
+                minCost(costMatrix, costMatrix.length, costMatrix[0].length));
+    } 
+}