Add minimum cost path problem

Author: tanmaydarmorha

DP/MinimumPathSum/minimumCostPath.java

@@ -0,0 +1,43 @@
+import java.util.Scanner;
+
+public class MinCostPath {
+	
+public static int minCostPathDP(int arr[][],int row, int column) {
+		int m = row;
+		int n = column;
+		int storage[][] = new int[m][n];
+		storage[m - 1][n - 1] = arr[m - 1][n - 1];
+		// Last Row
+		for (int j = n - 2; j >= 0; j--) {
+			storage[m - 1][j] = storage[m - 1][j + 1] + arr[m - 1][j];
+		}
+		// Last Column
+		for (int i = m - 2; i >= 0; i--) {
+			storage[i][n - 1] = storage[i + 1][n - 1] + arr[i][n - 1];
+		}
+		for (int i = m - 2; i >= 0; i--) {
+			for (int j = n - 2; j >= 0; j--) {
+				storage[i][j] = arr[i][j]
+						+ Math.min(storage[i][j + 1], Math.min(
+								storage[i + 1][j + 1], storage[i + 1][j]));
+			}
+		}
+		return storage[0][0]+arr[row][column];
+	}
+	public static void main(String args[]) {
+		Scanner s = new Scanner(System.in);
+		int rows = s.nextInt();
+		int columns = s.nextInt();
+		int arr[][] = new int[rows][columns];
+		for (int i = 0; i < rows; i++) {
+			for (int j = 0; j < columns; j++) {
+				arr[i][j] = s.nextInt();
+			}
+		}
+		int row = s.nextInt();
+		int column = s.nextInt();
+		System.out.println(minCostPathDP(arr,row,column));
+		s.close();
+	}
+}
+