add: MatrixPathways

Author: Jer3myYu

java/Dynamic Programming/MatrixPathways.java

@@ -0,0 +1,21 @@
+import java.util.Arrays;
+
+public class MatrixPathways {
+    public int matrixPathways(int m, int n) {
+        // Base cases: Set all cells in row 0 and column 0 to 1. We can
+        // do this by initializing all cells in the DP table to 1.
+        int[][] dp = new int[m][n];
+        for (int i = 0; i < m; i++) {
+            Arrays.fill(dp[i], 1);
+        }
+        // Fill in the rest of the DP table.
+        for (int r = 1; r < m; r++) {
+            for (int c = 1; c < n; c++) {
+                // Paths to current cell = paths from above + paths from 
+                // left.
+                dp[r][c] = dp[r - 1][c] + dp[r][c - 1];
+            }
+        }
+        return dp[m - 1][n - 1];
+    }
+}