add: MatrixPathwaysOptimized

Author: Jer3myYu

java/Dynamic Programming/MatrixPathwaysOptimized.java

@@ -0,0 +1,28 @@
+import java.util.Arrays;
+
+public class MatrixPathwaysOptimized {
+    public int matrixPathwaysOptimized(int m, int n) {
+        // Initialize 'prevRow' as the DP values of row 0, which are all 1s.
+        int[] prevRow = new int[n];
+        Arrays.fill(prevRow, 1);
+        // Iterate through the matrix starting from row 1.
+        for (int r = 1; r < m; r++) {
+            // Set the first cell of 'curr_row' to 1. This is done by
+            // setting the entire row to 1.
+            int[] currRow = new int[n];
+            Arrays.fill(currRow, 1);
+            for (int c = 1; c < n; c++) {
+                // The number of unique paths to the current cell is the sum
+                // of the paths from the cell above it ('prevRow[c]') and
+                // the cell to the left ('currRow[c - 1]').
+                currRow[c] = prevRow[c] + currRow[c - 1];
+            }
+            // Update 'prevRow' with 'currRow' values for the next
+            // iteration.
+            prevRow = currRow;
+        }
+        // The last element in 'prevRow' stores the result for the
+        // bottom-right cell.
+        return prevRow[n - 1];
+    }
+}