Add Matrix Pathways

Author: marttp

kotlin/Dynamic Programming/MatrixPathways.kt

@@ -0,0 +1,14 @@
+fun matrixPathways(m: Int, n: Int): Int {
+    // 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.
+    val dp = Array(m) { IntArray(n) { 1 } }
+    // Fill in the rest of the DP table.
+    for (r in 1 until m) {
+        for (c in 1 until n) {
+            // 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]
+}

kotlin/Dynamic Programming/MatrixPathwaysOptimized.kt

@@ -0,0 +1,22 @@
+fun matrixPathwaysOptimized(m: Int, n: Int): Int {
+    // Initialize 'prevRow' as the DP values of row 0, which are all 1s.
+    var prevRow = IntArray(n) { 1 }
+    // Iterate through the matrix starting from row 1.
+    for (r in 1 until m) {
+        // Set the first cell of 'currRow' to 1. This is done by
+        // setting the entire row to 1.
+        val currRow = IntArray(n) { 1 }
+        for (c in 1 until n) {
+            // 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]
+}