add: KnapsackOptimized

Author: Jer3myYu

java/Dynamic Programming/KnapsackOptimized.java

@@ -0,0 +1,30 @@
+public class KnapsackOptimized {
+    public int knapsackOptimized(int cap, int[] weights, int[] values) {
+        int n = values.length;
+        // Initialize 'prevRow' as the DP values of the row below the
+        // current row.
+        int[] prevRow = new int[cap + 1];
+        for (int i = n - 1; i >= 0; i--) {
+            // Set the first cell of the 'currRow' to 0 to set the base
+            // case for this row. This is done by initializing the entire
+            // row to 0.
+            int[] currRow = new int[cap + 1];
+            for (int c = 1; c < cap + 1; c++) {
+                // If item 'i' fits in the current knapsack capacity, the
+                // maximum value at 'currRow[c]' is the largest of either:
+                // 1. The maximum value if we include item 'i'.
+                // 2. The maximum value if we exclude item 'i'.
+                if (weights[i] <= c) {
+                    currRow[c] = Math.max(values[i] + prevRow[c - weights[i]], prevRow[c]);
+                }
+                // If item 'i' doesn't fit, we exclude it.
+                else {
+                    currRow[c] = prevRow[c];
+                }
+            }
+            // Set 'prevRow' to 'currRow' values for the next iteration.
+            prevRow = currRow;
+        }
+        return prevRow[cap];
+    }
+}