add: Knapsack

Author: Jer3myYu

java/Dynamic Programming/Knapsack.java

@@ -0,0 +1,26 @@
+public class Knapsack {
+    public int knapsack(int cap, int[] weights, int[] values) {
+        int n = values.length;
+        // Base case: Set the first column and last row to 0 by
+        // initializing the entire DP table to 0.
+        int[][] dp = new int[n + 1][cap + 1];
+
+        // Populate the DP table.
+        for (int i = n - 1; i >= 0; i--) {
+            for (int c = 1; c < cap + 1; c++) {
+                // If the item 'i' fits in the current knapsack capacity,
+                // the maximum value at 'dp[i][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) {
+                    dp[i][c] = Math.max(values[i] + dp[i + 1][c - weights[i]], dp[i + 1][c]);
+                }
+                // If it doesn't fit, we have to exclude it.
+                else {
+                    dp[i][c] = dp[i + 1][c];
+                }
+            }
+        }
+        return dp[0][cap];
+    }
+}