diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/Knapsack.java b/src/main/java/com/thealgorithms/dynamicprogramming/Knapsack.java
index 134561766830..0d4c8d501f9f 100644
--- a/src/main/java/com/thealgorithms/dynamicprogramming/Knapsack.java
+++ b/src/main/java/com/thealgorithms/dynamicprogramming/Knapsack.java
@@ -3,53 +3,76 @@
import java.util.Arrays;
/**
- * A Dynamic Programming based solution for the 0-1 Knapsack problem.
- * This class provides a method, `knapSack`, that calculates the maximum value that can be
- * obtained from a given set of items with weights and values, while not exceeding a
- * given weight capacity.
+ * 0/1 Knapsack Problem - Dynamic Programming solution.
*
- * @see 0-1 Knapsack Problem
+ * This algorithm solves the classic optimization problem where we have n items,
+ * each with a weight and a value. The goal is to maximize the total value
+ * without exceeding the knapsack's weight capacity.
+ *
+ * Time Complexity: O(n * W)
+ * Space Complexity: O(W)
+ *
+ * Example:
+ * values = {60, 100, 120}
+ * weights = {10, 20, 30}
+ * W = 50
+ * Output: 220
+ *
+ * @author Arpita
+ * @see Knapsack Problem
*/
public final class Knapsack {
private Knapsack() {
}
+ /**
+ * Validates the input to ensure correct constraints.
+ */
private static void throwIfInvalidInput(final int weightCapacity, final int[] weights, final int[] values) {
if (weightCapacity < 0) {
throw new IllegalArgumentException("Weight capacity should not be negative.");
}
if (weights == null || values == null || weights.length != values.length) {
- throw new IllegalArgumentException("Input arrays must not be null and must have the same length.");
+ throw new IllegalArgumentException("Weights and values must be non-null and of the same length.");
}
if (Arrays.stream(weights).anyMatch(w -> w <= 0)) {
- throw new IllegalArgumentException("Input array should not contain non-positive weight(s).");
+ throw new IllegalArgumentException("Weights must be positive.");
}
}
/**
- * Solves the 0-1 Knapsack problem using Dynamic Programming.
+ * Solves the 0/1 Knapsack problem using Dynamic Programming (bottom-up approach).
*
* @param weightCapacity The maximum weight capacity of the knapsack.
- * @param weights An array of item weights.
- * @param values An array of item values.
- * @return The maximum value that can be obtained without exceeding the weight capacity.
- * @throws IllegalArgumentException If the input arrays are null or have different lengths.
+ * @param weights The array of item weights.
+ * @param values The array of item values.
+ * @return The maximum total value achievable without exceeding capacity.
*/
- public static int knapSack(final int weightCapacity, final int[] weights, final int[] values) throws IllegalArgumentException {
+ public static int knapSack(final int weightCapacity, final int[] weights, final int[] values) {
throwIfInvalidInput(weightCapacity, weights, values);
- // DP table to store the state of the maximum possible return for a given weight capacity.
int[] dp = new int[weightCapacity + 1];
+ // Fill dp[] array iteratively
for (int i = 0; i < values.length; i++) {
- for (int w = weightCapacity; w > 0; w--) {
- if (weights[i] <= w) {
- dp[w] = Math.max(dp[w], dp[w - weights[i]] + values[i]);
- }
+ for (int w = weightCapacity; w >= weights[i]; w--) {
+ dp[w] = Math.max(dp[w], dp[w - weights[i]] + values[i]);
}
}
return dp[weightCapacity];
}
+
+ /*
+ // Example main method for local testing only.
+ public static void main(String[] args) {
+ int[] values = {60, 100, 120};
+ int[] weights = {10, 20, 30};
+ int weightCapacity = 50;
+
+ int maxValue = knapSack(weightCapacity, weights, values);
+ System.out.println("Maximum value = " + maxValue); // Output: 220
+ }
+ */
}