From e6fb81d1bbc4d30631368caae80df61741fcd3d3 Mon Sep 17 00:00:00 2001
From: Rajat Jain <rajatjain.jain29@gmail.com>
Date: Fri, 17 Sep 2021 22:32:57 +0530
Subject: [PATCH] Add knapsack problem (#2330)

---
 DynamicProgramming/BruteForceKnapsack.java    | 43 ++++++++++++++
 .../DyanamicProgrammingKnapsack.java          | 39 ++++++++++++
 .../MemoizationTechniqueKnapsack.java         | 59 +++++++++++++++++++
 3 files changed, 141 insertions(+)
 create mode 100644 DynamicProgramming/BruteForceKnapsack.java
 create mode 100644 DynamicProgramming/DyanamicProgrammingKnapsack.java
 create mode 100644 DynamicProgramming/MemoizationTechniqueKnapsack.java

diff --git a/DynamicProgramming/BruteForceKnapsack.java b/DynamicProgramming/BruteForceKnapsack.java
new file mode 100644
index 00000000..4ac2d5e2
--- /dev/null
+++ b/DynamicProgramming/BruteForceKnapsack.java
@@ -0,0 +1,43 @@
+package DynamicProgramming;
+
+/* A Naive recursive implementation
+of 0-1 Knapsack problem */
+public class BruteForceKnapsack {
+
+	// A utility function that returns
+	// maximum of two integers
+	static int max(int a, int b) {
+		return (a > b) ? a : b;
+	}
+
+	// Returns the maximum value that
+	// can be put in a knapsack of
+	// capacity W
+	static int knapSack(int W, int wt[], int val[], int n) {
+		// Base Case
+		if (n == 0 || W == 0)
+			return 0;
+
+		// If weight of the nth item is
+		// more than Knapsack capacity W,
+		// then this item cannot be included
+		// in the optimal solution
+		if (wt[n - 1] > W)
+			return knapSack(W, wt, val, n - 1);
+
+		// Return the maximum of two cases:
+		// (1) nth item included
+		// (2) not included
+		else
+			return max(val[n - 1] + knapSack(W - wt[n - 1], wt, val, n - 1), knapSack(W, wt, val, n - 1));
+	}
+
+	// Driver code
+	public static void main(String args[]) {
+		int val[] = new int[] { 60, 100, 120 };
+		int wt[] = new int[] { 10, 20, 30 };
+		int W = 50;
+		int n = val.length;
+		System.out.println(knapSack(W, wt, val, n));
+	}
+}
diff --git a/DynamicProgramming/DyanamicProgrammingKnapsack.java b/DynamicProgramming/DyanamicProgrammingKnapsack.java
new file mode 100644
index 00000000..96a4f132
--- /dev/null
+++ b/DynamicProgramming/DyanamicProgrammingKnapsack.java
@@ -0,0 +1,39 @@
+package DynamicProgramming;
+
+// A Dynamic Programming based solution
+// for 0-1 Knapsack problem
+public class DyanamicProgrammingKnapsack {
+	static int max(int a, int b) {
+		return (a > b) ? a : b;
+	}
+
+	// Returns the maximum value that can
+	// be put in a knapsack of capacity W
+	static int knapSack(int W, int wt[], int val[], int n) {
+		int i, w;
+		int K[][] = new int[n + 1][W + 1];
+
+		// Build table K[][] in bottom up manner
+		for (i = 0; i <= n; i++) {
+			for (w = 0; w <= W; w++) {
+				if (i == 0 || w == 0)
+					K[i][w] = 0;
+				else if (wt[i - 1] <= w)
+					K[i][w] = max(val[i - 1] + K[i - 1][w - wt[i - 1]], K[i - 1][w]);
+				else
+					K[i][w] = K[i - 1][w];
+			}
+		}
+
+		return K[n][W];
+	}
+
+	// Driver code
+	public static void main(String args[]) {
+		int val[] = new int[] { 60, 100, 120 };
+		int wt[] = new int[] { 10, 20, 30 };
+		int W = 50;
+		int n = val.length;
+		System.out.println(knapSack(W, wt, val, n));
+	}
+}
diff --git a/DynamicProgramming/MemoizationTechniqueKnapsack.java b/DynamicProgramming/MemoizationTechniqueKnapsack.java
new file mode 100644
index 00000000..823dfba2
--- /dev/null
+++ b/DynamicProgramming/MemoizationTechniqueKnapsack.java
@@ -0,0 +1,59 @@
+package DynamicProgramming;
+// Here is the top-down approach of 
+// dynamic programming
+public class MemoizationTechniqueKnapsack {
+
+//A utility function that returns 
+//maximum of two integers    
+	static int max(int a, int b) {
+		return (a > b) ? a : b;
+	}
+
+//Returns the value of maximum profit  
+	static int knapSackRec(int W, int wt[], int val[], int n, int[][] dp) {
+
+		// Base condition
+		if (n == 0 || W == 0)
+			return 0;
+
+		if (dp[n][W] != -1)
+			return dp[n][W];
+
+		if (wt[n - 1] > W)
+
+			// Store the value of function call
+			// stack in table before return
+			return dp[n][W] = knapSackRec(W, wt, val, n - 1, dp);
+
+		else
+
+			// Return value of table after storing
+			return dp[n][W] = max((val[n - 1] + knapSackRec(W - wt[n - 1], wt, val, n - 1, dp)),
+					knapSackRec(W, wt, val, n - 1, dp));
+	}
+
+	static int knapSack(int W, int wt[], int val[], int N) {
+
+		// Declare the table dynamically
+		int dp[][] = new int[N + 1][W + 1];
+
+		// Loop to initially filled the
+		// table with -1
+		for (int i = 0; i < N + 1; i++)
+			for (int j = 0; j < W + 1; j++)
+				dp[i][j] = -1;
+
+		return knapSackRec(W, wt, val, N, dp);
+	}
+
+//Driver Code
+	public static void main(String[] args) {
+		int val[] = { 60, 100, 120 };
+		int wt[] = { 10, 20, 30 };
+
+		int W = 50;
+		int N = val.length;
+
+		System.out.println(knapSack(W, wt, val, N));
+	}
+}