#### Knapsack Memoization

A
```package com.thealgorithms.dynamicprogramming;

/**
* Recursive Solution for 0-1 knapsack with memoization
* This method is basically an extension to the recursive approach so that we
* can overcome the problem of calculating redundant cases and thus increased
* complexity. We can solve this problem by simply creating a 2-D array that can
* store a particular state (n, w) if we get it the first time.
*/
public class KnapsackMemoization {

int knapSack(int capacity, int[] weights, int[] profits, int numOfItems) {

// Declare the table dynamically
int[][] dpTable = new int[numOfItems + 1][capacity + 1];

// Loop to initially fill the table with -1
for (int i = 0; i < numOfItems + 1; i++) {
for (int j = 0; j < capacity + 1; j++) {
dpTable[i][j] = -1;
}
}

return solveKnapsackRecursive(capacity, weights, profits, numOfItems, dpTable);
}

// Returns the value of maximum profit using recursive approach
int solveKnapsackRecursive(int capacity, int[] weights, int[] profits, int numOfItems, int[][] dpTable) {
// Base condition
if (numOfItems == 0 || capacity == 0) {
return 0;
}

if (dpTable[numOfItems][capacity] != -1) {
return dpTable[numOfItems][capacity];
}

if (weights[numOfItems - 1] > capacity) {
// Store the value of function call stack in table
dpTable[numOfItems][capacity] = solveKnapsackRecursive(capacity, weights, profits, numOfItems - 1, dpTable);
return dpTable[numOfItems][capacity];
} else {
// case 1. include the item, if it is less than the capacity
final int includeCurrentItem = profits[numOfItems - 1] + solveKnapsackRecursive(capacity - weights[numOfItems - 1], weights, profits, numOfItems - 1, dpTable);

// case 2. exclude the item if it is more than the capacity
final int excludeCurrentItem = solveKnapsackRecursive(capacity, weights, profits, numOfItems - 1, dpTable);

// Store the value of function call stack in table and return
dpTable[numOfItems][capacity] = Math.max(includeCurrentItem, excludeCurrentItem);
return dpTable[numOfItems][capacity];
}
}
}
```