class Solution {
    /** Recursion */
    public int knapSack(int val[], int wt[], int capacity) {
        int n = wt.length;
        
        return findMaxProfit(capacity, wt, val, n);
    }
    
    public int findMaxProfit(int W, int[] wt, int[] val, int n)
    {
        // Base case: no items or no remaining capacity
        if(n == 0 || W == 0)
            return 0;
        
        if(wt[n-1] <= W)
        {
            // pick the item (n stays the same because we can pick it again)
            int pick = val[n-1] + findMaxProfit(W - wt[n-1], wt, val, n);
            
            // do not pick the item (move to next item)
            int notPick = findMaxProfit(W, wt, val, n-1);
            return Math.max(pick, notPick);
        }
        // current weight exceed max weight, cannot pick the item
        return findMaxProfit(W, wt, val, n-1);
    }
    
    /** Memoization */
    public int knapSack(int val[], int wt[], int capacity) {
        int n = wt.length;
        
        int[][] t = new int[n+1][capacity+1];
        for(int i=0; i<n+1; i++)
            Arrays.fill(t[i], -1);
        
        return findMaxProfit(capacity, wt, val, n, t);
    }
    
    public int findMaxProfit(int W, int[] wt, int[] val, int n, int[][] t)
    {
        // Base case: no items or no remaining capacity
        if(n == 0 || W == 0)
            return 0;
        
        if(t[n][W] != -1)
            return t[n][W];
            
        if(wt[n-1] <= W)
        {
            // pick the item (n stays the same because we can pick it again)
            int pick = val[n-1] + findMaxProfit(W - wt[n-1], wt, val, n, t);
            
            // do not pick the item (move to next item)
            int notPick = findMaxProfit(W, wt, val, n-1, t);
            t[n][W] = Math.max(pick, notPick);
            return t[n][W];
        }
        // current weight exceed max weight, cannot pick the item
        t[n][W] = findMaxProfit(W, wt, val, n-1, t);
        return t[n][W];
    }
    
    /** Top-down approach */
    public int knapSack(int val[], int wt[], int capacity) {
        int n = wt.length;
        
        int[][] t = new int[n+1][capacity+1];
        
        // base condition: no items or no remaining capacity
        for(int i=0; i<n+1; i++)
        {
            for(int j=0; j<capacity+1; j++)
            {
                if(i == 0 || j == 0)
                    t[i][j] = 0;
            }
        }
        
        for(int i=1; i<n+1; i++)
        {
            for(int j=1; j<capacity+1; j++)
            {
                if(wt[i-1] <= j)
                {
                    // pick the item (n stays the same because we can pick it again)
                    int pick = val[i-1] + t[i][j - wt[i-1]];
                    // do not pick the item (move to next item)
                    int notPick = t[i-1][j];
                    t[i][j] = Math.max(pick, notPick);
                }
                // current weight exceed max weight, cannot pick the item
                else
                    t[i][j] = t[i-1][j];
            }
        }
        return t[n][capacity];
    }
}