class Solution {
    // Similar to Count of partitions with given difference

    /** Recursive code */
    public int findTargetSumWays(int[] arr, int target) {
        int n = arr.length;
        
        int totalSum = 0;
        for(int ele : arr)
            totalSum += ele;
        
        // target cannot be larger than possible sum range
        if(Math.abs(target) > totalSum)
            return 0;
        
        // we can't divide if sum is not even
        if( (totalSum+target) % 2 != 0)
            return 0;
        
        int sum = (totalSum+target)/2;

        return findSubsetSum(arr, sum, n);
    }

    public int findSubsetSum(int[] arr, int sum, int n)
    {
        if(n == 0)
        {
            if(sum == 0)
                return 1;
            return 0;
        }
        
        if(arr[n-1] <= sum)
        {
            int pick = findSubsetSum(arr, sum - arr[n-1], n-1);
            int notPick = findSubsetSum(arr, sum, n-1);
            return pick + notPick;
        }
        return findSubsetSum(arr, sum, n-1);
    }
    
    /** Memoization code */
    public int findTargetSumWays(int[] arr, int target) {
        int n = arr.length;
        
        int totalSum = 0;
        for(int ele : arr)
            totalSum += ele;
        
        // target cannot be larger than possible sum range
        if(Math.abs(target) > totalSum)
            return 0;
        
        // we can't divide if sum is not even
        if( (totalSum+target) % 2 != 0)
            return 0;
        
        int sum = (totalSum+target)/2;

        int[][] t = new int[n+1][sum+1];

        for(int i=0; i<n+1; i++)
            Arrays.fill(t[i], -1);

        return findSubsetSum(arr, sum, n, t);
    }

    public int findSubsetSum(int[] arr, int sum, int n, int[][] t)
    {
        if(n == 0)
        {
            if(sum == 0)
                return 1;
            return 0;
        }

        if(t[n][sum] != -1)
            return t[n][sum];
        
        if(arr[n-1] <= sum)
        {
            int pick = findSubsetSum(arr, sum - arr[n-1], n-1, t);
            int notPick = findSubsetSum(arr, sum, n-1, t);
            t[n][sum] = pick + notPick;
            return t[n][sum];
        }
        t[n][sum] = findSubsetSum(arr, sum, n-1, t);
        return t[n][sum];
    }
    
    /** Top-down approach */
    public int findTargetSumWays(int[] arr, int target) {
        int n = arr.length;
        
        int totalSum = 0;
        for(int ele : arr)
            totalSum += ele;
        
        // target cannot be larger than possible sum range
        if(Math.abs(target) > totalSum)
            return 0;
        
        // we can't divide if sum is not even
        if( (totalSum+target) % 2 != 0)
            return 0;
        
        int sum = (totalSum+target)/2;

        int[][] t = new int[n+1][sum+1];

        for(int i=0; i<n+1; i++)
        {
            for(int j=0; j<sum+1; j++)
            {
                // when array is empty
                if(i == 0)
                    t[i][j] = 0;

                // when sum is always 0
                if(j == 0)
                    t[i][j] = 1;
            }
        }

        for(int i=1; i<n+1; i++)
        {
            for(int j=0; j<sum+1; j++)
            {
                if(arr[i-1] <= j)
                {
                    int pick = t[i-1][j - arr[i-1]];
                    int notPick = t[i-1][j];
                    t[i][j] = pick + notPick;
                }
                else
                    t[i][j] = t[i-1][j];
            }
        }

        return t[n][sum];
    }
}