DP - 1:Number of Balanced BTs Using DP

public class Solution {
    public static int balancedTreesOfHeightH(int height){
        if(height==0 || height==1)
            return 1;
        if(height==2)
            return 3;
        int storage[]=new int[height+1];
        storage[0]=1;
        storage[1]=1;
        storage[2]=3;
        int mod=(int)Math.pow(10,9)+7;
        for(int i=3;i<storage.length;i++)
        {  
    int x = storage[i-1];
            int y = storage[i-2];
            long a=(long)x*x;
            long b=(long)x*y*2;
            int value1=(int)(a%mod);
            int value2=(int)(b%mod);
            storage[i]=(value1+value2)%mod;
        }
        return storage[height];
    }
}


// 

/////memoization/////////////
// public class Solution 
// {
//     public static int balancedTreesOfHeightH(int height)
//     {
//         int storage[]=new int[height+1];
//         for(int i=0;i<storage.length;i++)
//         {
//             storage[i]=-1;
//         }
//         int mod=(int)Math.pow(10,9)+7;
//         return balancedOfTreesHeightH(storage,height,mod);
//     }
//     private static int balancedOfTreesHeightH(int storage[],int height,int mod){
//         if(height==0 || height==1){
//             storage[height]=1;
//             return 1;}
//         if(storage[height]!=-1)
//             return storage[height];

//         int x=balancedOfTreesHeightH(storage,height-1,mod);
//         int y=  balancedOfTreesHeightH(storage,height-2,mod);
//         long value1=(long)x*x;
//         long value2=(long)y*x*2;
//         int res1=(int)(value1%mod);
//         int res2=(int)(value2%mod);
//         storage[height]=(res1+res2)%mod;
//         return storage[height];

//     }


// }