- Practice
- Data Structures
- Advanced
- Cube Summation

# Cube Summation

# Cube Summation

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Define a 3-D Matrix in which each block contains 0 initially. The first block is defined by the coordinates (1,1,1) and the last block is defined by the coordinates (n,n,n). There are two types of queries.

```
UPDATE x y z W
```

Update the value of block (x,y,z) to W.

```
QUERY x1 y1 z1 x2 y2 z2
```

Calculate the sum of the values of blocks whose x coordinate is between x1 and x2 (inclusive), y coordinate between y1 and y2 (inclusive) and z coordinate between z1 and z2 (inclusive).

**Function Description**

Complete the *cubeSum* function in the editor below.

*cubeSum* has the following parameters:
- *int n: the dimensions of the 3-d matrix
- *string operations[m]:* the operations to perform

**Returns**

- *int[]:* the results of each `QUERY`

operation

**Input Format**

The first line contains an integer , the number of test-cases. testcases follow.

For each test case, the first line contains two space-separated integers, and .
defines the matrix.

defines the number of operations.

The next lines will contain an operation either of these forms:

```
1. UPDATE x y z W
2. QUERY x1 y1 z1 x2 y2 z2
```

**Constraints**

-10^{9} \le W \le 10^{9}

**Sample Input**

```
2
4 5
UPDATE 2 2 2 4
QUERY 1 1 1 3 3 3
UPDATE 1 1 1 23
QUERY 2 2 2 4 4 4
QUERY 1 1 1 3 3 3
2 4
UPDATE 2 2 2 1
QUERY 1 1 1 1 1 1
QUERY 1 1 1 2 2 2
QUERY 2 2 2 2 2 2
```

**Sample Output**

```
4
4
27
0
1
1
```

**Explanation**

In the first test case, there is a cube of 4 * 4 * 4 and there are 5 queries. Initially all the cells (1,1,1) to (4,4,4) are 0.

`UPDATE 2 2 2 4`

makes the cell (2,2,2) = 4

`QUERY 1 1 1 3 3 3`

. As (2,2,2) is updated to 4 and the rest are all 0. The answer to this query is 4.

`UPDATE 1 1 1 23`

. updates the cell (1,1,1) to 23.
`QUERY 2 2 2 4 4 4`

. Only the cell (1,1,1) and (2,2,2) are non-zero and (1,1,1) is not between (2,2,2) and (4,4,4). So, the answer is 4.

`QUERY 1 1 1 3 3 3`

. 2 cells are non-zero and their sum is 23+4 = 27.