IOI '01 P1 - Mobile Phones

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Points: 15 (partial)
Time limit: 0.6s
Memory limit: 8M

Problem type
IOI '01 - Tampere, Finland

Suppose that the fourth generation mobile phone base stations in the Tampere area operate as follows. The area is divided into squares. The squares form an S \times S matrix with the rows and columns numbered from 0 to S-1. Each square contains a base station. The number of active mobile phones inside a square can change because a phone is moved from a square to another or a phone is switched on or off. At times, each base station reports the change in the number of active phones to the main base station along with the row and the column of the matrix.

Write a program, which receives these reports and answers queries about the current total number of active mobile phones in any rectangle-shaped area.

Input Specification

The input is read from standard input as integers and the answers to the queries are written to standard output as integers. The input is encoded as follows. Each input comes on a separate line, and consists of one instruction integer and a number of parameter integers according to the following table.

Instruction Parameters Meaning
0 S Initialize the matrix size to S \times S containing all zeros. This instruction is given only once and it will be the first instruction.
1 X\ Y\ A Add A to the number of active phones in table square (X, Y). A may be positive or negative.
2 L\ B\ R\ T Query the current sum of numbers of active mobile phones in squares (X, Y), where L \le X \le R, B \le Y \le T.
3 Terminate program. This instruction is given only once and it will be the last instruction.

The values will always be in range, so there is no need to check them. In particular, if A is negative, it can be assumed that it will not reduce the square value below zero. The indexing starts at 0, e.g. for a table of size 4 \times 4, we have 0 \le X \le 3 and 0 \le Y \le 3.

Output Specification

Your program should not answer anything to lines with an instruction other than 2. If the instruction is 2, then your program is expected to answer the query by writing the answer as a single line containing a single integer to standard output.

Sample Input

0 4
1 1 2 3
2 0 0 2 2
1 1 1 2
1 1 2 -1
2 1 1 2 3

Sample Output


Explanation for Sample Output

Input Output Explanation
0 4 Initialize table size to 4 \times 4.
1 1 2 3 Update table at (1,2) with +3.
2 0 0 2 2 3 Query sum of rectangle 0 \le X \le 2, 0 \le Y \le 2.
1 1 1 2 Update table at (1, 1) with +2.
1 1 2 -1 Update table at (1, 2) with -1.
2 1 1 2 3 4 Query sum of rectangle 1 \le X \le 2, 1 \le Y \le 3.
3 Terminate program.


Table size S \times S 1 \times 1 \le S \times S \le 1024 \times 1024
Cell value V at any time V 0 \le V \le 2^{15}-1 (= 32\,767)
Update amount A -2^{15} \le A \le 2^{15}-1 (= 32\,767)
No. of instructions in input U 3 \le U \le 60\,002
Maximum number of
phones in the whole table
M M = 2^{30}

Out of the 20 inputs, 16 are such that the table size is at most 512 \times 512.


  • 11
    aeternalis1  commented on Aug. 22, 2017, 4:15 p.m.

    Why am I TLE'ing? I'm implementing a 2-d BIT but I can't AC any of the test cases. My code works for the sample, and even if the code were to be too slow, it should at least pass a few cases. So what's wrong with my code?

    • 24
      wleung_bvg  commented on Aug. 22, 2017, 5:12 p.m. edited

      Binary indexed trees are generally indexed starting from 1. If you start from 0, your range query indices may become negative, and you may end up with an infinite loop.