Another Contest 3 Problem 4 - Range Updates and Range Queries

Points: 15

Time limit: 0.25s

Memory limit: 256M

Problem types

You have an array of $N$ ~N~ integers, initialized all to zero to begin with. Support two operations.

INCREMENT l r a - For each index $i$ ~i~ between $l$ ~l~ and $r$ ~r~, increase the $i$ ~i~th element of the array by $a \cdot (i-l+1)$ ~a \cdot (i-l+1)~.

SUM l r - Compute the sum of the integers between indices $l$ ~l~ and $r$ ~r~, inclusive.

Constraints

$1 \le N \le 10^6$ ~1 \le N \le 10^6~

$1 \le Q \le 10^5$ ~1 \le Q \le 10^5~

$1 \le l_i \le r_i \le N$ ~1 \le l_i \le r_i \le N~

$1 \le a_i \le 5$ ~1 \le a_i \le 5~

Input Specification

The first line contains two positive integers, $N$ ~N~ and $Q$ ~Q~.

The next $Q$ ~Q~ lines each contain a sequence of positive integers. If the first integer in the line is $1$ ~1~, then three integers follow, $l_i$ ~l_i~, $r_i$ ~r_i~, and $a_i$ ~a_i~, indicating an INCREMENT operation.

Otherwise, the first integer in the line is $2$ ~2~, and then two integers follow, $l_i$ ~l_i~ and $r_i$ ~r_i~, indicating a SUM operation.

Output Specification

For each SUM operation, output on its own line the result of the query.

Sample Input

Sample Output

0
2
4

Comments

0

myl commented on March 22, 2021, 2:47 p.m.

I am assuming the array starts at index 0?

1

BalintR commented on March 22, 2021, 2:57 p.m.

$1 \le l_i \le r_i \le N$ ~ 1 \le l_i \le r_i \le N ~ so no, the array starts at index 1.

-1

AlanCCCL2S18 commented on Feb. 6, 2020, 11:51 p.m.

Can anyone tell me why I'm TLEing on testcase 5? I know there's some sort of optimization but I don't know the specifics.

8

richardzhang commented on Feb. 8, 2020, 1:08 a.m.

Your time complexity is currently $O(NQ\log N)$ ~O(NQ\log N)~, which is insufficient given the constraints (this is on the order of $10^{12}$ ~10^{12}~ operations, give or take). If you are stumped, you can try reading the tutorial :)).