USUBQSUB - Update Sub-Matrix & Query Sub-Matrix
题意翻译
给定一个$N*N$且每个单元初始值都为0的矩阵,你将进行$M$次如下两种之一的操作:
操作一 1 $x_1$ $y_1$ $x_2$ $y_2$ 询问以 $x_1$ $y_1$ 单元为左上角, $x_2$ $y_2$ 单元为右下角的子矩阵内所有单元值的总和。
操作二 2 $x_1$ $y_1$ $x_2$ $y_2$ $k$ 使以 $x_1$ $y_1$ 单元为左上角, $x_2$ $y_2$ 单元为右下角的子矩阵内所有单元的值加上$k$。
对于每个操作一,输出它的结果。
题目描述
Updating and querying 1 dimensional arrays is a popular question. How about updating and quering sub-matrices of a matrix?
A sub-matrix will be depicted as (a, b), (c, d). This implies that it will include all the cells (x, y) such that a<=x<=c and b<=y<=d.
The matrix is indexed from \[1..N\]\[1..N\], where N is the size.
You are given a matrix of size NxN, with each element initially set to 0. There are M queries and each query can be of one of the two types:
1 x1 y1 x2 y2: This query asks you to return the sum of all the elements in the sub-matrix (x1, y1), (x2, y2).
2 x1 y1 x2 y2 K: This query asks you to add K to each element in the sub-matrix (x1, y1), (x2, y2).
输入输出格式
输入格式
The first line of input contains N, M.
The next M lines contain queries in the same forms as stated above.
You may assume that x1<=x2 and y1<=y2 for all queries.
Also N<=1000 and M<=10 $ ^{5} $ . K<=10 $ ^{9} $
输出格式
The answer to all the queries wherein you need to return the sum of elements in the sub-matrix, i.e., all the queries of type 1.