题目描述

输入一个n行m列的整数矩阵，再输入q个操作，每个操作包含五个整数x1, y1, x2, y2, c，其中(x1, y1)和(x2, y2)表示一个子矩阵的左上角坐标和右下角坐标。

每个操作都要将选中的子矩阵中的每个元素的值加上c。

请你将进行完所有操作后的矩阵输出。

输入格式

第一行包含整数n,m,q。

接下来n行，每行包含m个整数，表示整数矩阵。

接下来q行，每行包含5个整数x1, y1, x2, y2, c，表示一个操作。

输出格式

共 n 行，每行 m 个整数，表示所有操作进行完毕后的最终矩阵。

数据范围

1≤n,m≤1000,
1≤q≤100000,
1≤x1≤x2≤n,
1≤y1≤y2≤m,
−1000≤c≤1000,
−1000≤矩阵内元素的值≤1000

输入样例：

3 4 3
1 2 2 1
3 2 2 1
1 1 1 1
1 1 2 2 1
1 3 2 3 2
3 1 3 4 1

输出样例：

2 3 4 1
4 3 4 1
2 2 2 2

代码

from typing import List

def finite_difference(sums: List[List[int]]) -> List[List[int]]:
    """
    Args:
        sums (List[List[int]]): the origin second dimention list.

    Returns:
        (List[List[int]]): the finite difference of the origin sums.
    """
    differences = [[0 for j in i] for i in sums]
    for i in range(len(sums)):
        for j in range(len(sums[i])):
            add_range(differences, i, j, i, j, sums[i][j])
    return differences

def add_range(differences: List[List[int]], x1: int, y1: int, x2: int, y2: int, value: int):
    """
    Args:
        differences (List[List[int]]): the finite difference of the origin sums.
        x1 (int): the x of the upper left index.
        y1 (int): the y of the upper left index.
        x2 (int): the x of the bottom right index.
        y2 (int): the y of the bottom right index.
        value (int): add value to the origin sums[x1:x2+1][y1:y2+1].
    """
    differences[x1][y1] += value
    if x2 + 1 < len(differences):
        differences[x2 + 1][y1] -= value
    if y2 + 1 < len(differences[x1]):
        differences[x1][y2 + 1] -= value
    if x2 + 1 < len(differences) and y2 + 1 < len(differences[x2 + 1]):
        differences[x2 + 1][y2 + 1] += value

def prefix_sum(differences: List[List[int]]) -> List[List[int]]:
    """
    Args:
        differences (List[List[int]]): the source second dimension list.

    Returns:
        List[List[int]]: the prefix sums of the given differences. The item (i,j) equals to sum(difference[:i+1][:j+1]).
    """
    sums = [[0 for _ in range(len(differences[0])+1)]]
    sums += [[0] + d[:] for d in differences]

    for i in range(1, len(sums)):
        for j in range(1, len(sums[i])):
            sums[i][j] += sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1]

    return [s[1:] for s in sums[1:]]

def add_ranges(matrix: List[List[int]], operations: List[int]) -> List[int]:
    differences = finite_difference(matrix)

    for x1, y1, x2, y2, value in operations:
        add_range(differences, x1-1, y1-1, x2-1, y2-1, value)

    return prefix_sum(differences)

if __name__ == '__main__':
    from sys import stdin

    def readline() -> List[int]:
        return [int(i) for i in stdin.readline().split()]

    N, M, Q = readline()

    matrix = [readline() for _ in range(N)]
    operations = [readline() for _ in range(Q)]

    for line in add_ranges(matrix, operations):
        print(' '.join((str(i) for i in line)))