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为了高效处理大规模矩阵的多个区间加法操作，我们采用差分数组（Difference Array）方法。这种方法将每个操作分解为四个点的增减，避免了直接遍历矩阵的高时间复杂度。

方法思路

解决代码

import java.io.*;class Main {    public static void main(String[] args) throws Exception {        BufferedReader buf = new BufferedReader(new InputStreamReader(System.in));        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));        String[] strNums = buf.readLine().split(" ");        int m = Integer.valueOf(strNums[0]);        int n = Integer.valueOf(strNums[1]);        int q = Integer.valueOf(strNums[2]);        int[][] a = new int[m + 2][n + 2];        int[][] diff = new int[m + 2][n + 2];        for (int i = 1; i <= m; ++i) {            String[] nums = buf.readLine().split(" ");            for (int j = 1; j <= n; ++j) {                int k = Integer.valueOf(nums[j - 1]);                diff[i][j] += k;            }        }        for (int i = 0; i < q; ++i) {            String[] nums = buf.readLine().split(" ");            int x1 = Integer.valueOf(nums[0]);            int y1 = Integer.valueOf(nums[1]);            int x2 = Integer.valueOf(nums[2]);            int y2 = Integer.valueOf(nums[3]);            int k = Integer.valueOf(nums[4]);            diff[x1][y1] += k;            if (y2 + 1 <= m) {                diff[x1][y2 + 1] -= k;            }            if (x2 + 1 <= n) {                diff[x2 + 1][y1] -= k;                if (y2 + 1 <= m) {                    diff[x2 + 1][y2 + 1] += k;                }            }        }        for (int i = 1; i <= m; ++i) {            for (int j = 1; j <= n; ++j) {                if (i > 1) {                    diff[i][j] += diff[i - 1][j];                }                if (j > 1) {                    diff[i][j] += diff[i][j - 1];                    if (i > 1) {                        diff[i][j] -= diff[i - 1][j - 1];                    }                }            }        }        for (int i = 1; i <= m; ++i) {            for (int j = 1; j <= n; ++j) {                a[i][j] += diff[i][j];            }        }        for (int i = 1; i <= m; ++i) {            writer.write(String.join(" ", String.valueOf(a[i][j]) + "\n"));        }        buf.close();        writer.flush();        writer.close();    }}

代码解释

这种方法通过差分数组将多个区间加法操作高效处理，避免了直接遍历矩阵的高时间复杂度，确保了程序在大规模数据下的性能。

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