6.二维前缀和

二维前缀和

• 公式：

题目：子矩阵的和

• 当前值+上面的和左边的-重复的

   public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        // 定义常量
        final int MAXN = 1011;
        int[][] a = new int[MAXN][MAXN];
        int[][] s = new int[MAXN][MAXN];

        // 输入 n, m, q
        int n = sc.nextInt();
        int m = sc.nextInt();
        int q = sc.nextInt();

        // 初始化数组并输入矩阵
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                a[i][j] = sc.nextInt();
            }
        }

        // 计算二维前缀和
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                s[i][j] = s[i][j - 1] + s[i - 1][j] - s[i - 1][j - 1] +a[i][j];
            }
        }

        // 处理每个查询
        while (q-- > 0) {
            int x1 = sc.nextInt();
            int y1 = sc.nextInt();
            int x2 = sc.nextInt();
            int y2 = sc.nextInt();

            // 计算矩形区域的和
            int res = s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1];
            System.out.println(res);
        }

        sc.close();
    }