(A)

2-D array 元素位址的公式如下：

row-major :
addr (i,j) = B + W * ( Nc * (i - Lr) + (j - Lc) )
column-major :
addr (i,j) = B + W * ( (i - Lr) + Nr * (j - Lc) )
where:
i, j = subscript number
B = base address
W = width (size) of each element
Nc = number of Columns
Nr = Number of Rows
Lc = Lower-bound of Column
Lr = Lower-bound of Row

Row major:
(1, 1) is 2
-> Lc = 0, Lr = 0 can't be true

assume Lc, Lr both are 1:
(1, 1) = B + W * 0 = 2
--> B = 2

(2, 3) = 2 + W (Nc * 1 + 2) = 18
(3, 2) = 2 + W (Nc * 2 + 1) = 28
-->
W (Nc * 1 + 2) = 16
W (Nc * 2 + 1) = 26

Nc + 2 / 2Nc + 1 = 8 / 13
-> Nc = 6
-> W = 2

(4, 5) = 2 + 2 (6 * 3 + 4) = 46

column major:
(1, 1) is 2
--> Lc = 0, Lr = 0 can't be true

assume Lc, Lr both are 1:
(1, 1) = B + W * 0 = 2
--> B = 2

(2, 3) = 2 + W (1 + Nr * 2) = 18
(3, 2) = 2 + W (2 + Nr * 1) = 28
-->
W (1 + Nr * 2) = 16
W (2 + Nr * 1) = 26
-->
(1 + Nr * 2) / (2 + Nr * 1) = 8 / 13
--> Nr can't be found
--> The orignal 2-D array can't be arranged in column-major form.

所以我對這個問題的回答是 46 。

(B)

也可以參考 Wikipedia 提供的 2-D array 位址公式:

B + c · i + d · j (0)

B: fixed base address
c: row address increments
d: column address increments

(1, 1) = 2
--> B + c + d = 2 (1)
(2, 3) = 18
--> B + 2c + 3d = 18 (2)
(3, 2) = 28
--> B + 3c + 2d = 28 (3)

由 (1)
--> B = 2 - c - d (4)

(4) 帶入 (2)
--> 2 - c - d + 2c + 3d = 18
--> c = 16 - 2d (5)

(5) 帶入 (4)
--> B = 2 - (16 - 2d) - d
--> B = d - 14 (6)

(5), (6) 帶入 (3)
--> d - 14 + 3 (16 - 2d) + 2d = 28
--> 34 - 3d = 28
--> d = 6/3 = 2 (7)

(7) 帶入 (5)
--> c = 12 (8)

(7), (8) 帶入 (4)
--> B = 2 - 12 - 2 = -12 (9)

(7), (8), (9) 帶入 (0)
--> -12 + 12 * i + 2 * j (10)

(i, j) = (4, 5) 帶入 (10)
--> -12 + 12 * 4 + 2 * 5
--> 46

這個公式算出來的答案也是 46 。

Ans:46
畫一個二維>5*>4的方格，(上下>=6，左右>=5)將題目的數字填入格裡
1,1=2 2,3=18 3,2=28, 如果要將數字填入，並符合題目要求，那麼
出現在4,5就是46。
要用數學表示式或寫程式解，這、、這，、、、，我不懂@@

需要做一些假設：

1. 陣列及位址都是1 base（從1開始算）
2. 假設每行有Y個元素，每個元素的size是Z
3. 從題目條件可知：
   Z = 2
   y + 3Z = 18
   2Y + 2Z = 28
4. 所以Y = 12
5. 所以X(4,5)的位址在3*12+2*5 = 46