设某n阶三对角矩阵Anxn的示意图如下图所示。若将该三对角矩阵的非零元素按行存储在一维数组B[k]（1≤k≤3×n-2）中，则k与i、j的对应关系是（ ）。
- A.k=2i+j+2
- B.k=i-j+1
- C.k=3i+j-2
- D.k=2i+j-2
正确答案及解析
正确答案
解析
本题考查数据结构基础知识。解答该问题需先计算排列在Ai，j之前的元素个数。在按行存储方式下，存储在Ai，j之前的元素分为i-1行，除第1行外，每行3个元素。在第i行上，Ai，j之前的元素个数分为三种情况：i＞j时为0个，i=j时有1个，i＜j时为2个，概括为j-i+1个。综上，排列在Ai，j之前的元素个数为(i-1) ×3-1+j-i+1，即2i+j-3。由于数组B的下标从1开始，所以k=2i+j-3+1。
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