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AB合并,最多比较次数 35+10-1 = 44 +2. AB与C合并,最多比较次数 40+45-1=84 +3. DE合并,最多比较次数50+60-1=109 +4. ABC与DE合并,最多比较次数85+110-1=194 +5. ABCDE与F合并,最多比较次数195+200-1 = 394 + +比较的总次数最多 = 825次 + +(2) + +对多个有序表进行两两合并时,若表长不同,则最坏情况下总得比较次数依赖于表的合并次序,借助哈夫曼树的思想,依次选择最短的两个表进行合并,此时可以获得最坏情况下的最佳合并效率 + + +--- + +![](../../images/《数据结构》大题/大题4.jpg) + +(1) + +有两类结点:叶结点数$n_0$,度为k的分支结点$n_k$ + +则$n_{总} = n_0 + n_k = n_0+m,$树的边e = n -1 + +且e = mk,的$n_0+m = mk+1$ + +因此,$n_0 = (k-1)m+1$ + +(2) + +最多即为满k叉树,第j层结点为$k^{j-1}$ + +所以 最多 = $\sum_{j=1}^n k^{j-1} = \frac{k^h-1}{k-1}$ + +最少 = $1+(h-2)k+k = 1+(h-1)k$ + + +--- + +![](../../images/《数据结构》大题/大题5.jpg) + +(2) + +唯一,若AE替代CE,则形成了回路 + +(3) + +当带权连通图的任意一个环中所包含的边权值不相同时,MST是唯一的 + + +--- + +![](../../images/《数据结构》大题/大题6.jpg) + +(1) + +$A = \begin{bmatrix} + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 0 & 0 & 1 & 1 \\\\ + 1 & 0 & 0 & 1 & 0 \\\\ + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 1 & 0 & 1 & 0 \\\\ +\end{bmatrix}$ + +(2) + +$$ +A^2 = \begin{bmatrix} + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 0 & 0 & 1 & 1 \\\\ + 1 & 0 & 0 & 1 & 0 \\\\ + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 1 & 0 & 1 & 0 \\\\ +\end{bmatrix} +\times +\begin{bmatrix} + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 0 & 0 & 1 & 1 \\\\ + 1 & 0 & 0 & 1 & 0 \\\\ + 0 & 1 & 1 & 0 & 1 \\\\ + 1 & 1 & 0 & 1 & 0 \\\\ +\end{bmatrix} = +\begin{bmatrix} + 3 & 1 & 0 & 3 & 1 \\\\ + 1 & 3 & 2 & 1 & 2 \\\\ + 0 & 2 & 2 & 0 & 2 \\\\ + 3 & 1 & 0 & 3 & 1 \\\\ + 1 & 1 & 2 & 1 & 3 \\\\ +\end{bmatrix} +$$ + +0行3列的值表示从顶点0到顶点3之间长度为2的路径共有3条 + +(3) + +从顶点i到顶点j的长度为m的路径条数 + +--- + +![](../../images/《数据结构》大题/大题7.jpg) + +(1) + +无向图 + +(2) + +链式存储结构 + +$$ +\begin{array} + |\text{Flag = 1} | \text{Next}| \\\\ + \hline + \text{ID}| \\\\ + \hline + \text{IP}| \\\\ + \hline + \text{Metrix}| \\\\ +\end{array} +$$ + +$$ +\begin{array} + |\text{Flag = 2} | \text{Next}| \\\\ + \hline + \text{Prefix}| \\\\ + \hline + \text{Mask}| \\\\ + \hline + \text{Metrix}| \\\\ +\end{array} +$$ + +表头结点 + +|RouterID| +|:---:| +|LN-link| +|Next| + +数据结构类型 + +```c +//link的结构 +typedef Struct +{ + unsigned int ID,IP; + +}LinkNode; + +//net的结构 +typedef Struct{ + unsigned int prefix,Mask; +}NetNode; +//弧结点 +typedef struct{ + int Flag; + union{ + LinkNode Lnode; + NetNode Noded; + }LinkOrNet; + unsigned int *next; +}arcNode; + +//表头结点 +typedef struct hNode +{ + unsigned int RouterID; + ArcNode * LN_link; + struct hNode *next; +}HNode; + +``` + +(3) + +![](../../images/《数据结构》大题/大题7图1.jpg) + +|目的网络|路径|代价| +|:---:|:---:|:---:| +|192.1.1.0/24|直接到达|1| +|192.1.5.0/24|R1->R3->192.1.5.0/24|3 +|192.1.6.0/24|R1->R2->192.1.6.0/24|4 +|192.1.7.0/24|R1->R2->R4->192.1.7.0/24|8 + + +--- + +![](../../images/《数据结构》大题/大题8.jpg) + +不一定能求得最短路径 + +按题方法求得最短路径:A->B->C + +实际最短路径:A->D->C + +--- + +![](../../images/《数据结构》大题/大题9.jpg) + +(1) + +$$ +A=\begin{bmatrix} + 0 & 4 & 6 & \infty & \infty & \infty \\\\ + \infty & 0 & 5 & \infty & \infty & \infty \\\\ + \infty & \infty & 0 & 4 & 3 & \infty \\\\ + \infty & \infty & \infty & 0 & \infty & 3 \\\\ + \infty & \infty & \infty & \infty & 0 & 3 \\\\ + \infty & \infty & \infty & \infty & \infty & 0 \\\\ +\end{bmatrix} +$$ + +(2) + +![](../../images/《数据结构》大题/大题9图1.png) + +(3) + +关键路径 0->1->2->3->5 + +长度为 4+5+4+3 = 16 + + +--- + +![](../../images/《数据结构》大题/大题10.jpg) + +总费用均为16 + +(2) + +用邻接矩阵存储,构造最小生成树则使用Prim算法 + +(3) + +TTL = 5=>IP分组的最大传递距离 = 5 + +方案一太远,不能收到 + +方案二邻近可以收到 + + +--- + +![](../../images/《数据结构》大题/大题11.jpg) + +(1) + +一维数组大小7/0.7 = 10,下标为 0~9 + +$$ +\begin{array}{c|lcr} + \text{key} & 7 & 8 & 30 & 11 & 18 & 9 & 14 \\\\ + \hline + \text{H(key)} & 0 & 3 & 6 & 5 & 5 & 6 & 0 \\\\ +\end{array} +$$ + +$$ +\begin{array}{c|lcr} + \text{地址} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\\ + \hline + \text{关键字} & 7 & 14 & & 8 & & 11 & 30 & 18 & 9 & \\\\ +\end{array} +$$ + + +(2) + +查找成功: + +$$ +\begin{array}{c|lcr} + \text{key} & 7 & 8 & 30 & 11 & 18 & 9 & 14 \\\\ + \hline + \text{比较次数} & 1 & 1 & 1 & 1 & 3 & 3 & 2 \\\\ +\end{array} +$$ + +$ASL_{成功} = \frac{1+1+1+1+3+3+2}{7} = \frac{12}{7}$ + +查找失败: + +$$ +\begin{array}{c|lcr} + \text{地址} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\\ + \hline + \text{关键字} & 3 & 2 & 1 & 2 & 1 & 5 & 4 \\\\ +\end{array} +$$ + +$ASL_{失败} = \frac{3+2+1+2+1+5+4}{7} = \frac{18}{7}$ + +--- + +![](../../images/《数据结构》大题/大题12.jpg) + +(1) + +按查找概率逆序排列 + +顺序查找方法 + +平均查找长度 = $1\times 0.35 + 2\times 0.35+3\times 0.15+4\times 0.15 = 2.1$ + +(2) + +方法一: + +按查找概率逆序排列 + +顺序查找方法 + +平均查找长度 = $1\times 0.35 + 2\times 0.35+3\times 0.15+4\times 0.15 = 2.1$ + +方法二: + +二叉排序树的查找方法: + +$ASL=0.15\times1 + 0.35\times2 + 0.35\times2 + 0.15\times3 = 2.0$ + +--- + +![](../../images/《数据结构》大题/大题13.jpg) + +(1) + +b的内容为{-10,10,11,19,25,25} + +(2) + +比较次数 = (n-1) + (n-2)+(n-3)$\cdots$+1 = $\frac{n(n-1)}{2}$ + +(3) + +不是 + +将if修改为 + +```c +if(a[i]<=a[j]) +{ + count[j]++; +} +else +{ + count[i]++; +} +``` + +如果不加=,两个相等的元素在比较时,前面的元素的count值会加1,导致原序列中靠前的元素在排序后的序列处于靠后的位置 + +--- \ No newline at end of file diff --git a/static/images/《数据结构》大题/大题1.jpg b/static/images/《数据结构》大题/大题1.jpg new file mode 100644 index 0000000000000000000000000000000000000000..6cafd12fc3b60d83d54beb13b2610f783700c84e GIT binary patch literal 127050 zcmeFZbzD^4_b7Y_K?G?KPyq>1x)CI#L8QBLfT4yik+DILkPZRq25AWy6%c9Z7HMf2 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