练习72

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72. (NOI'95.1_2)　在一个园形操场的四周摆放 N 堆石子(N≤100)， 现要将石子
有次序地合并成一堆。规定每次只能选相邻的两堆合并成新的一堆，并将新的一堆
的石子数，记为该次合并的得分。
　　编一程序，由文件读入堆数 N 及每堆的石子数(≤20)，
　　① 选择一种合并石子的方案, 使得做N-1次合并, 得分的总和最小;
② 选择一种合并石子的方案, 使得做N-1次合并, 得分的总和最大.
例如, 图 2-1 所示的4堆石子,每堆的石子数(从最上面的一堆数起, 顺时针数)
依次为4  5  9  4. 则 3 次合并得分总和最小的方案为图2-2,得分总和最大的方案
为图 2-3.
(加图)
　　输入数据:
文件名由键盘输入，该文件内容为;
第一行为石子堆数 N;
第二行为每堆的石子数, 每两个数之间用一个空格符分隔
输出数据:
输出文件名为 OUTPUT.TXT
　　第 1 至 N-1 行为得分最小的合并过程. 每行包含两个数, 表示应该合并的两
堆石子的数目, 小数在前, 大数在后, 第 N 行为合并成一堆后的最小得分总和;
第 N+1 行为空行, 第 N+2 至 2N+1 行为得分最大合并过程(格式同前). 第 2N+2
行为最大得分总和.

**********************************************************************************/

#include <stdio.h>
#include <malloc.h>

typedef struct tagTreeNode
{
int data;
tagTreeNode *left;
tagTreeNode *right;
} TreeNode;

typedef struct tagLinkNode
{
TreeNode *pTreeNode;
tagLinkNode *pNext;
} LinkNode;

LinkNode *head = NULL;
LinkNode *tail = NULL;
TreeNode *root = NULL;

//创建一个链表,保存数列
void CreateLink(FILE *fp, int n)
{
int i;
int data;
TreeNode *tempTreeNode;
LinkNode *tempLinkNode;

for(i=0; i<n; i++)
{
fscanf(fp,"%d",&data);
tempTreeNode = (TreeNode*)malloc(sizeof(TreeNode));
tempTreeNode->data = data;
tempTreeNode->left = NULL;
tempTreeNode->right = NULL;
tempLinkNode = (LinkNode*)malloc(sizeof(LinkNode));
tempLinkNode->pTreeNode = tempTreeNode;
tempLinkNode->pNext = NULL;
if(!head)
{
head = tail = tempLinkNode;
tail->pNext = head;//尾节点指向头节点
}
else
{
tail->pNext = tempLinkNode;
tail = tail->pNext;
tail->pNext = head;//尾节点指向头节点
}
}
}

//插入元素
LinkNode* InsertAfter(LinkNode *pLinkNode,int data)
{
TreeNode *tempTreeNode;
LinkNode *tempLinkNode = NULL;

if(pLinkNode)
{
tempTreeNode = (TreeNode*)malloc(sizeof(TreeNode));
tempTreeNode->data = data;
tempTreeNode->left = NULL;
tempTreeNode->right = NULL;
tempLinkNode = (LinkNode*)malloc(sizeof(LinkNode));
tempLinkNode->pTreeNode = tempTreeNode;
tempLinkNode->pNext = NULL;

tempLinkNode->pNext = pLinkNode->pNext;
pLinkNode->pNext = tempLinkNode;
if(pLinkNode == tail)
tail = tempLinkNode;
}

return tempLinkNode;
}

//删除元素
void DeleteLinkNode(LinkNode *pLinkNode)
{
LinkNode *p,*q;
if(pLinkNode == head)
{
if(head == tail)
{
head = tail = NULL;
}
else
{
head = head->pNext;
tail->pNext = head;
}
free(pLinkNode);
}
else
{
p = tail;
q = head;
while(q != tail)
{
if(q == pLinkNode)
{
p->pNext = q->pNext;
free(pLinkNode);
break;
}
p = q;
q = q->pNext;
}
if(q == tail)
{
tail = p;
p->pNext = q->pNext;
free(pLinkNode);
}
}
}

//计算
int CalcMin()
{
int sum = 0;
int min_sum;
LinkNode *p,*q,*min,*pnew;

while(head != tail)
{
p = tail;
q = head;
min = p;
min_sum = min->pTreeNode->data + min->pNext->pTreeNode->data;
do
{
if(q->pTreeNode->data + p->pTreeNode->data <
min_sum)
{
min = p;
min_sum = min->pTreeNode->data + min->pNext->pTreeNode->data;
}
p = q;
q = q->pNext;
}while(q != head);
sum += min_sum;
pnew = InsertAfter(min->pNext,min_sum);
pnew->pTreeNode->left = min->pTreeNode;
pnew->pTreeNode->right = min->pNext->pTreeNode;
DeleteLinkNode(min->pNext);
DeleteLinkNode(min);
}
root = head->pTreeNode;
DeleteLinkNode(head);

return sum;
}

int CalcMax()
{
int sum = 0;
int max_sum;
LinkNode *p,*q,*max,*pnew;

while(head != tail)
{
p = tail;
q = head;
max = p;
max_sum = max->pTreeNode->data + max->pNext->pTreeNode->data;
do
{
if(q->pTreeNode->data + p->pTreeNode->data >
max_sum)
{
max = p;
max_sum = max->pTreeNode->data + max->pNext->pTreeNode->data;
}
p = q;
q = q->pNext;
}while(q != head);
sum += max_sum;
pnew = InsertAfter(max->pNext,max_sum);
pnew->pTreeNode->left = max->pTreeNode;
pnew->pTreeNode->right = max->pNext->pTreeNode;
DeleteLinkNode(max->pNext);
DeleteLinkNode(max);
}
root = head->pTreeNode;
DeleteLinkNode(head);

return sum;
}

//打印结果

void main()
{
int n;
FILE *fp,*fpw;
int rs;

fp = fopen("input.txt","r");
if(!fp)
{
printf("fail to open the file input.txt!/n");
return;
}
fscanf(fp,"%d",&n);
printf("石子堆数N: %d/n", n);

//  fpw = fopen("output.txt","w");
CreateLink(fp,n);
rs = CalcMin();
printf("min = %d/n",rs);

fseek(fp,0,SEEK_SET);
fscanf(fp,"%d",&n);
CreateLink(fp,n);
rs = CalcMax();
printf("max = %d/n",rs);

fclose(fp);

}