In 1953, David A. Huffman published his paper
“A Method for the Construction of Minimum-Redundancy Codes”,
and hence printed his name in the history of computer science.
As a professor who gives the final exam problem on Huffman codes,
I am encountering a big problem:
the Huffman codes are NOT unique.
For example, given a string “aaaxuaxz”,
we can observe that the frequencies of
the characters ‘a’, ‘x’, ‘u’ and ‘z’ are 4, 2, 1 and 1, respectively.
We may either encode the symbols as
{‘a’=0, ‘x’=10, ‘u’=110, ‘z’=111},
or in another way as {‘a’=1, ‘x’=01, ‘u’=001, ‘z’=000},
both compress the string into 14 bits.
Another set of code can be given as
{‘a’=0, ‘x’=11, ‘u’=100, ‘z’=101},
but {‘a’=0, ‘x’=01, ‘u’=011, ‘z’=001} is NOT correct
since “aaaxuaxz” and “aazuaxax”
can both be decoded from the code 00001011001001.
The students are submitting all kinds of codes,
and I need a computer program to help me
determine which ones are correct and which ones are not.
include
include
define MinData 0
typedef struct TreeNode* HuffmanTree;
struct TreeNode
{
int weight;
HuffmanTree Left;
HuffmanTree Right;
};
typedef struct HeapStruct *MinHeap;
struct HeapStruct{
HuffmanTree elements;
int size;
int capacity;
};
MinHeap MinHeap_Build(int weight[], int Maxsize);
MinHeap MinHeap_Creat(int Maxsize);
void MinHeap_Insert(MinHeap H, HuffmanTree HT);
HuffmanTree MinHeap_Delete(MinHeap H);
HuffmanTree HuffmanTree_Build(MinHeap H);
void Get_wpl(HuffmanTree HT, int *wpl, int layer);
int code_length(char *a);
int compare(char *c1, char *c2);
int main(int argc, char const argv[])
{
//freopen("test.txt", "r", stdin);
int N;
scanf("%d\n", &N);
char c[N];
int f[N];
for (int i = 0; i < N; ++i){
if(i == N-1)
scanf("%c %d", &c[i], &f[i]);
else
scanf("%c %d ", &c[i], &f[i]);
}
MinHeap MH = MinHeap_Build(f, N);
HuffmanTree HT = HuffmanTree_Build(MH);
int MinWpl = 0;
Get_wpl(HT, &MinWpl, 0);
int M;
scanf("%d\n", &M);
char ch[N], code[N][64];
for (int j = 0; j < M; ++j){
for (int i = 0; i < N; ++i)
scanf("%c %s\n", &ch[i], code[i]);
int flag = 1;
for (int i = 0; i < N; ++i){
for (int k = i+1; k < N; ++k){
if(compare(code[i], code[k])){
if(flag)
printf("No\n");
flag = 0;
}
}
}
int stu_wpl = 0;
if(flag){
for (int i = 0; i < N; ++i)
stu_wpl += f[i]*code_length(code[i]);
if(MinWpl == stu_wpl)
printf("Yes\n");
else
printf("No\n");
}
}
return 0;
}
int code_length(char *a)
{
int len = 0;
char *p = a;
while(*p != '\0'){
p++;
len++;
}
return len;
}
int compare(char*c1, char*c2)
{
char *a = c1, *b = c2;
while(*a!='\0' && *b!='\0'){
if(*a != *b)
return 0;
a++;
b++;
}
return 1;
}
MinHeap MinHeap_Build(int weight[], int Maxsize)
{
MinHeap H = MinHeap_Creat(Maxsize);
HuffmanTree Temp = (HuffmanTree)malloc(sizeof(struct TreeNode));
for (int i = 0; i < Maxsize; ++i){
Temp->weight = weight[i];
Temp->Left = NULL;
Temp->Right = NULL;
MinHeap_Insert(H, Temp);
}
free(Temp);
return H;
}
MinHeap MinHeap_Creat(int MaxSize)
{
MinHeap H = (MinHeap)malloc(sizeof(struct HeapStruct));
H->elements = (HuffmanTree)malloc(sizeof(struct TreeNode)(MaxSize + 1));
//因为elemens[0]作为哨兵，从[1]开始存放，所以分配MaxSize+1空间
H->size = 0;
H->capacity = MaxSize;
H->elements[0].weight = MinData;//将elements[0]作为哨兵
return H;
}
void MinHeap_Insert(MinHeap H, HuffmanTree HT)
{
if(H->size == H->capacity)
return;
int i;
i = ++H->size;//i指向插入后堆中的最后一个元素的位置
for(; H->elements[i/2].weight > HT->weight; i/=2)
//比较插入的结点和其父结点的大小
H->elements[i].weight = H->elements[i/2].weight;
H->elements[i] = *HT;
}
HuffmanTree MinHeap_Delete(MinHeap H)
{
HuffmanTree Temp, MinNode;
if(H->size == 0)
return NULL;
MinNode = (HuffmanTree)malloc(sizeof(struct TreeNode));
Temp = (HuffmanTree)malloc(sizeof(struct TreeNode));
*MinNode = H->elements[1];//取出根结点的最小值
*Temp = H->elements[H->size--];
//用最小堆的最后一个元素从根结点开始向上过滤下层结点
int Parent, Child;
for(Parent = 1; Parent*2 <= H->size; Parent = Child){
Child = Parent*2;
if(Child != H->size &&
(H->elements[Child].weight > H->elements[Child+1].weight))
Child++;
//当存在右子结点，且右子节点小于左子节点时，Child指向较小者
if(Temp->weight > H->elements[Child].weight)
H->elements[Parent] = H->elements[Child];
//移动Temp到下一层
else
break;
}
H->elements[Parent] = *Temp;
free(Temp);
return MinNode;
}
HuffmanTree HuffmanTree_Build(MinHeap H)
{
HuffmanTree HT;
int times = H->size;//H->size的值会发生变化，所以要用另一个变量来存储
for (int i = 1; i < times; ++i){//执行初始 H->size-1 次合并
HT = (HuffmanTree)malloc(sizeof(struct TreeNode));
HT->Left = MinHeap_Delete(H);
HT->Right = MinHeap_Delete(H);
HT->weight = HT->Left->weight + HT->Right->weight;
MinHeap_Insert(H, HT);
}
HT = MinHeap_Delete(H);
return HT;
}
void Get_wpl(HuffmanTree HT, int *wpl, int layer)
{
if(HT->Left == NULL && HT->Right == NULL)
*wpl += layer * HT->weight;
else{
Get_wpl(HT->Left, wpl, layer+1);
Get_wpl(HT->Right, wpl, layer+1);
}
}