全排列算法(字典序法、SJT Algorithm 、Heap's Algorithm)

1、字典序法

1) 從序列P的右端開始向左掃描，直至找到第一個比其右邊數字小的數字，即。

2) 從右邊找出全部比大的數中最小的數字，即。

3) 交換與。

4) 將右邊的序列翻轉，便可獲得字典序的下一個排列。

5) 重複上面的步驟，直至獲得字典序最大的排列，即左邊數字比右邊的大的降序排列。

//字典序法
void dictionary(int length){
	int * data = (int *)malloc(sizeof(int) * length);
	int index;
	for (index = 0; index < length; ++index)
		data[index] = index + 1;
	FILE * fp = fopen("dictionary.txt", "w");
	print(fp, data, length);
	while (nextPermutation(data, 0, length)){
		print(fp, data, length);
	}
	fclose(fp);
	free(data);
}

void swap(int data[], int i, int j){//交換兩個元素
	char temp;
	temp = data[i];
	data[i] = data[j];
	data[j] = temp;
}

void reverse(int data[], int first, int last){//翻轉序列
	last--;
	while (first < last){
		swap(data, first++, last--);
	}
}

int nextPermutation(int data[], int first, int last){
	int i, j;
	i = last - 2;
	while (i >= 0 && data[i] >= data[i+1])
		--i;
	if (i == -1){
		reverse(data, first, last);
		return 0;
	}
	j = last - 1;
	while (data[j] <= data[i]){
		--j;
	}
	swap(data, i, j);
	reverse(data, i + 1, last);
	return 1;
}

void print(FILE * fp, int data[], int length){
	int index;
	for (index = 0; index < length; ++index){
		fprintf(fp, "%d ", data[index]);
	}
	fprintf(fp, "\n");
}

 

2、SJT Algorithm

初始狀態爲。

1) 找到最大的可移動數m(當一個數指向一個比它小的數是，該數就是可移動數)

2) 交換m和m所指向的數

3) 改變全部比m大的數的方向

4) 重複上面的步驟，直至找不到可移動數

//鄰位對換法
void exchange(int length){
	Item * data = (Item *)malloc(sizeof(Item) * length);
	int index, indexOfMax;
	for (index = 0; index < length; ++index){
		data[index].digit = index + 1;
		data[index].direction = -1;
		data[index].mobile = (index != 0) ? 1 : 0;
	}
	indexOfMax = length - 1;
	FILE * fp = fopen("exchange.txt", "w");
	exPrint(data, length, fp);
	while (1== data[indexOfMax].mobile || existMobile(data, length)){
		if (1== data[indexOfMax].mobile){
			int direction = data[indexOfMax].direction;
			exSwap(data, indexOfMax, indexOfMax+direction);
			indexOfMax += direction;
			if ((indexOfMax == 0 && direction == -1) || (indexOfMax == length-1 && direction == 1)){
				toMobileorNot(data, length);
			}
		} else{
			index = findMax(data, length);
			if (index == -1)
				break;
			int direction = data[index].direction;
			exSwap(data, index, index + direction);
			index += direction;
			changeDirection(data, length, index);
			toMobileorNot(data, length);
		}
		exPrint(data, length, fp);
	}
	fclose(fp);
	free(data);
}

int existMobile(Item data[], int length){//判斷是否存在可移動數
	int index;
	for (index = 0; index < length; ++index){
		if (data[index].mobile == 1)
			return 1;
	}
	return 0;
}

int findMax(Item data[], int length){//找到最大的可移動數
	int ans = -1;
	for (int index = 0; index < length; ++index){
		if (data[index].mobile == 1){
			if (ans == -1)
				ans = index;
			else if (data[index].digit > data[ans].digit)
				ans = index;
		}
	}

	return ans;
}

void changeDirection(Item data[], int length, int index){//改變大於可移動數的數的方向
	for (int i = 0; i < length; ++i){
		if (data[i].digit > data[index].digit){
			data[i].direction = -data[i].direction;
		}
	}
}

void toMobileorNot(Item data[], int length){
	if (data[0].direction == 1 && data[0].digit > data[1].digit)
		data[0].mobile = 1;
	else
		data[0].mobile = 0;

	for (int i = 1; i < (length - 1); ++i){
		int direction = data[i].direction;
		if (data[i].digit > data[i+direction].digit)
			data[i].mobile = 1;
		else
			data[i].mobile = 0;
	}

	if (data[length-1].direction == -1 && data[length-1].digit > data[length-2].digit)
		data[length-1].mobile = 1;
	else
		data[length-1].mobile = 0;
}

void exPrint(Item data[], int length, FILE * fp){
	for (int index = 0; index < length; ++index){
		fprintf(fp, "%d ", data[index].digit);
	}
	fprintf(fp, "\n");
}

void exSwap(Item data[], int i, int j){
	Item tmp = data[i];
	data[i] = data[j];
	data[j] = tmp;
}

 3、Heap's Algorithm

    procedure generate(n : integer, A : array of any):  
        if n = 1 then  
              output(A)  
        else  
            for i := 1; i ≤ n; i += 1 do  
                generate(n - 1, A)  
                if n is odd then  
                    j ← 1  
                else  
                    j ← i  
                swap(A[j], A[n])  

 以上算法描述摘自維基百科

 

//Recursive implementation.
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

FILE * fp = NULL;
int len;

int str2int(char str[]){
	int i = 0;
	int result = 0;
	while (str[i] != '\0'){
		result = result * 10 + str[i] - '0';
		++i;
	}
	return result;
}

void print(int data[]){
	int i;
	for (i = 0; i < len; ++i)
		fprintf(fp, "%d ", data[i]);
	fprintf(fp, "\n");
}

void swap(int *x, int *y){
	int tmp = *x;
	*x = *y;
	*y = tmp;
}

void generate(int data[], int n){
	int i;
	if (1 == n)
		print(data);
		//return;
	else{
		for (i = 0; i < n; ++i){
			generate(data, n-1);
			if (n % 2 == 1){
				swap(&data[1], &data[n-1]);
			} else{
				swap(&data[i], &data[n-1]);
			}
		}
	}
}

void heapAlgorithm(int n){
	int * data = (int *)malloc(sizeof(int) * n);
	int i;
	for(i = 0; i < n; ++i)
		data[i] = i + 1;
	generate(data, n);
	free(data);
}
int main(int argc, char **argv){
	fp = fopen("heap.txt", "w");
	len = (argc > 1) ? str2int(argv[1]) : 10;
	clock_t time = clock();
	heapAlgorithm(len);
	time = clock() - time;
	printf("Heap's Algorithm takes %d clocks(%f seconds).\n", time, ((float)time)/CLOCKS_PER_SEC);
	return 0;
}