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


    一、字典序法

    1) 从序列P的右端开始向左扫描,直至找到第一个比其右边数字小的数字,即

    2) 从右边找出所有比大的数中最小的数字,即

    3) 交换

    4) 将右边的序列翻转,即可得到字典序的下一个排列。

    5) 重复上面的步骤,直至得到字典序最大的排列,即左边数字比右边的大的降序排列。

    //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){//交换两个元素
    	char temp;
    	temp = data[i];
    	data[i] = data[j];
    	data[j] = temp;
    }
    
    void reverse(int data[], int first, int last){//翻转序列
    	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, "
    ");
    }
    

    二、SJT Algorithm

    初始状态为

    1) 找到最大的可移动数m(当一个数指向一个比它小的数是,该数就是可移动数)

    2) 交换m和m所指向的数

    3) 改变所有比m大的数的方向

    4) 重复上面的步骤,直至找不到可移动数

    //邻位对换法
    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){//判断是否存在可移动数
    	int index;
    	for (index = 0; index < length; ++index){
    		if (data[index].mobile == 1)
    			return 1;
    	}
    	return 0;
    }
    
    int findMax(Item data[], int length){//找到最大的可移动数
    	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){//改变大于可移动数的数的方向
    	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, "
    ");
    }
    
    void exSwap(Item data[], int i, int j){
    	Item tmp = data[i];
    	data[i] = data[j];
    	data[j] = tmp;
    }
    

     三、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])  
    

     以上算法描述摘自维基百科

    //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] != ''){
    		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, "
    ");
    }
    
    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).
    ", time, ((float)time)/CLOCKS_PER_SEC);
    	return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/liushaobo/p/4380559.html
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