[Java]图解Perfect shuffle[Jai04]

最新推荐文章于 2025-09-04 18:30:36 发布

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本文介绍了一个能在O(n)时间内及O(1)额外空间中实现数组完美洗牌的算法。该算法通过递归方式处理特定长度的数组，并利用数学运算完成元素的重新排列。

数组2n [a1, a2, ...an, b1, b2, ...bn] 在时间O(n),空间 O(1) 条件下，生成[b1,a1,b2,a2....an,bn]

对于3^k-1 < 2n < 3^(k+1) -1 的情况，取 2m = 3^k -1 递归求解:

对于2m = 3^k -1 的perfect shuffle

public class PerfectShuffleJai04 {	
	
	static public void shuffle(char[] unshuffled){
		shuffle(unshuffled, 0, unshuffled.length);
	}

	static void shuffle(char[] unshuffled, int start, int len){
		if( len >= 2){
			int n =  len / 2;
			int k = getK(n);
			int m = (int) ((Math.pow(3, k) - 1) / 2);
			if (m < n && n > 0) {
				shiftRight(unshuffled, start + m, n, m);
				cycle(unshuffled, start, m * 2);				
				//Recursive
				shuffle(unshuffled, start + m * 2, len - m * 2 );
			} else if( m == n) {
				cycle(unshuffled, start, len);
			}			
		}		
	}
	
	//Get k, 3^k <= (n * 2 +1) < 3^(k+1) 
	static int getK(int n){
		int k = 0;
		for (;; k++) {
			if (Math.pow(3, k) <= n * 2 + 1 && Math.pow(3, k + 1) > n * 2 + 1) {
				break;
			}
		}
		return k;		
	}
	
	//Cycle header
	static void cycle(char[] c, int start, int len){
		int k = getK(len/2);
		int mod = (int) Math.pow(3, k); 
		char tmp = ' ';
		for(int i = 0; i < k; i++ ){
			int cycleHead = start + (int) Math.pow(3,i) - 1;
			int current = cycleHead;	
			int next = 0;
			do{
				next = (current - start + 1) * 2 % mod + start - 1;
				tmp = c[next];
				c[next] = c[cycleHead];
				c[cycleHead] = tmp;				
				current = next;				
			}while(current != cycleHead);			
		}
	}
		
	//Shift Right 
	static public void shiftRight(char[] c, int start, int len, int m){
		m = m % len;
		if (m < 0){
			m = m + len;
		}
		reverse(c, start + len - m , start + len - 1);  
		reverse(c, start, start + len - m - 1 );	    
	    reverse(c, start, start + len - 1);
	}
	
	static void reverse(char[] c, int m, int n){
		char t;
		for (; m < n; m++, n--){
			t = c[m];
			c[m] = c[n];
			c[n] = t;
		}		
	}	
	
	static public void printArray(char[] arr){
		for(int i = 0; i < arr.length; i++){
			System.out.print(arr[i]+" ");
		}
		System.out.println();
		
	}
	
	public static void main(String[] args){
		String s = "12345678ABCDEFGH";
		char[] a = s.toCharArray();
		printArray(a);
		shuffle(a);
		printArray(a);
	}	

}