假设我有ABCDEF
。然后,有6个!重新排序该字符串的排列。现在,我只想处理没有相邻字符的排列。这意味着,我想看看满足这些约束条件的所有排列:
我对此算法的处理方法是以下伪代码:
//generate all 6! permutations
//check all permutations and see where B is next to A || C
//remove all instances
//check all permutations and see where C is next to D
//remove all instances
//check all permutations and see where D is next to E
//remove all instances
//check all permutations and see where E is next to F
//remove all instances
然而,这些屏蔽操作变得非常低效并且花费我太长时间,特别是如果我的字符串长度大于6.我怎样才能更有效地做到这一点?我看到这些类似的帖子1,2,并希望提取一些可能对我有帮助的重要提示。但是,这也是强力检查。我想从头开始实际生成唯一的模式,而不必生成所有内容并逐个检查。
编辑:目前我正在使用它来生成所有排列。
static String[] designs;
static int index;
protected static String[] generateDesigns(int lengthOfSequence, int numOfPermutations){
designs = new String[numOfPermutations];
StringBuilder str = new StringBuilder("1");
for(int i = 2; i <= lengthOfSequence; i++)
str.append(i);
genDesigns("", str.toString()); //genDesigns(6) = 123456 will be the unique characters
return designs;
}
//generate all permutations for lenOfSequence characters
protected static void genDesigns(String prefix, String data){
int n = data.length();
if (n == 0) designs[index++] = prefix;
else {
for (int i = 0; i < n; i++)
genDesigns(prefix + data.charAt(i), data.substring(0, i) + data.substring(i+1, n));
}
}
答案 0 :(得分:5)
用于生成长度为O(n!)
的字符串的所有排列的典型n
伪代码算法:
function permute(String s, int left, int right)
{
if (left == right)
print s
else
{
for (int i = left; i <= right; i++)
{
swap(s[left], s[i]);
permute(s, left + 1, right);
swap(s[left], s[i]); // backtrack
}
}
}
字符串ABC
的相应递归树看起来像[从互联网上拍摄的图像]:
在交换之前,检查您是否可以交换满足给定约束(检查s[left]
和s[i]
的新的前一个和新的下一个字符)。这也将从递归树中删除许多分支。
答案 1 :(得分:0)
这是一个相当简单的回溯解决方案,在将相邻字符添加到排列之前修剪搜索。
public class PermutationsNoAdjacent {
private char[] inputChars;
private boolean[] inputUsed;
private char[] outputChars;
private List<String> permutations = new ArrayList<>();
public PermutationsNoAdjacent(String inputString) {
inputChars = inputString.toCharArray();
inputUsed = new boolean[inputString.length()];
outputChars = new char[inputString.length()];
}
private String[] generatePermutations() {
tryFirst();
return permutations.toArray(new String[permutations.size()]);
}
private void tryFirst() {
for (int inputIndex = 0; inputIndex < inputChars.length; inputIndex++) {
assert !inputUsed[inputIndex] : inputIndex;
outputChars[0] = inputChars[inputIndex];
inputUsed[inputIndex] = true;
tryNext(inputIndex, 1);
inputUsed[inputIndex] = false;
}
}
private void tryNext(int previousInputIndex, int outputIndex) {
if (outputIndex == outputChars.length) { // done
permutations.add(new String(outputChars));
} else {
// avoid previousInputIndex and adjecent indices
for (int inputIndex = 0; inputIndex < previousInputIndex - 1; inputIndex++) {
if (!inputUsed[inputIndex]) {
outputChars[outputIndex] = inputChars[inputIndex];
inputUsed[inputIndex] = true;
tryNext(inputIndex, outputIndex + 1);
inputUsed[inputIndex] = false;
}
}
for (int inputIndex = previousInputIndex + 2; inputIndex < inputChars.length; inputIndex++) {
if (!inputUsed[inputIndex]) {
outputChars[outputIndex] = inputChars[inputIndex];
inputUsed[inputIndex] = true;
tryNext(inputIndex, outputIndex + 1);
inputUsed[inputIndex] = false;
}
}
}
}
public static void main(String... args) {
String[] permutations = new PermutationsNoAdjacent("ABCDEF").generatePermutations();
for (String permutation : permutations) {
System.out.println(permutation);
}
}
}
它打印出ABCDEF的90种排列。我将引用开头和结尾:
ACEBDF
ACEBFD
ACFDBE
ADBECF
…
FDBEAC
FDBECA