我对位向量如何实现此操作感到困惑（对位向量不太熟悉）。 这是给出的代码。 请有人能帮我解释一下吗？
public static boolean isUniqueChars(String str) {
int checker = 0;
for (int i = 0; i < str.length(); ++i) {
int val = str.charAt(i) - 'a';
if ((checker & (1 << val)) > 0) return false;
checker |= (1 << val);
}
return true;
}
具体而言，checker在做什么？
00000000000000000000000000000001 a 2^0
00000000000000000000000000000010 b 2^1
00000000000000000000000000000100 c 2^2
00000000000000000000000000001000 d 2^3
00000000000000000000000000010000 e 2^4
00000000000000000000000000100000 f 2^5
00000000000000000000000001000000 g 2^6
00000000000000000000000010000000 h 2^7
00000000000000000000000100000000 i 2^8
00000000000000000000001000000000 j 2^9
00000000000000000000010000000000 k 2^10
00000000000000000000100000000000 l 2^11
00000000000000000001000000000000 m 2^12
00000000000000000010000000000000 n 2^13
00000000000000000100000000000000 o 2^14
00000000000000001000000000000000 p 2^15
00000000000000010000000000000000 q 2^16
00000000000000100000000000000000 r 2^17
00000000000001000000000000000000 s 2^18
00000000000010000000000000000000 t 2^19
00000000000100000000000000000000 u 2^20
00000000001000000000000000000000 v 2^21
00000000010000000000000000000000 w 2^22
00000000100000000000000000000000 x 2^23
00000001000000000000000000000000 y 2^24
00000010000000000000000000000000 z 2^25
a =00000000000000000000000000000001
checker=00000000000000000000000000000000
checker='a' or checker;
// checker now becomes = 00000000000000000000000000000001
checker=00000000000000000000000000000001
a and checker=0 no dupes condition
字符串 'az'
checker=00000000000000000000000000000001
z =00000010000000000000000000000000
z and checker=0 no dupes
checker=z or checker;
// checker now becomes 00000010000000000000000000000001
字符串 'azy'
checker= 00000010000000000000000000000001
y = 00000001000000000000000000000000
checker and y=0 no dupes condition
checker= checker or y;
// checker now becomes = 00000011000000000000000000000001
字符串 'azya'
checker= 00000011000000000000000000000001
a = 00000000000000000000000000000001
a and checker=1 we have a dupe
int checker被用作位的存储器。整数值中的每一位都可以被视为一个标志，因此int实际上是一个位（标志）数组。您可以使用位向量来代替int，原因如下：
大小：int有固定的大小, 通常为4个字节，即8个* 4 = 32位（标志）。位向量通常可以具有不同的大小或在构造函数中指定大小。
API：使用位向量可以让您编写更易读的代码，类似于：
vector.SetFlag(4, true); //将索引4处的标志设置为true
对于int，您需要编写较低级别的位逻辑代码：
checker |= (1 << 5); //将索引5处的标志设置为true
int可能会更快一些，因为位操作非常底层，可以由CPU直接执行。BitVector允许编写稍微不那么难懂的代码，而且它可以存储更多的标志。我认为所有这些答案都解释了它是如何工作的，然而我想给出我的意见，通过重新命名一些变量，添加一些其他变量，并对其添加注释，让它更易于理解：
public static boolean isUniqueChars(String str) {
/*
checker is the bit array, it will have a 1 on the character index that
has appeared before and a 0 if the character has not appeared, you
can see this number initialized as 32 0 bits:
00000000 00000000 00000000 00000000
*/
int checker = 0;
//loop through each String character
for (int i = 0; i < str.length(); ++i) {
/*
a through z in ASCII are charactets numbered 97 through 122, 26 characters total
with this, you get a number between 0 and 25 to represent each character index
0 for 'a' and 25 for 'z'
renamed 'val' as 'characterIndex' to be more descriptive
*/
int characterIndex = str.charAt(i) - 'a'; //char 'a' would get 0 and char 'z' would get 26
/*
created a new variable to make things clearer 'singleBitOnPosition'
It is used to calculate a number that represents the bit value of having that
character index as a 1 and the rest as a 0, this is achieved
by getting the single digit 1 and shifting it to the left as many
times as the character index requires
e.g. character 'd'
00000000 00000000 00000000 00000001
Shift 3 spaces to the left (<<) because 'd' index is number 3
1 shift: 00000000 00000000 00000000 00000010
2 shift: 00000000 00000000 00000000 00000100
3 shift: 00000000 00000000 00000000 00001000
Therefore the number representing 'd' is
00000000 00000000 00000000 00001000
*/
int singleBitOnPosition = 1 << characterIndex;
/*
This peforms an AND between the checker, which is the bit array
containing everything that has been found before and the number
representing the bit that will be turned on for this particular
character. e.g.
if we have already seen 'a', 'b' and 'd', checker will have:
checker = 00000000 00000000 00000000 00001011
And if we see 'b' again:
'b' = 00000000 00000000 00000000 00000010
it will do the following:
00000000 00000000 00000000 00001011
& (AND)
00000000 00000000 00000000 00000010
-----------------------------------
00000000 00000000 00000000 00000010
Since this number is different than '0' it means that the character
was seen before, because on that character index we already have a
1 bit value
*/
if ((checker & singleBitOnPosition) > 0) {
return false;
}
/*
Remember that
checker |= singleBitOnPosition is the same as
checker = checker | singleBitOnPosition
Sometimes it is easier to see it expanded like that.
What this achieves is that it builds the checker to have the new
value it hasnt seen, by doing an OR between checker and the value
representing this character index as a 1. e.g.
If the character is 'f' and the checker has seen 'g' and 'a', the
following will happen
'f' = 00000000 00000000 00000000 00100000
checker(seen 'a' and 'g' so far) = 00000000 00000000 00000000 01000001
00000000 00000000 00000000 00100000
| (OR)
00000000 00000000 00000000 01000001
-----------------------------------
00000000 00000000 00000000 01100001
Therefore getting a new checker as 00000000 00000000 00000000 01100001
*/
checker |= singleBitOnPosition;
}
return true;
}
str.charAt(i) - 'a' will be less than 32 (the size of the int variable checker)."checker variable as an array of bits. Let's look at an example:"str equals "test"."" ""checker == 0 (00000000000000000000000000000000)
" "
In ASCII, val = str.charAt(i) - 'a' = 116 - 97 = 19
What about 1 << val ?
1 == 00000000000000000000000000000001
1 << 19 == 00000000000010000000000000000000
checker |= (1 << val) means checker = checker | (1 << val)
so checker = 00000000000000000000000000000000 | 00000000000010000000000000000000
checker == 524288 (00000000000010000000000000000000)
checker == 524288 (00000000000010000000000000000000)
val = 101 - 97 = 4
1 == 00000000000000000000000000000001
1 << 4 == 00000000000000000000000000010000
checker |= (1 << val)
so checker = 00000000000010000000000000000000 | 00000000000000000000000000010000
checker == 524304 (00000000000010000000000000010000)
一直这样循环，直到我们通过条件在checker中找到特定字符的已设置位为止。
(checker & (1 << val)) > 0
int val = str.charAt(i) - 'a';
以下是一个程序，它使用位运算符执行与上述程序相同的操作，但该程序将适用于具有ASCII字符集中任何字符的字符串。
public static boolean isUniqueStringUsingBitVectorClass(String s) {
final int ASCII_CHARACTER_SET_SIZE = 256;
final BitSet tracker = new BitSet(ASCII_CHARACTER_SET_SIZE);
// if more than 256 ASCII characters then there can't be unique characters
if(s.length() > 256) {
return false;
}
//this will be used to keep the location of each character in String
final BitSet charBitLocation = new BitSet(ASCII_CHARACTER_SET_SIZE);
for(int i = 0; i < s.length(); i++) {
int charVal = s.charAt(i);
charBitLocation.set(charVal); //set the char location in BitSet
//check if tracker has already bit set with the bit present in charBitLocation
if(tracker.intersects(charBitLocation)) {
return false;
}
//set the tracker with new bit from charBitLocation
tracker.or(charBitLocation);
charBitLocation.clear(); //clear charBitLocation to store bit for character in the next iteration of the loop
}
return true;
}
for(int i = 0; i < s.length(); i++) { int charVal = s.charAt(i); if(tracker.get(charVal)) { return false; } tracker.set(charVal); } - zambro简单的解释（下面附有JS代码）
32位DEC64。a，则设置0th索引，对于b设置1st等等。操作摘要：
checker和index之间执行AND操作Int-32-Arrays1output == 1
checker变量在两个数组中都设置了该特定索引位output == 0
checker和index之间执行OR操作1checker假设：
a的ASCII码为97考虑96作为参考点开始计数索引下面是JavaScript源代码。
function checkIfUniqueChars (str) {
var checker = 0; // 32 or 64 bit integer variable
for (var i = 0; i< str.length; i++) {
var index = str[i].charCodeAt(0) - 96;
var bitRepresentationOfIndex = 1 << index;
if ( (checker & bitRepresentationOfIndex) > 1) {
console.log(str, false);
return false;
} else {
checker = (checker | bitRepresentationOfIndex);
}
}
console.log(str, true);
return true;
}
checkIfUniqueChars("abcdefghi"); // true
checkIfUniqueChars("aabcdefghi"); // false
checkIfUniqueChars("abbcdefghi"); // false
checkIfUniqueChars("abcdefghii"); // false
checkIfUniqueChars("abcdefghii"); // false
注意：在JS中，尽管整数为64位，但按位操作始终在32位上执行。
示例：
如果字符串是aa，则：
// checker is intialized to 32-bit-Int(0)
// therefore, checker is
checker= 00000000000000000000000000000000
i = 0
str[0] is 'a'
str[i].charCodeAt(0) - 96 = 1
checker 'AND' 32-bit-Int(1) = 00000000000000000000000000000000
Boolean(0) == false
// So, we go for the '`OR`' operation.
checker = checker OR 32-bit-Int(1)
checker = 00000000000000000000000000000001
i = 1
str[1] is 'a'
str[i].charCodeAt(0) - 96 = 1
checker= 00000000000000000000000000000001
a = 00000000000000000000000000000001
checker 'AND' 32-bit-Int(1) = 00000000000000000000000000000001
Boolean(1) == true
// We've our duplicate now
让我们逐行分解代码。
int checker = 0; 我们初始化了一个checker，它将帮助我们找到重复的值。
int val = str.charAt(i) - 'a'; 我们正在获取字符串中“i”位置处字符的ASCII值，并将其与“a”的ASCII值相减。由于假设该字符串仅包含小写字母，因此字符数限制为26个。因此，“val”的值始终为≥0。
if ((checker & (1 << val)) > 0) return false;
checker |= (1 << val);
现在是棘手的部分。让我们以字符串“abcda”为例。这应该理想地返回false。
for循环迭代1：
Checker：00000000000000000000000000000000
val：97-97=0
1 << 0：00000000000000000000000000000001
checker & (1 << val)：00000000000000000000000000000000不大于0
因此checker：00000000000000000000000000000001
for循环迭代2：
Checker：00000000000000000000000000000001
val：98-97=1
1 << 1：00000000000000000000000000000010
checker & (1 << val)：00000000000000000000000000000000不大于0
因此checker：00000000000000000000000000000011
for循环迭代3：
Checker：00000000000000000000000000000011
val：99-97=2
1 << 2：00000000000000000000000000000100
checker & (1 << val)：00000000000000000000000000000000不大于0
因此checker：00000000000000000000000000000111
for循环迭代4：
Checker：00000000000000000000000000000111
val：100-97=3
1 << 3：00000000000000000000000000001000
检查器& (1 << val) ：00000000000000000000000000000000 不大于 0
因此，检查器：00000000000000000000000000001111
For循环迭代5:
检查器：00000000000000000000000000001111
val：97-97 = 0
1 << 0: 00000000000000000000000000000001
检查器 & (1 << val) ：00000000000000000000000000000001 大于 0
因此返回false。
public static void main (String[] args)
{
//In order to understand this algorithm, it is necessary to understand the following:
//int checker = 0;
//Here we are using the primitive int almost like an array of size 32 where the only values can be 1 or 0
//Since in Java, we have 4 bytes per int, 8 bits per byte, we have a total of 4x8=32 bits to work with
//int val = str.charAt(i) - 'a';
//In order to understand what is going on here, we must realize that all characters have a numeric value
for (int i = 0; i < 256; i++)
{
char val = (char)i;
System.out.print(val);
}
//The output is something like:
// !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ ¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ
//There seems to be ~15 leading spaces that do not copy paste well, so I had to use real spaces instead
//To only print the characters from 'a' on forward:
System.out.println();
System.out.println();
for (int i=0; i < 256; i++)
{
char val = (char)i;
//char val2 = val + 'a'; //incompatible types. required: char found: int
int val2 = val + 'a'; //shift to the 'a', we must use an int here otherwise the compiler will complain
char val3 = (char)val2; //convert back to char. there should be a more elegant way of doing this.
System.out.print(val3);
}
//Notice how the following does not work:
System.out.println();
System.out.println();
for (int i=0; i < 256; i++)
{
char val = (char)i;
int val2 = val - 'a';
char val3 = (char)val2;
System.out.print(val3);
}
//I'm not sure why this spills out into 2 lines:
//EDIT I cant seem to copy this into stackoverflow!
System.out.println();
System.out.println();
//So back to our original algorithm:
//int val = str.charAt(i) - 'a';
//We convert the i'th character of the String to a character, and shift it to the right, since adding shifts to the right and subtracting shifts to the left it seems
//if ((checker & (1 << val)) > 0) return false;
//This line is quite a mouthful, lets break it down:
System.out.println(0<<0);
//00000000000000000000000000000000
System.out.println(0<<1);
//00000000000000000000000000000000
System.out.println(0<<2);
//00000000000000000000000000000000
System.out.println(0<<3);
//00000000000000000000000000000000
System.out.println(1<<0);
//00000000000000000000000000000001
System.out.println(1<<1);
//00000000000000000000000000000010 == 2
System.out.println(1<<2);
//00000000000000000000000000000100 == 4
System.out.println(1<<3);
//00000000000000000000000000001000 == 8
System.out.println(2<<0);
//00000000000000000000000000000010 == 2
System.out.println(2<<1);
//00000000000000000000000000000100 == 4
System.out.println(2<<2);
// == 8
System.out.println(2<<3);
// == 16
System.out.println("3<<0 == "+(3<<0));
// != 4 why 3???
System.out.println(3<<1);
//00000000000000000000000000000011 == 3
//shift left by 1
//00000000000000000000000000000110 == 6
System.out.println(3<<2);
//00000000000000000000000000000011 == 3
//shift left by 2
//00000000000000000000000000001100 == 12
System.out.println(3<<3);
// 24
//It seems that the - 'a' is not necessary
//Back to if ((checker & (1 << val)) > 0) return false;
//(1 << val means we simply shift 1 by the numeric representation of the current character
//the bitwise & works as such:
System.out.println();
System.out.println();
System.out.println(0&0); //0
System.out.println(0&1); //0
System.out.println(0&2); //0
System.out.println();
System.out.println();
System.out.println(1&0); //0
System.out.println(1&1); //1
System.out.println(1&2); //0
System.out.println(1&3); //1
System.out.println();
System.out.println();
System.out.println(2&0); //0
System.out.println(2&1); //0 0010 & 0001 == 0000 = 0
System.out.println(2&2); //2 0010 & 0010 == 2
System.out.println(2&3); //2 0010 & 0011 = 0010 == 2
System.out.println();
System.out.println();
System.out.println(3&0); //0 0011 & 0000 == 0
System.out.println(3&1); //1 0011 & 0001 == 0001 == 1
System.out.println(3&2); //2 0011 & 0010 == 0010 == 2, 0&1 = 0 1&1 = 1
System.out.println(3&3); //3 why?? 3 == 0011 & 0011 == 3???
System.out.println(9&11); // should be... 1001 & 1011 == 1001 == 8+1 == 9?? yay!
//so when we do (1 << val), we take 0001 and shift it by say, 97 for 'a', since any 'a' is also 97
//why is it that the result of bitwise & is > 0 means its a dupe?
//lets see..
//0011 & 0011 is 0011 means its a dupe
//0000 & 0011 is 0000 means no dupe
//0010 & 0001 is 0011 means its no dupe
//hmm
//only when it is all 0000 means its no dupe
//so moving on:
//checker |= (1 << val)
//the |= needs exploring:
int x = 0;
int y = 1;
int z = 2;
int a = 3;
int b = 4;
System.out.println("x|=1 "+(x|=1)); //1
System.out.println(x|=1); //1
System.out.println(x|=1); //1
System.out.println(x|=1); //1
System.out.println(x|=1); //1
System.out.println(y|=1); // 0001 |= 0001 == ?? 1????
System.out.println(y|=2); // ??? == 3 why??? 0001 |= 0010 == 3... hmm
System.out.println(y); //should be 3??
System.out.println(y|=1); //already 3 so... 0011 |= 0001... maybe 0011 again? 3?
System.out.println(y|=2); //0011 |= 0010..... hmm maybe.. 0011??? still 3? yup!
System.out.println(y|=3); //0011 |= 0011, still 3
System.out.println(y|=4); //0011 |= 0100.. should be... 0111? so... 11? no its 7
System.out.println(y|=5); //so we're at 7 which is 0111, 0111 |= 0101 means 0111 still 7
System.out.println(b|=9); //so 0100 |= 1001 is... seems like xor?? or just or i think, just or... so its 1101 so its 13? YAY!
//so the |= is just a bitwise OR!
}
public static boolean isUniqueChars(String str) {
int checker = 0;
for (int i = 0; i < str.length(); ++i) {
int val = str.charAt(i) - 'a'; //the - 'a' is just smoke and mirrors! not necessary!
if ((checker & (1 << val)) > 0) return false;
checker |= (1 << val);
}
return true;
}
public static boolean is_unique(String input)
{
int using_int_as_32_flags = 0;
for (int i=0; i < input.length(); i++)
{
int numeric_representation_of_char_at_i = input.charAt(i);
int using_0001_and_shifting_it_by_the_numeric_representation = 1 << numeric_representation_of_char_at_i; //here we shift the bitwise representation of 1 by the numeric val of the character
int result_of_bitwise_and = using_int_as_32_flags & using_0001_and_shifting_it_by_the_numeric_representation;
boolean already_bit_flagged = result_of_bitwise_and > 0; //needs clarification why is it that the result of bitwise & is > 0 means its a dupe?
if (already_bit_flagged)
return false;
using_int_as_32_flags |= using_0001_and_shifting_it_by_the_numeric_representation;
}
return true;
}
之前的帖子已经很好地解释了代码块的功能，我想使用Java数据结构BitSet来添加我的简单解决方案：
private static String isUniqueCharsUsingBitSet(String string) {
BitSet bitSet =new BitSet();
for (int i = 0; i < string.length(); ++i) {
int val = string.charAt(i);
if(bitSet.get(val)) return "NO";
bitSet.set(val);
}
return "YES";
}