4646
4747<!-- 这里可写通用的实现逻辑 -->
4848
49+ ** 方法一:位运算**
50+ 51+ 题目需要我们找到两个没有公共字母的字符串,使得它们的长度乘积最大。我们可以将每个字符串用一个二进制数 $mask[ i] $ 表示,这个二进制数的每一位表示字符串中是否含有某个字母。如果两个字符串没有公共字母,那么这两个字符串对应的二进制数的按位与的结果为 0ドル,ドル即 $mask[ i] \& mask[ j] = 0$。
52+ 53+ 我们遍历每个字符串,对于当前遍历到的字符串 $words[ i] ,ドル我们先算出对应的二进制数 $mask[ i] ,ドル然后再遍历 $j \in [ 0, i)$ 的所有字符串 $words[ j] ,ドル检查 $mask[ i] \& mask[ j] = 0$ 是否成立,如果成立就更新答案为 $\max(ans, |words[ i] | \times |words[ j] |)$。
54+ 55+ 遍历结束后,返回答案即可。
56+ 57+ 时间复杂度 $O(n^2 + L),ドル空间复杂度 $O(n)$。其中 $n$ 是字符串数组 $words$ 的长度,而 $L$ 是字符串数组所有字符串的长度之和。
58+ 4959<!-- tabs:start -->
5060
5161### ** Python3**
5565``` python
5666class Solution :
5767 def maxProduct (self words : List[str ]) -> int :
58- n = len (words)
59- mask = [0 ] * n
60- for i, word in enumerate (words):
61- for ch in word:
62- mask[i] |= 1 << (ord (ch) - ord (' a'
68+ mask = [0 ] * len (words)
69+ ans = 0
70+ for i, s in enumerate (words):
71+ for c in s:
72+ mask[i] |= 1 << (ord (c) - ord (" a"
73+ for j, t in enumerate (words[:i]):
74+ if (mask[i] & mask[j]) == 0 :
75+ ans = max (ans, len (s) * len (t))
76+ return ans
77+ ```
78+ 79+ ``` python
80+ class Solution :
81+ def maxProduct (self words : List[str ]) -> int :
82+ mask = defaultdict(int )
6383 ans = 0
64- for i in range (n - 1 ):
65- for j in range (i + 1 , n):
66- if mask[i] & mask[j] == 0 :
67- ans = max (ans, len (words[i]) * len (words[j]))
84+ for s in words:
85+ a = len (s)
86+ x = 0
87+ for c in s:
88+ x |= 1 << (ord (c) - ord (" a"
89+ for y, b in mask.items():
90+ if (x & y) == 0 :
91+ ans = max (ans, a * b)
92+ mask[x] = max (mask[x], a)
6893 return ans
6994```
7095
@@ -76,19 +101,41 @@ class Solution:
76101class Solution {
77102 public int maxProduct (String [] words ) {
78103 int n = words. length;
79- int [] masks = new int [n];
104+ int [] mask = new int [n];
105+ int ans = 0 ;
80106 for (int i = 0 ; i < n; ++ i) {
81107 for (char c : words[i]. toCharArray()) {
82- masks[i] |= (1 << (c - ' a'
108+ mask[i] |= 1 << (c - ' a'
109+ }
110+ for (int j = 0 ; j < i; ++ j) {
111+ if ((mask[i] & mask[j]) == 0 ) {
112+ ans = Math . max(ans, words[i]. length() * words[j]. length());
113+ }
83114 }
84115 }
116+ return ans;
117+ }
118+ }
119+ ```
120+ 121+ ``` java
122+ class Solution {
123+ public int maxProduct (String [] words ) {
124+ Map<Integer , Integer > mask = new HashMap<> ();
85125 int ans = 0 ;
86- for (int i = 0 ; i < n - 1 ; ++ i) {
87- for (int j = i + 1 ; j < n; ++ j) {
88- if ((masks[i] & masks[j]) == 0 ) {
89- ans = Math . max(ans, words[i]. length() * words[j]. length());
126+ for (var s : words) {
127+ int a = s. length();
128+ int x = 0 ;
129+ for (char c : s. toCharArray()) {
130+ x |= 1 << (c - ' a'
131+ }
132+ for (var e : mask. entrySet()) {
133+ int y = e. getKey(), b = e. getValue();
134+ if ((x & y) == 0 ) {
135+ ans = Math . max(ans, a * b);
90136 }
91137 }
138+ mask. merge(x, a, Math :: max);
92139 }
93140 return ans;
94141 }
@@ -102,15 +149,43 @@ class Solution {
102149public:
103150 int maxProduct(vector<string >& words) {
104151 int n = words.size();
105- vector<int > mask(n);
106- for (int i = 0; i < n; ++i)
107- for (char ch : words[ i] )
108- mask[ i] |= 1 << (ch - 'a');
152+ int mask[ n] ;
153+ memset(mask, 0, sizeof(mask));
109154 int ans = 0;
110- for (int i = 0; i < n - 1; ++i)
111- for (int j = i + 1; j < n; ++j)
112- if (!(mask[ i] & mask[ j] ))
155+ for (int i = 0; i < n; ++i) {
156+ for (char& c : words[ i] ) {
157+ mask[ i] |= 1 << (c - 'a');
158+ }
159+ for (int j = 0; j < i; ++j) {
160+ if ((mask[ i] & mask[ j] ) == 0) {
113161 ans = max(ans, (int) (words[ i] .size() * words[ j] .size()));
162+ }
163+ }
164+ }
165+ return ans;
166+ }
167+ };
168+ ```
169+
170+ ```cpp
171+ class Solution {
172+ public:
173+ int maxProduct(vector<string>& words) {
174+ unordered_map<int, int> mask;
175+ int ans = 0;
176+ for (auto& s : words) {
177+ int a = s.size();
178+ int x = 0;
179+ for (char& c : s) {
180+ x |= 1 << (c - 'a');
181+ }
182+ for (auto& [y, b] : mask) {
183+ if ((x & y) == 0) {
184+ ans = max(ans, a * b);
185+ }
186+ }
187+ mask[x] = max(mask[x], a);
188+ }
114189 return ans;
115190 }
116191};
@@ -119,23 +194,82 @@ public:
119194### ** Go**
120195
121196``` go
122- func maxProduct(words []string) int {
197+ func maxProduct (words []string ) ( ans int ) {
123198 n := len (words)
124199 mask := make ([]int , n)
125- for i, word := range words {
126- for _, c := range word {
127- mask[i] |= ( 1 << (c - 'a') )
200+ for i , s := range words {
201+ for _ , c := range s {
202+ mask[i] |= 1 << (c - ' a'
128203 }
129- }
130- ans := 0
131- for i := 0; i < n-1; i++ {
132- for j := i + 1; j < n; j++ {
204+ for j , t := range words[:i] {
133205 if mask[i]&mask[j] == 0 {
134- ans = max(ans, len(words[i])*len(words[j]))
206+ ans = max (ans, len (s)*len (t))
207+ }
208+ }
209+ }
210+ return
211+ }
212+ ```
213+ 214+ ``` go
215+ func maxProduct (words []string ) (ans int ) {
216+ mask := map [int ]int {}
217+ for _ , s := range words {
218+ a := len (s)
219+ x := 0
220+ for _ , c := range s {
221+ x |= 1 << (c - ' a'
222+ }
223+ for y , b := range mask {
224+ if x&y == 0 {
225+ ans = max (ans, a*b)
135226 }
136227 }
228+ mask[x] = max (mask[x], a)
137229 }
138- return ans
230+ return
231+ }
232+ ```
233+ 234+ ### ** TypeScript**
235+ 236+ ``` ts
237+ function maxProduct(words : string []): number {
238+ const = words .length ;
239+ const : number [] = Array (n ).fill (0 );
240+ let ans = 0 ;
241+ for (let i = 0 ; i < n ; ++ i ) {
242+ for (const of words [i ]) {
243+ mask [i ] |= 1 << (c .charCodeAt (0 ) - ' a' charCodeAt (0 ));
244+ }
245+ for (let j = 0 ; j < i ; ++ j ) {
246+ if ((mask [i ] & mask [j ]) === 0 ) {
247+ ans = Math .max (ans , words [i ].length * words [j ].length );
248+ }
249+ }
250+ }
251+ return ans ;
252+ }
253+ ```
254+ 255+ ``` ts
256+ function maxProduct(words : string []): number {
257+ const : Map <number , number > = new Map ();
258+ let ans = 0 ;
259+ for (const of words ) {
260+ const = s .length ;
261+ let x = 0 ;
262+ for (const of s ) {
263+ x |= 1 << (c .charCodeAt (0 ) - ' a' charCodeAt (0 ));
264+ }
265+ for (const of mask .entries ()) {
266+ if ((x & y ) === 0 ) {
267+ ans = Math .max (ans , a * b );
268+ }
269+ }
270+ mask .set (x , Math .max (mask .get (x ) || 0 , a ));
271+ }
272+ return ans ;
139273}
140274```
141275
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