Strings
- Reloaded -
20231019 校隊培訓簡報
32717 高翊恩
關於講師
- OJ handle: Pring, PringDeSu
- 左閉右開教
- 終於沒有複賽燒雞了
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
Hash
Hash
- 把一個字串當作是一個超級大的數字
- 利用「27進位法」，\(a\rightarrow1,b\rightarrow2,\dots\)
- 因為會溢位所以取個模
當兩個字串所得的大數字相等時，這兩個字串一定相等。
當兩個字串所得的數字取模後相等，視為這兩個字串相等。
Facts
- 算 hash 值：\(O(n)\)
- 預處理（前綴和）後算任意子字串 hash 值：\(O(n),O(1)\)
- 字串匹配問題：\(O(n)\)
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
KMP
CPS
若一個字串有一組前後綴滿足他們兩個相同，則放入 CPS 集合中
\(s=abbabba\)
\(s.CPS=\{abbabba,abba,a,0\}\)
[0]
[1]
[2]
[3]
\(s.CPS[2]=S.CPS[1].CPS[1]\)
\(\pi\)陣列
對一個字串的每一個前綴\(p_i\)都記錄\(p_i.CPS[1]\)的長度
| 0 | "" | -1 |
| 1 | "a" | 0 |
| 2 | "ab" | 0 |
| 3 | "abb" | 0 |
| 4 | "abba" | 1 |
| 5 | "abbab" | 2 |
| 6 | "abbabb" | 3 |
| 7 | "abbabba" | 4 |
製造\(\pi\)陣列
使用DP
\(\$\$\$\$\$\$\$\$\$\ \$\)
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
如果有那麼一個CPS的話…
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
如果有那麼一個CPS的話…
綠線一定會相等！
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
窮舉這些相等的綠線，看他們下一個字元是否相等
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
窮舉這些相等的綠線，看他們下一個字元是否相等
我們只要找最長的紅線，所以綠線從長窮舉到短，找到為止
製造\(\pi\)陣列
\(\$\$\$\$\$\$\$\$\$\ \$\)
窮舉這些相等的綠線，看他們下一個字元是否相等
我們只要找最長的紅線，所以綠線從長窮舉到短，找到為止
綠線是前一個字串的CPS[1], CPS[2], ...
如何找\(CPS\)
\(s.CPS[2]=s.CPS[1].CPS[1]\)
\(s.CPS[2].size()=\pi[\pi[s.size()]]\)
將綠線的長度利用\(j\)存起來
就可以透過\(j\leftarrow\pi[j]\)的方式迭代每個CPS
時間複雜度：均攤\(O(n)\)
CODE
void KMP(string s, int *pi) {
int n = s.size();
pi[0] = -1;
pi[1] = 0;
for (int i = 1; i < s.size(); i++) {
int j = pi[i];
while (j >= 0 && s[j] != s[i]) j = pi[j];
pi[i + 1] = j + 1;
}
}
字串匹配
\(aabaaabab\)
\(aabab\)
\(aab\)
\(aabab\)
字串匹配
\(aabaaabab\)
\(aabab\)
\(aab\)
\(aabab\)
每次配爛時，就跳到「當前字串」的CPS[1]繼續試試看
複雜度：\(O(n)\)
CODE
void matching(string s, string t, int *pi) {
int now = 0;
for (int i = 0; i < s.size(); i++) {
if (now == t.size()) {
cout << "MATCHED: pos " << i - t.size() << endl;
now = pi[now];
}
while (now >= 0 && s[i] != t[now]) now = pi[now];
now++;
}
if (now == t.size()) {
cout << "MATCHED: pos " << s.size() - t.size() << endl;
}
}
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
| Word Combinations |
| String Matching |
| Finding Borders |
| Finding Periods |
| Minimal Rotation |
| Longest Palindrome |
| Required Substring |
| Palindrome Queries |
| Finding Patterns |
| Counting Patterns |
| Pattern Positions |
| Distinct Substrings |
| Repeating Substring |
| String Functions |
| Substring Order I |
| Substring Order II |
| Substring Distribution |
strings
By pringdesu
strings
- 156
