鉴于小写字母字符长度为n的字符串，我们需要计算这个字符串的不同子的总数。
例子：
Input : str = “ababa”
Output : 10
Total number of distinct substring are 10, which are,
"", "a", "b", "ab", "ba", "aba", "bab", "abab", "baba"
and "ababa"
这个想法是创建给定字符串所有后缀的Trie。一旦收缩了Trie，我们的答案就是构造的Trie中的节点总数。例如，下图表示“ ababa”的所有后缀的Trie。节点总数为10，这就是我们的答案。
这是如何运作的?
- Trie的每个根到节点路径代表Trie中存在的单词的前缀。在这里，我们的单词是后缀。因此，每个节点都代表后缀的前缀。
- 字符串“ str”的每个子字符串“ str”后缀的前缀。
下面是基于以上思想的实现。
C++
// A C++ program to find the count of distinct substring
// of a string using trie data structure
#include
#define MAX_CHAR 26
using namespace std;
// A Suffix Trie (A Trie of all suffixes) Node
class SuffixTrieNode
{
public:
SuffixTrieNode *children[MAX_CHAR];
SuffixTrieNode() // Constructor
{
// Initialize all child pointers as NULL
for (int i = 0; i < MAX_CHAR; i++)
children[i] = NULL;
}
// A recursive function to insert a suffix of the s
// in subtree rooted with this node
void insertSuffix(string suffix);
};
// A Trie of all suffixes
class SuffixTrie
{
SuffixTrieNode *root;
int _countNodesInTrie(SuffixTrieNode *);
public:
// Constructor (Builds a trie of suffies of the given text)
SuffixTrie(string s)
{
root = new SuffixTrieNode();
// Consider all suffixes of given string and insert
// them into the Suffix Trie using recursive function
// insertSuffix() in SuffixTrieNode class
for (int i = 0; i < s.length(); i++)
root->insertSuffix(s.substr(i));
}
// method to count total nodes in suffix trie
int countNodesInTrie() { return _countNodesInTrie(root); }
};
// A recursive function to insert a suffix of the s in
// subtree rooted with this node
void SuffixTrieNode::insertSuffix(string s)
{
// If string has more characters
if (s.length() > 0)
{
// Find the first character and convert it
// into 0-25 range.
char cIndex = s.at(0) - 'a';
// If there is no edge for this character,
// add a new edge
if (children[cIndex] == NULL)
children[cIndex] = new SuffixTrieNode();
// Recur for next suffix
children[cIndex]->insertSuffix(s.substr(1));
}
}
// A recursive function to count nodes in trie
int SuffixTrie::_countNodesInTrie(SuffixTrieNode* node)
{
// If all characters of pattern have been processed,
if (node == NULL)
return 0;
int count = 0;
for (int i = 0; i < MAX_CHAR; i++)
{
// if children is not NULL then find count
// of all nodes in this subtrie
if (node->children[i] != NULL)
count += _countNodesInTrie(node->children[i]);
}
// return count of nodes of subtrie and plus
// 1 because of node's own count
return (1 + count);
}
// Returns count of distinct substrings of str
int countDistinctSubstring(string str)
{
// Construct a Trie of all suffixes
SuffixTrie sTrie(str);
// Return count of nodes in Trie of Suffixes
return sTrie.countNodesInTrie();
}
// Driver program to test above function
int main()
{
string str = "ababa";
cout << "Count of distinct substrings is "
<< countDistinctSubstring(str);
return 0;
} Java
// A Java program to find the count of distinct substring
// of a string using trie data structure
public class Suffix
{
// A Suffix Trie (A Trie of all suffixes) Node
static class SuffixTrieNode
{
static final int MAX_CHAR = 26;
SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];
SuffixTrieNode() // Constructor
{
// Initialize all child pointers as NULL
for (int i = 0; i < MAX_CHAR; i++)
children[i] = null;
}
// A recursive function to insert a suffix of the s in
// subtree rooted with this node
void insertSuffix(String s)
{
// If string has more characters
if (s.length() > 0)
{
// Find the first character and convert it
// into 0-25 range.
char cIndex = (char) (s.charAt(0) - 'a');
// If there is no edge for this character,
// add a new edge
if (children[cIndex] == null)
children[cIndex] = new SuffixTrieNode();
// Recur for next suffix
children[cIndex].insertSuffix(s.substring(1));
}
}
}
// A Trie of all suffixes
static class Suffix_trie
{
static final int MAX_CHAR = 26;
SuffixTrieNode root;
// Constructor (Builds a trie of suffies of the given text)
Suffix_trie(String s) {
root = new SuffixTrieNode();
// Consider all suffixes of given string and insert
// them into the Suffix Trie using recursive function
// insertSuffix() in SuffixTrieNode class
for (int i = 0; i < s.length(); i++)
root.insertSuffix(s.substring(i));
}
// A recursive function to count nodes in trie
int _countNodesInTrie(SuffixTrieNode node)
{
// If all characters of pattern have been processed,
if (node == null)
return 0;
int count = 0;
for (int i = 0; i < MAX_CHAR; i++) {
// if children is not NULL then find count
// of all nodes in this subtrie
if (node.children[i] != null)
count += _countNodesInTrie(node.children[i]);
}
// return count of nodes of subtrie and plus
// 1 because of node's own count
return (1 + count);
}
// method to count total nodes in suffix trie
int countNodesInTrie()
{
return _countNodesInTrie(root);
}
}
// Returns count of distinct substrings of str
static int countDistinctSubstring(String str)
{
// Construct a Trie of all suffixes
Suffix_trie sTrie = new Suffix_trie(str);
// Return count of nodes in Trie of Suffixes
return sTrie.countNodesInTrie();
}
// Driver program to test above function
public static void main(String args[])
{
String str = "ababa";
System.out.println("Count of distinct substrings is "
+ countDistinctSubstring(str));
}
}
// This code is contributed by Sumit GhoshC#
// C# program to find the count of distinct substring
// of a string using trie data structure
using System;
public class Suffix
{
// A Suffix Trie (A Trie of all suffixes) Node
public class SuffixTrieNode
{
static readonly int MAX_CHAR = 26;
public SuffixTrieNode[] children = new SuffixTrieNode[MAX_CHAR];
public SuffixTrieNode() // Constructor
{
// Initialize all child pointers as NULL
for (int i = 0; i < MAX_CHAR; i++)
children[i] = null;
}
// A recursive function to insert a suffix of the s in
// subtree rooted with this node
public void insertSuffix(String s)
{
// If string has more characters
if (s.Length > 0)
{
// Find the first character and convert it
// into 0-25 range.
char cIndex = (char) (s[0] - 'a');
// If there is no edge for this character,
// add a new edge
if (children[cIndex] == null)
children[cIndex] = new SuffixTrieNode();
// Recur for next suffix
children[cIndex].insertSuffix(s.Substring(1));
}
}
}
// A Trie of all suffixes
public class Suffix_trie
{
static readonly int MAX_CHAR = 26;
public SuffixTrieNode root;
// Constructor (Builds a trie of suffies of the given text)
public Suffix_trie(String s)
{
root = new SuffixTrieNode();
// Consider all suffixes of given string and insert
// them into the Suffix Trie using recursive function
// insertSuffix() in SuffixTrieNode class
for (int i = 0; i < s.Length; i++)
root.insertSuffix(s.Substring(i));
}
// A recursive function to count nodes in trie
public int _countNodesInTrie(SuffixTrieNode node)
{
// If all characters of pattern have been processed,
if (node == null)
return 0;
int count = 0;
for (int i = 0; i < MAX_CHAR; i++)
{
// if children is not NULL then find count
// of all nodes in this subtrie
if (node.children[i] != null)
count += _countNodesInTrie(node.children[i]);
}
// return count of nodes of subtrie and plus
// 1 because of node's own count
return (1 + count);
}
// method to count total nodes in suffix trie
public int countNodesInTrie()
{
return _countNodesInTrie(root);
}
}
// Returns count of distinct substrings of str
static int countDistinctSubstring(String str)
{
// Construct a Trie of all suffixes
Suffix_trie sTrie = new Suffix_trie(str);
// Return count of nodes in Trie of Suffixes
return sTrie.countNodesInTrie();
}
// Driver program to test above function
public static void Main(String []args)
{
String str = "ababa";
Console.WriteLine("Count of distinct substrings is "
+ countDistinctSubstring(str));
}
}
// This code contributed by Rajput-Ji输出：
Count of distinct substrings is 10
我们将很快讨论基于后缀数组和后缀树的方法。