给定两个字符串A和B ，任务是将字符串A 拆分为最少数量的子字符串，使得每个子字符串都在字符串B 中。
注意：如果没有办法分割字符串，则打印-1
例子：
Input: A = “abcdab”, B = “dabc”
Output: 2
Explanation:
The two substrings of A which is also present in B are –
{“abc”, “dab”}
Input: A = “abcde”, B = “edcb”
Output: -1
Explanation:
There is no way to split the string A into substring
Such that each string is also present in the B.
方法：
- 构造 B 的每个子串的 trie。
- 之后，我们将使用动态规划来找到打破字符串A 的最小部分数，使得每个部分都是 B 的子字符串。
动态规划中的递归关系：
dp[i] = minimum number of parts to break the string A up to ith prefix.
dp[0] = 0
for i in {0, S1.length}
for j in {i, S1.length}
if(S1[i, ... j] is found in trie
dp[j] = min(dp[j], dp[i] + 1);
else
break;
dp[S1.length] is the
minimum number of parts.
下面是上述方法的实现：
C++
// C++ implementation to split the
// string into minimum number of
// parts such that each part is also
// present in the another string
#include
using namespace std;
const int INF = 1e9 + 9;
// Node of Trie
struct TrieNode {
TrieNode* child[26] = { NULL };
};
// Function to insert a node in the
// Trie Data Structure
void insert(int idx, string& s,
TrieNode* root)
{
TrieNode* temp = root;
for (int i = idx; i < s.length(); i++) {
// Inserting every character from idx
// till end to string into trie
if (temp->child[s[i] - 'a'] == NULL)
// if there is no edge corresponding
// to the ith character,
// then make a new node
temp->child[s[i] - 'a'] = new TrieNode;
temp = temp->child[s[i] - 'a'];
}
}
// Function to find the minimum
// number of parts such that each
// part is present into another string
int minCuts(string S1, string S2)
{
int n1 = S1.length();
int n2 = S2.length();
// Making a new trie
TrieNode* root = new TrieNode;
for (int i = 0; i < n2; i++) {
// Inserting every substring
// of S2 in trie
insert(i, S2, root);
}
// Creating dp array and
// init it with infinity
vector dp(n1 + 1, INF);
// Base Case
dp[0] = 0;
for (int i = 0; i < n1; i++) {
// Starting the cut from ith character
// taking temporary node pointer
// for checking whether the substring
// [i, j) is present in trie of not
TrieNode* temp = root;
for (int j = i + 1; j <= n1; j++) {
if (temp->child[S1[j - 1] - 'a'] == NULL)
// if the jth character is not in trie
// we'll break
break;
// Updating the the ending of
// jth character with dp[i] + 1
dp[j] = min(dp[j], dp[i] + 1);
// Descending the trie pointer
temp = temp->child[S1[j - 1] - 'a'];
}
}
// Answer not possible
if (dp[n1] >= INF)
return -1;
else
return dp[n1];
}
// Driver Code
int main()
{
string S1 = "abcdab";
string S2 = "dabc";
cout << minCuts(S1, S2);
} Java
// Java implementation to split the
// String into minimum number of
// parts such that each part is also
// present in the another String
import java.util.*;
class GFG{
static int INF = (int)(1e9 + 9);
// Node of Trie
static class TrieNode
{
TrieNode []child = new TrieNode[26];
};
// Function to insert a node in the
// Trie Data Structure
static void insert(int idx, String s,
TrieNode root)
{
TrieNode temp = root;
for(int i = idx; i < s.length(); i++)
{
// Inserting every character from idx
// till end to String into trie
if (temp.child[s.charAt(i) - 'a'] == null)
// If there is no edge corresponding
// to the ith character,
// then make a new node
temp.child[s.charAt(i) - 'a'] = new TrieNode();
temp = temp.child[s.charAt(i) - 'a'];
}
}
// Function to find the minimum
// number of parts such that each
// part is present into another String
static int minCuts(String S1, String S2)
{
int n1 = S1.length();
int n2 = S2.length();
// Making a new trie
TrieNode root = new TrieNode();
for(int i = 0; i < n2; i++)
{
// Inserting every subString
// of S2 in trie
insert(i, S2, root);
}
// Creating dp array and
// init it with infinity
int []dp = new int[n1 + 1];
Arrays.fill(dp, INF);
// Base Case
dp[0] = 0;
for(int i = 0; i < n1; i++)
{
// Starting the cut from ith character
// taking temporary node pointer
// for checking whether the subString
// [i, j) is present in trie of not
TrieNode temp = root;
for(int j = i + 1; j <= n1; j++)
{
if (temp.child[S1.charAt(j - 1) - 'a'] == null)
// If the jth character is not in trie
// we'll break
break;
// Updating the the ending of
// jth character with dp[i] + 1
dp[j] = Math.min(dp[j], dp[i] + 1);
// Descending the trie pointer
temp = temp.child[S1.charAt(j - 1) - 'a'];
}
}
// Answer not possible
if (dp[n1] >= INF)
return -1;
else
return dp[n1];
}
// Driver Code
public static void main(String[] args)
{
String S1 = "abcdab";
String S2 = "dabc";
System.out.print(minCuts(S1, S2));
}
}
// This code is contributed by Rajput-JiPython3
# Python3 implementation to split the
# string into minimum number of
# parts such that each part is also
# present in the another string
INF = 1e9 + 9
# Node of Trie
class TrieNode():
def __init__(self):
self.child = [None] * 26
# Function to insert a node in the
# Trie Data Structure
def insert(idx, s, root):
temp = root
for i in range(idx, len(s)):
# Inserting every character from idx
# till end to string into trie
if temp.child[ord(s[i]) -
ord('a')] == None:
# If there is no edge corresponding
# to the ith character,
# then make a new node
temp.child[ord(s[i]) -
ord('a')] = TrieNode()
temp = temp.child[ord(s[i]) - ord('a')]
# Function to find the minimum
# number of parts such that each
# part is present into another string
def minCuts(S1, S2):
n1 = len(S1)
n2 = len(S2)
# Making a new trie
root = TrieNode()
for i in range(n2):
# Inserting every substring
# of S2 in trie
insert(i, S2, root)
# Creating dp array and
# init it with infinity
dp = [INF] * (n1 + 1)
# Base Case
dp[0] = 0
for i in range(n1):
# Starting the cut from ith character
# taking temporary node pointer
# for checking whether the substring
# [i, j) is present in trie of not
temp = root
for j in range(i + 1, n1 + 1):
if temp.child[ord(S1[j - 1]) -
ord('a')] == None:
# If the jth character is not
# in trie we'll break
break
# Updating the the ending of
# jth character with dp[i] + 1
dp[j] = min(dp[j], dp[i] + 1)
# Descending the trie pointer
temp = temp.child[ord(S1[j - 1]) -
ord('a')]
# Answer not possible
if dp[n1] >= INF:
return -1
else:
return dp[n1]
# Driver Code
S1 = "abcdab"
S2 = "dabc"
print(minCuts(S1, S2))
# This code is contributed by Shivam SinghC#
// C# implementation to split the
// String into minimum number of
// parts such that each part is also
// present in the another String
using System;
class GFG{
static int INF = (int)(1e9 + 9);
// Node of Trie
class TrieNode
{
public TrieNode []child =
new TrieNode[26];
};
// Function to insert a node in the
// Trie Data Structure
static void insert(int idx, String s,
TrieNode root)
{
TrieNode temp = root;
for(int i = idx; i < s.Length; i++)
{
// Inserting every character from idx
// till end to String into trie
if (temp.child[s[i] - 'a'] == null)
// If there is no edge corresponding
// to the ith character,
// then make a new node
temp.child[s[i] - 'a'] =
new TrieNode();
temp = temp.child[s[i] - 'a'];
}
}
// Function to find the minimum
// number of parts such that each
// part is present into another String
static int minCuts(String S1, String S2)
{
int n1 = S1.Length;
int n2 = S2.Length;
// Making a new trie
TrieNode root = new TrieNode();
for(int i = 0; i < n2; i++)
{
// Inserting every subString
// of S2 in trie
insert(i, S2, root);
}
// Creating dp array and
// init it with infinity
int []dp = new int[n1 + 1];
for(int i = 0; i <= n1; i++)
dp[i] = INF;
// Base Case
dp[0] = 0;
for(int i = 0; i < n1; i++)
{
// Starting the cut from ith character
// taking temporary node pointer
// for checking whether the subString
// [i, j) is present in trie of not
TrieNode temp = root;
for(int j = i + 1; j <= n1; j++)
{
if (temp.child[S1[j-1] - 'a'] == null)
// If the jth character is not in trie
// we'll break
break;
// Updating the the ending of
// jth character with dp[i] + 1
dp[j] = Math.Min(dp[j], dp[i] + 1);
// Descending the trie pointer
temp = temp.child[S1[j - 1] - 'a'];
}
}
// Answer not possible
if (dp[n1] >= INF)
return -1;
else
return dp[n1];
}
// Driver Code
public static void Main(String[] args)
{
String S1 = "abcdab";
String S2 = "dabc";
Console.Write(minCuts(S1, S2));
}
}
// This code is contributed by shikhasingrajput输出：
2
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