LeetCode139：Word Break

题目：

Given a string s and a dictionary of words dict, determine if s can be segmented into a space-separated sequence of one or more dictionary words.

For example, given
s = "leetcode",
dict = ["leet", "code"].

Return true because "leetcode" can be segmented as "leet code".

解题思路：

这是一道DP题，说实话，本人也是算法方面的菜鸟一枚，关于DP方面的题，还不太会解，没办法，只能多练习了。

这里采用DP中的两种方式实现：自顶向下和自底向上。

dp[i]表示前i个字符能否进行Wordbreak。当求解dp[i]时，可利用已经求解的dp[i-1],dp[i-2]…dp[1],dp[0]进行求解。

对于dp[n]的求解，我们可以将n个字符进行切分求解，分为前i个字符和后n-i个字符，i可以为（0,1,2,3,4…n-1)

假设i为1时，可根据dp[i]和后面的n-1个字符组成的单词是否在dict中来判断dp[n]，只要i（0,1,2,3,4…n-1)其中一种

情况为真，则dp[n]为true，表示可以进行workbreak。

实现代码：

#include <iostream>
#include <string>
#include <vector>
#include <unordered_set>
using namespace std;

/*
Given a string s and a dictionary of words dict, determine if s can be segmented into a space-separated sequence of one or more dictionary words.

For example, given
s = "leetcode",
dict = ["leet", "code"].

Return true because "leetcode" can be segmented as "leet code".
*/
class Solution {
public:
    bool wordBreak(string s, unordered_set<string> &dict) {
        if(s.size() ==  || dict.size() == )
            return false;
        int len = s.size();
        vector<bool> dp(len+, false);//保存状态，dp[i]表示前i个字符是否可以进行wordBread
        dp[] = true;
        for(int i = ; i <= len; i++)
            for(int j = ; j < i; j++)
            {
                if(dp[j] && dict.count(s.substr(j, i-j)) == )//对前i个字符进行切分时，只要有一种情况为true，则dp[i]=true
                {
                    dp[i] = true;
                    break;
                }
            }
        return dp[len];

    }

    bool wordBreak2(string s, unordered_set<string> &dict) {
        if(s.size() ==  || dict.size() == )
            return false;
        int len = s.size();
        vector<bool> dp(len+, false);//保存状态，dp[i]表示前i个字符是否可以进行wordBread
        dp[] = true;
        for(int i = ; i < len; i++)
            if(dp[i])
            {
                for(int j = ; j <= len-i; j++)
                    if(dict.count(s.substr(i, j)) == )
                        dp[i+j] = true;
            }

        return dp[len];

    }

    //DP：自顶向下，
    int wordBreak3_core(string s, unordered_set<string> &dict, int *dp)
    {
        int len = s.size();
        if(dp[len] >= )
            return dp[len];//如果值已经改变即不再是初始值，说明dp[len]已经求得，直接返回即可，不必再求
        int isBreak;
        if(len == )
            isBreak = ;
        else
        {
            int ret = ;
            for(int i = ; i < len; i++)
            {
                if(wordBreak3_core(s.substr(, i), dict, dp) ==  && dict.count(s.substr(i, len-i)) == )
                {
                    ret = ;
                    break;
                }

            }
            isBreak = ret;

        }
        dp[len] = isBreak;
        return isBreak;
    }
    //DP：自顶向下，
    bool wordBreak3(string s, unordered_set<string> &dict)
    {
        if(s.size() ==  || dict.size() == )
            return false;
        int len = s.size();
        int *dp = new int[len+];//保存状态，dp[i]表示前i个字符是否可以进行wordBread
        for(int i = ; i <= len; i++)
            dp[i] = -;//每个状态进行初始化
        int ret = wordBreak3_core(s, dict, dp);
        delete [] dp;
        return ret;

    }

};

int main(void)
{
    string s("leetcode");
    unordered_set<string> dict;
    dict.insert("leet");
    dict.insert("code");
    Solution solution;
    bool ret = solution.wordBreak3(s, dict);
    cout<<ret<<endl;

    return ;
}

网上还有通过trie树实现的，这里直接引用http://www.iteye.com/topic/1132188#2402159，就不多写了

代码如下：

class Solution {
public:

    class Node {
    public:
        Node* next[];
        bool end;
        Node(): end(false) { for (int i = ; i < ; i++) next[i] = NULL;}
        void insert(string a) {
            Node * cur = this;
            for (int i = ; i < a.size(); i++) {
                if (cur->next[a[i]-'a'] == NULL) {
                    cur->next[a[i]-'a'] = new Node();
                }
                cur = cur->next[a[i]-'a'];
            }
            cur->end = true;
        }
        ~Node () {
            for (int i = ;i < ; i++) delete next[i];
        }
    };

    bool wordBreak(string s, unordered_set<string> &dict) {
        Node root;
        for (auto it = dict.begin(); it != dict.end(); ++it) {
            root.insert(*it);
        }

        vector<bool> v(s.size(), false);
        findMatch(s, &root, , v);
        for (int i = ; i < s.size(); i++)
            if (v[i]) findMatch(s, &root, i+, v);
        return v[s.size() - ];
    }

    void findMatch(const string& s, Node* cur, int start, vector<bool> &v) {
        int i = start, n = s.size();
        while (i < n) {
            if (cur->next[s[i] - 'a'] != NULL) {
                if (cur->next[s[i] - 'a']->end) v[i] = true;
                cur = cur->next[s[i] - 'a'];
            }
            else break;
            i++;
        }

    }
};