UVALive - 3942 Remember the Word （Trie + DP）

题意：

给定一篇长度为L的小写字母文章， 然后给定n个字母， 问有多少种方法用这些字母组成文章。

思路：

用dp[i]来表达[i , L]的方法数， 那么dp[i] 就可以从dp[len(x) + i]转移过来， 注意dp[L+1]要初始化为1.

递推写法

#include <bits/stdc++.h>
using namespace std;
const int maxN = 3e5 + ;
const int mod =  ;
char in[maxN];
int n;
struct Trie {
    int ch[maxN][];
    int val[maxN];
    int sz;
    void Init(){sz = ; memset(ch[], , sizeof(ch[])); memset(val, , sizeof(val));}
    int idx(char c) {return c - 'a';}
    void Insert(char *s){
        int u = , n = strlen(s);
        for(int i = ; i < n; i++){
            int c = idx(s[i]);
            if(!ch[u][c]){
                memset(ch[sz], , sizeof(ch[sz]));
                val[sz] = ;
                ch[u][c] = sz++;
            }
            u = ch[u][c];
        }
        val[u] = n;
    }

}tree;
long long dp[maxN];
int main(){
//    freopen("1.txt","r", stdin);
    int kase = ;
    while(~scanf("%s", in)){
        tree.Init();
        memset(dp ,  , sizeof(dp));
        scanf("%d", &n);
        char word[];
        for(int i = ; i < n; i++){
            scanf("%s", word);
            tree.Insert(word);
        }
        int len = strlen(in);
        dp[len] = ;
        for(int pos = len ; pos >= ; pos--){
            int u = ;
            for(int i = pos, wordLen = ; i < len; i++, wordLen++){
                int c = tree.idx(in[i]);
                if(tree.ch[u][c] == ) break;
                u = tree.ch[u][c];
                if(tree.val[u] != ){
                    dp[pos] += dp[pos + wordLen];
                    dp[pos] %= mod;
                }
            }
        }
        printf("Case %d: %lld\n", kase++, dp[]);
    }

    return ;
}

记忆化搜索

#include <bits/stdc++.h>
using namespace std;
const int maxN = 2e6 + ;
const int mod =  ;
char in[maxN];
int n;
struct Trie {
    int ch[maxN][];
    int val[maxN];
    int sz;
    void Init(){
        sz = ;
        memset(ch[], , sizeof(ch[]));
        memset(val, , sizeof(val));
    }
    int idx(char c) {return c - 'a';}
    void Insert(char *s){
        int u = , n = strlen(s);
        for(int i = ; i < n; i++){
            int c = idx(s[i]);
            if(!ch[u][c]){
                memset(ch[sz], , sizeof(ch[sz]));
                val[sz] = ;
                ch[u][c] = sz++;
            }
            u = ch[u][c];
        }
        val[u] = n;
    }

}tree;

long long dp[maxN];
int dfs(int pos){
    int temp = pos;
    if(dp[pos] > ) return dp[pos];
    int ret = ;
    int adr = ;
    while(tree.ch[adr][in[pos] - 'a']){
        adr = tree.ch[adr][in[pos] - 'a'];
        if(tree.val[adr] != ){
            ret = (ret + dfs(pos + )) % mod;
        }
        pos ++;

    }
    dp[temp] = ret;
    return ret;
}

int main(){
    freopen("1.txt","r", stdin);
    int ncase = ;
    while(~scanf("%s", in)){
        tree.Init();
        scanf("%d", &n);
        char word[];
        for(int i = ; i < n; i++){
            scanf("%s", word);
            tree.Insert(word);
        }

        int l = strlen(in);
        for(int i = ;i <= l; i ++)dp[i] = ;
        dp[l] = ;
        printf("Case %d: %d\n",ncase ++ , dfs());
    }

    return ;
}