区间DP UVA 10453 Make Palindrome

 1 /*
 2     题意：问最少插入多少个字符使得字符串变成回文串
 3     区间DP：dp[i][j]表示[l, r]的字符串要成为回文需要插入几个字符串，那么dp[l][r] = dp[l+1][r-1]; (str[l] == str[r])
 4             dp[l][r] = min (dp[l+1][r], dp[l][r-1]) + 1，然后按照状态转移递归输出路径
 5 */
 6 /************************************************
 7 * Author        :Running_Time
 8 * Created Time  :2015-8-17 14:42:57
 9 * File Name     :UVA_10453.cpp
10  ************************************************/
11 
12 #include <cstdio>
13 #include <algorithm>
14 #include <iostream>
15 #include <sstream>
16 #include <cstring>
17 #include <cmath>
18 #include <string>
19 #include <vector>
20 #include <queue>
21 #include <deque>
22 #include <stack>
23 #include <list>
24 #include <map>
25 #include <set>
26 #include <bitset>
27 #include <cstdlib>
28 #include <ctime>
29 using namespace std;
30 
31 #define lson l, mid, rt << 1
32 #define rson mid + 1, r, rt << 1 | 1
33 typedef long long ll;
34 const int MAXN = 1e3 + 10;
35 const int INF = 0x3f3f3f3f;
36 const int MOD = 1e9 + 7;
37 char str[MAXN];
38 int dp[MAXN][MAXN];
39 
40 void print(int l, int r)    {
41     if (l > r)  return ;
42     if (l == r) printf ("%c", str[l]);
43     else if (str[l] == str[r])   {
44         printf ("%c", str[l]);
45         print (l + 1, r - 1);
46         printf ("%c", str[l]);
47     }
48     else if (dp[l][r] == dp[l+1][r] + 1)    {
49         printf ("%c", str[l]);
50         print (l + 1, r);
51         printf ("%c", str[l]);
52     }
53     else    {
54         printf ("%c", str[r]);
55         print (l, r - 1);
56         printf ("%c", str[r]);
57     }
58 }
59 
60 void work(void) {
61     memset (dp, 0, sizeof (dp));
62     int len = strlen (str);
63     for (int i=2; i<=len; ++i)  {
64         for (int j=0; j+i-1<len; ++j)   {
65             int k = j + i - 1;
66             int &res = dp[j][k] = INF;
67             if (str[j] == str[k])   res = dp[j+1][k-1];
68             res = min (res, min (dp[j+1][k], dp[j][k-1]) + 1);
69         }
70     }
71     printf ("%d ", dp[0][len-1]);
72     print (0, len - 1); puts ("");
73 }
74 
75 int main(void)    {     //UVA 10453 Make Palindrome
76     while (scanf ("%s", str) == 1)  {
77         work ();
78     }
79 
80     return 0;
81 }
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