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51nod 1092 回文字符串 (dp)

时间:2015-04-22 17:42:45      阅读:120      评论:0      收藏:0      [点我收藏+]

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http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1092

这个题是poj-3280的简化版,这里只可以增加字符,设 dp[i][j] 为把以i开头j结尾的子串变为回文串的最少次数,

if(s[i]==s[j])  dp[i][j]=dp[i+1][j-1];

else dp[i][j]=min(dp[i+1][j],dp[i][j-1])+1;   

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cmath>
 4 #include <vector>
 5 #include <cstring>
 6 #include <string>
 7 #include <algorithm>
 8 #include <string>
 9 #include <set>
10 #include <functional>
11 #include <numeric>
12 #include <sstream>
13 #include <stack>
14 #include <map>
15 #include <queue>
16 #pragma comment(linker, "/STACK:102400000,102400000")
17 #define CL(arr, val)    memset(arr, val, sizeof(arr))
18 
19 #define ll long long
20 #define inf 0x7f7f7f7f
21 #define lc l,m,rt<<1
22 #define rc m + 1,r,rt<<1|1
23 #define pi acos(-1.0)
24 
25 #define L(x)    (x) << 1
26 #define R(x)    (x) << 1 | 1
27 #define MID(l, r)   (l + r) >> 1
28 #define Min(x, y)   (x) < (y) ? (x) : (y)
29 #define Max(x, y)   (x) < (y) ? (y) : (x)
30 #define E(x)        (1 << (x))
31 #define iabs(x)     (x) < 0 ? -(x) : (x)
32 #define OUT(x)  printf("%I64d\n", x)
33 #define lowbit(x)   (x)&(-x)
34 #define Read()  freopen("a.txt", "r", stdin)
35 #define Write() freopen("b.txt", "w", stdout);
36 #define maxn 1000000000
37 #define N 1010
38 #define mod 1000000000
39 using namespace std;
40 
41 int dp[N][N];
42 char s[N];
43 
44 int main()
45 {
46     //Read();
47     scanf("%s",s);
48     int m=strlen(s);
49     memset(dp,0,sizeof(dp));
50     for(int i=m-1;i>=0;i--)
51     {
52         for(int j=i+1;j<m;j++)
53         {
54                 if(s[i]==s[j]) dp[i][j]=dp[i+1][j-1];
55                 else dp[i][j]=min(dp[i+1][j],dp[i][j-1])+1;
56                 //printf("%d\n",dp[i][j]);
57         }
58     }
59     printf("%d\n",dp[0][m-1]);
60     return 0;
61 }

 

还可以转化为最长公共子序列的问题求解,求最少变成回文串的操作次数,就是求有几个字符与对应的字符不一样,那么只要我把原字符翻转,然后求最长公共子序列,

用字符串长度减去公共子序列长度即可求解。

因为dp[i+1]计算时只用到了dp[i],dp[i+1],所以可以结合奇偶性用滚动数组优化空间。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cmath>
 4 #include <vector>
 5 #include <cstring>
 6 #include <string>
 7 #include <algorithm>
 8 #include <string>
 9 #include <set>
10 #include <functional>
11 #include <numeric>
12 #include <sstream>
13 #include <stack>
14 #include <map>
15 #include <queue>
16 #pragma comment(linker, "/STACK:102400000,102400000")
17 #define CL(arr, val)    memset(arr, val, sizeof(arr))
18 
19 #define ll long long
20 #define inf 0x7f7f7f7f
21 #define lc l,m,rt<<1
22 #define rc m + 1,r,rt<<1|1
23 #define pi acos(-1.0)
24 
25 #define L(x)    (x) << 1
26 #define R(x)    (x) << 1 | 1
27 #define MID(l, r)   (l + r) >> 1
28 #define Min(x, y)   (x) < (y) ? (x) : (y)
29 #define Max(x, y)   (x) < (y) ? (y) : (x)
30 #define E(x)        (1 << (x))
31 #define iabs(x)     (x) < 0 ? -(x) : (x)
32 #define OUT(x)  printf("%I64d\n", x)
33 #define lowbit(x)   (x)&(-x)
34 #define Read()  freopen("a.txt", "r", stdin)
35 #define Write() freopen("b.txt", "w", stdout);
36 #define maxn 1000000000
37 #define N 1010
38 #define mod 1000000000
39 using namespace std;
40 
41 int dp[2][N];
42 char s[N],ss[N];
43 
44 int main()
45 {
46     //Read();
47     scanf("%s",s);
48     int m=strlen(s);
49     for(int i=0;i<m;i++)
50         ss[i]=s[m-i-1];
51     ss[m]=\0;
52     memset(dp,0,sizeof(dp));
53     for(int i=0;i<m;i++)
54     {
55         for(int j=0;j<m;j++)
56         {
57             if(s[i]==ss[j]) dp[(i+1) & 1][j+1]=dp[i & 1][j]+1;
58             else dp[(i+1) & 1][j+1]=max(dp[i & 1][j+1],dp[(i+1) & 1][j]);
59             //printf("%d\n",dp[i+1][j+1]);
60         }
61     }
62    // printf("%d\n",dp[m][m]);
63     printf("%d\n",m-dp[m&1][m]);
64     return 0;
65 }

 

51nod 1092 回文字符串 (dp)

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原文地址:http://www.cnblogs.com/nowandforever/p/4447877.html

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