URAL 1635. Mnemonics and Palindromes(DP)

题目链接

本来用区间DP，3次方的复杂度，T了，看了看题解，降维，直接二次方的复杂度可以解。然后折腾一下输出路径。。终于过了。

 1 #include <cstring>

 2 #include <cstdio>

 3 #include <string>

 4 #include <iostream>

 5 #include <algorithm>

 6 #include <cmath>

 7 using namespace std;

 8 char str[4001];

 9 int dp[4001][4001];

10 int p[4001];

11 int pre[4001];

12 int flag[4001];

13 int main()

14 {

15     int i,len,j;

16     scanf("%s",str);

17     len = strlen(str);

18     for(i = 0; i <= len; i ++)

19     {

20         dp[i][i] = 1;

21         for(j = 1;; j ++)

22         {

23             if(i-j+1 < 0)break;

24             if(i+j >= len) break;

25             if(str[i-j] != str[i+j]) break;

26             dp[i-j][i+j] = 1;

27         }

28         for(j = 1;; j ++)

29         {

30             if(i-j+1 < 0)break;

31             if(i+j >= len) break;

32             if(str[i-j+1] != str[i+j]) break;

33             dp[i-j+1][i+j] = 1;

34         }

35     }

36     for(i = 0; i < len; i ++)

37         p[i] = 100000000;

38     p[0] = 1;

39     for(i = 1; i < len; i ++)

40     {

41         if(dp[0][i])

42         {

43             pre[i] = 0;

44             p[i] = 1;

45         }

46     }

47     for(i = 0; i < len; i ++)

48     {

49         if(p[i] == 1) continue;

50         for(j = 0; j < i; j ++)

51         {

52             if(dp[j+1][i])

53             {

54                 if(p[i] > p[j] + 1)

55                 {

56                     pre[i] = j+1;

57                     p[i] = p[j]+1;

58                 }

59             }

60         }

61     }

62     printf("%d\n",p[len-1]);

63     int a = pre[len-1];

64     if(a != 0)

65     flag[a] = 1;

66     a --;

67     while(p[len-1] >= 2)

68     {

69         a = pre[a];

70         if(a != 0)

71         flag[a] = 1;

72         a --;

73         p[len-1] --;

74     }

75     for(i = 0; i < len; i ++)

76     {

77         if(flag[i]) printf(" ");

78         printf("%c",str[i]);

79     }

80     printf("\n");

81     return 0;

82 }