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  • CF Round 427 D. Palindromic characteristics

    题目链接:http://codeforces.com/contest/835/problem/

    思路:dp[i][j]表示子串[i, j]的阶数,则:

    dp[i][i] = 1;

    dp[i][i + 1] = (str[i] == str[i + 1])? 2: 0;

    if(str[i] != str[j] || dp[i + 1][j - 1] == 0)

      dp[i][j] = 0;
    else  

      dp[i][j] = dp[i][i + (j - i + 1) / 2 - 1] + 1;

    而所有的k阶回文串必定是k - 1, k - 2....1阶回文川,因此 cnt[i] += sum(cnt[i + 1 -> len])

    代码:

     1 const int inf = 0x3f3f3f3f;
     2 const int maxn = 5e3 + 5; 
     3 
     4 int dp[maxn][maxn], cnt[maxn];
     5 char str[maxn];
     6 
     7 int main(){
     8     memset(dp, 0, sizeof(dp));
     9     memset(cnt, 0, sizeof(cnt));
    10     scanf("%s", &str[1]);
    11     int slen = strlen(str + 1);
    12     for(int i = 1; i <= slen; i++) dp[i][i] = 1;
    13     for(int i = slen - 1; i > 0; i--){
    14         dp[i][i + 1] = str[i] == str[i + 1]? 2: 0;
    15         for(int j = i + 2; j <= slen; j++){
    16             if(str[i] != str[j] || dp[i + 1][j - 1] == 0) dp[i][j] = 0;
    17             else dp[i][j] = dp[i][i + (j - i + 1) / 2 - 1] + 1;
    18         }
    19     }
    20     for(int i = 1; i <= slen; i++){
    21         for(int j = i; j <= slen; j++){
    22 //            debug
    23 //            printf("[%d, %d]: %d
    ", i, j, dp[i][j]);
    24             cnt[dp[i][j]]++;
    25         }
    26     }
    27     for(int i = 1; i <= slen; i++){
    28         for(int j = i + 1; j <= slen; j++){
    29             cnt[i] += cnt[j];
    30         }
    31     }
    32     for(int i = 1; i <= slen; i++){
    33         printf("%d", cnt[i]);
    34         if(i != slen) putchar(' ');
    35         else puts("");
    36     }
    37 }

    题目:

    D. Palindromic characteristics
    time limit per test
    3 seconds
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes.

    A string is 1-palindrome if and only if it reads the same backward as forward.

    A string is k-palindrome (k > 1) if and only if:

    1. Its left half equals to its right half.
    2. Its left and right halfs are non-empty (k - 1)-palindromes.

    The left half of string t is its prefix of length ⌊|t| / 2⌋, and right half — the suffix of the same length. ⌊|t| / 2⌋ denotes the length of string tdivided by 2, rounded down.

    Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.

    Input

    The first line contains the string s (1 ≤ |s| ≤ 5000) consisting of lowercase English letters.

    Output

    Print |s| integers — palindromic characteristics of string s.

    Examples
    input
    abba
    output
    6 1 0 0 
    input
    abacaba
    output
    12 4 1 0 0 0 0 
    Note

    In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.

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  • 原文地址:https://www.cnblogs.com/bolderic/p/7270337.html
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