题意 判断一个串最少可以分解为多少个对称串 一个串从左往后和从右往左是一样的 这个串就称为对沉串
令d[i]表示给定串的前i个字母至少可以分解为多少个对称串 那么对于j=1~i 若(i,j)是一个对称串 那么有 d[i]=min(d[i],d[j-1]+1) 然后就得到答案了
#include<cstdio> #include<cstring> #include<algorithm> using namespace std; const int N = 1005; int d[N]; char s[N]; bool isPal (int a, int b) { while (a <= b && s[a] == s[b]) ++a, --b; return a >= b; } int main() { int cas, l; scanf ("%d", &cas); for (int ca = 1; ca <= cas; ++ca) { scanf ("%s", s + 1); l = strlen (s + 1); memset (d, 0x3f, sizeof (d)); d[0] = 0; for (int i = 1; i <= l; ++i) { for (int j = 1; j <= i; ++j) if (isPal (j, i)) d[i] = min (d[i], d[j - 1] + 1); } printf ("%d\n", d[l]); } return 0; }
We say a sequence of characters is a palindromeif it is the same written forwards and backwards. For example, ‘racecar‘ is a palindrome, but ‘fastcar‘ is not.
A partition of a sequence of characters is a list of one or more disjoint non-empty groups of consecutive characters whose concatenation yields the initial sequence. For example, (‘race‘, ‘car‘) is a partition of ‘racecar‘ into two groups.
Given a sequence of characters, we can always create a partition of these characters such that each group in the partition is a palindrome! Given this observation it is natural to ask: what is the minimum number of groups needed for a given string such that every group is a palindrome?
For example:
Input begins with the number n of test cases. Each test case consists of a single line of between 1 and 1000 lowercase letters, with no whitespace within.
For each test case, output a line containing the minimum number of groups required to partition the input into groups of palindromes.
3 racecar fastcar aaadbccb
1 7 3
UVa 11584 Partitioning by Palindromes(DP 最少对称串)
原文地址:http://blog.csdn.net/acvay/article/details/38820795