Palindrome Partitioning II
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Given a string s, partition s such that every substring of the partition is a palindrome.
Return the minimum cuts needed for a palindrome partitioning ofs.
For example, given s = "aab"
,
Return 1
since the palindrome partitioning ["aa","b"]
could be produced using 1 cut.
DP.
res[i] 区间[i,n]之间最小的cut数,n为字符串长度, 则,
res[i] = min(1+res[j+1], res[i] ) i<=j <n.
有个转移函数之后,一个问题出现了,就是如何判断[i,j]是否是回文?每次都从i到j比较一遍?太浪费了,这里也是一个DP问题。
定义函数
P[i][j] = true if [i,j]为回文
那么
P[i][j] = (str[i] == str[j] && P[i+1][j-1]);
class Solution {public: int minCut(string s) { // Start typing your C/C++ solution below // DO NOT write int main() function int n = s.size(); vector<int > res(n+1); vector<vector<bool> > p(n, vector<bool>(n, false)); for(int i = 0 ;i <= n; ++i){ res[i] = n - i; } for(int i = n - 1; i >=0; --i){ for(int j = i; j < n; ++j){ if(s[i] == s[j] && (j - i < 2 || p[i + 1][j - 1])){ p[i][j] = true; res[i] = min(res[i], res[j + 1] + 1); } } } return res[0] - 1; }};
也可以从前往后数。
class Solution {public: int minCut(string s) { // Start typing your C/C++ solution below // DO NOT write int main() function int n = s.size(); vector<int> res(n+1); for(int i = 0 ; i< n + 1 ; ++i){ res[i] = i - 1; } vector<vector<bool> > p(n, vector<bool>(n, false)); for(int i = 0; i< n; ++i){ for(int j = 0; j <= i ; ++j){ if(s[i] == s[j] && (i - j < 2 || p[j + 1][i - 1])){ p[j][i] = true; res[i + 1] = min(res[i + 1], res[j] + 1); } } } return res[n]; }};
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