Given a string S, find the number of different non-empty palindromic subsequences in S, and return that number modulo 10^9 + 7.
A subsequence of a string S is obtained by deleting 0 or more characters from S.
A sequence is palindromic if it is equal to the sequence reversed.
Two sequences A_1, A_2, ... and B_1, B_2, ... are different if there is some i for which A_i != B_i.
Example 1:
Input:
S = 'bccb'
Output: 6
Explanation:
The 6 different non-empty palindromic subsequences are 'b', 'c', 'bb', 'cc', 'bcb', 'bccb'.
Note that 'bcb' is counted only once, even though it occurs twice.
Example 2:
Input:
S = 'abcdabcdabcdabcdabcdabcdabcdabcddcbadcbadcbadcbadcbadcbadcbadcba'
Output: 104860361
Explanation:
There are 3104860382 different non-empty palindromic subsequences, which is 104860361 modulo 10^9 + 7.
Note:
The length of S will be in the range [1, 1000].
Each character S[i] will be in the set {'a', 'b', 'c', 'd'}.
很有难度的一道题，
时间和空间复杂度 o(n^2)
class Solution {
public int countPalindromicSubsequences(String S) {
int n = S.length();
int[][] dp = new int[n][n];
int M = 1000000007;
//长读为1的字符串 是一个回文
for(int i = 0; i < n; i++){
dp[i][i] = 1;
}
for(int len = 1; len < n;len++){
for(int i = 0 ; i < n - len; i++){
int j = i + len;
if(S.charAt(j) == S.charAt(i)){
int left = i + 1;
int right = j -1;
//从s[i] 的下一个，到s[j]的前一个开始找，遇到和s[i]相同的，就停止，停止时，如果left 小于right，说明遇到了和s[i]一样的字符，
//如果left 大于 right，说明没有遇到相同的字符，while循环是根据left 《= right 终止的，如果left == right，说明只有一个和s[i]相同的字符
while(left<= right && S.charAt(left) != S.charAt(j)) left++;
while(left<= right && S.charAt(right) != S.charAt(j)) right--;
//中间没有和收尾相同的字符
if(left > right){
dp[i][j] = dp[i+1][j-1]*2 + 2;
}
else if(left == right){
dp[i][j] = dp[i+1][j-1]*2 + 1;
}
else{
//重复计算的个数，就是两个重复相同字符之间所有字符的回文个数
dp[i][j] = dp[i+1][j-1]*2 - dp[left+1][right-1];
}
}else{
dp[i][j] = dp[i][j-1] + dp[i+1][j] - dp[i+1][j-1];
}
//or
dp[i][j] = (dp[i][j] + M)%M
dp[i][j] = (dp[i][j] < 0)? dp[i][j] + M : dp[i][j] % M;
}
}
return dp[0][n-1];
}
}
