# 5.longest-palindromic-substring

## Statement

• Difficulty: Medium
• Tag: `字符串` `动态规划`

``````输入：s = "babad"

``````

``````输入：s = "cbbd"

``````

• `1 <= s.length <= 1000`
• `s` 仅由数字和英文字母组成

Given a string `s`, return the longest palindromic substring in `s`.

Example 1:

``````Input: s = "babad"
Output: "bab"
Explanation: "aba" is also a valid answer.
``````

Example 2:

``````Input: s = "cbbd"
Output: "bb"
``````

Constraints:

• `1 <= s.length <= 1000`
• `s` consist of only digits and English letters.

## Solution

``````#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define endl "\n"
#define fi first
#define se second
#define all(x) begin(x), end(x)
#define rall rbegin(a), rend(a)
#define bitcnt(x) (__builtin_popcountll(x))
#define complete_unique(a) a.erase(unique(begin(a), end(a)), end(a))
#define mst(x, a) memset(x, a, sizeof(x))
#define MP make_pair

using ll = long long;
using ull = unsigned long long;
using db = double;
using ld = long double;
using VLL = std::vector<ll>;
using VI = std::vector<int>;
using PII = std::pair<int, int>;
using PLL = std::pair<ll, ll>;

using namespace __gnu_pbds;
using namespace std;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll mod = 1e9 + 7;

template <typename T, typename S>
inline bool chmax(T &a, const S &b) {
return a < b ? a = b, 1 : 0;
}

template <typename T, typename S>
inline bool chmin(T &a, const S &b) {
return a > b ? a = b, 1 : 0;
}

#ifdef LOCAL
#include <debug.hpp>
#else
#define dbg(...)
#endif

const int N = 1e5 + 10;

struct Manacher {
int len, l;
char Ma[N << 1];
int Mp[N << 1];
void work(const char *s) {
len = strlen(s);
l = 0;
Ma[l++] = '\$';
Ma[l++] = '#';
for (int i = 0; i < len; ++i) {
Ma[l++] = s[i];
Ma[l++] = '#';
}
Ma[l] = 0;
int mx = 0, id = 0;
for (int i = 0; i < l; ++i) {
Mp[i] = mx > i ? min(Mp[2 * id - i], mx - i) : 1;
while ((i - Mp[i]) >= 0 && Ma[i + Mp[i]] == Ma[i - Mp[i]]) Mp[i]++;
if (i + Mp[i] > mx) {
mx = i + Mp[i];
id = i;
}
}
}
bool check(int l, int r) {
int il = (l + 1) * 2, ir = (r + 1) * 2;
int mid = (il + ir) / 2;
int len = (r - l + 2) / 2;
return (Mp[mid] / 2) >= len;
}
} man;

class Solution {
public:
string longestPalindrome(string s) {
man.work(s.c_str());

for (int i = s.length(); i >= 1; i--) {
for (int j = s.length() - i; j >= 0; j--) {
if (man.check(j, j + i - 1)) {
return s.substr(j, i);
}
}
}

return 0;
}
};

#ifdef LOCAL

int main() {
return 0;
}

#endif
``````