manachar算法学习笔记

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manachar算法用来处理字符串的最长回文子串的算法,其核心就是预处理len数组.

假设原串是s[0...n-1],len[i]表示以s[i]为回文中心的最长回文串的右下标到i的长度,

然后递推瞎搞.

因为算法本身比较简单网上烂大街,主要还是想了一下复杂度.

容易发现Max指针最多扩展到n,而复杂度主要在于while循环,每次都会增加Max指

针或者跳出while循环,所以复杂度最多就是O(n+chang(Max))=O(n).

HDU 3068:点击打开链接

模板题

#include <bits/stdc++.h>using namespace std;#define maxn 111111int len[maxn<<1];char a[maxn];int manachar (char *p) {    char s[maxn<<1];//构造新串    int n = strlen (p), l = 0;    s[l++] = '@';    s[l++] = '#';    for (int i = 0; i < n; i++) {        s[l++] = p[i];        s[l++] = '#';    }    s[l++] = '~'; s[l] = 0;    //cout << s << endl;    int Max = 0, pos = 0, ans = 0;    for (int i = 1; i < l; i++) {        if (Max > i) {            len[i] = min (len[2*pos-i], Max-i);        }        else            len[i] = 1;        while (s[i+len[i]] == s[i-len[i]])            len[i]++;        ans = max (ans, len[i]);        if (len[i]+i > Max) {            Max = len[i]+i;            pos = i;        }    }    return ans-1;}int main () {    while (scanf ("%s", a) == 1) printf ("%d\n", manachar (a));    return 0;}

POJ 3974:点击打开链接

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>#include <iostream>using namespace std;#define maxn 2211111int len[maxn];char s[maxn];char a[maxn];int Manachar (char *p) {    int n = strlen (p), l = 0;    s[l++] = '@';    s[l++] = '#';    for (int i = 0; i < n; i++) {        s[l++] = p[i];        s[l++] = '#';    }    s[l] = 0;    int Max = 0, pos = 0, ans = 0;    for (int i = 1; i < l; i++) {        if (Max > i) {            len[i] = min (len[2*pos-i], Max-i);        }        else            len[i] = 1;        while (s[i+len[i]] == s[i-len[i]])            len[i]++;        ans = max (ans, len[i]);        if (len[i]+i > Max) {            Max = len[i]+i;            pos = i;        }    }    return ans-1;}int main () {    int kase = 0;    while (scanf ("%s", a) == 1) {        if (a[0] == 'E')            break;        printf ("Case %d: %d\n", ++kase, Manachar (a));    }    return 0;}

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