Hash~

优势：任意给定一段区间[L,R]可以用O（1）的时间算出来

#include <iostream>
#include <string.h>
using namespace std;

typedef unsigned long long ull;
const int N = 1000010;
const int base = 131;

char str[N];
ull h[N];

int main()
{
    scanf("%s",str + 1);
    //算每个前缀的哈希值
    int n = strlen(str + 1);

    for(int i = 1;i <= n;i++)
    {
        h[i] = h[i - 1] * base + str[i] - 'a' + 1;
    }
    for(int i = 1;i <= n;i++)
    {
        printf("%llu\n",h[i]);
    }
    return 0;
}
//abc
//1
//133
//17426

算任意两段的哈希值的代码：
求某两段是不是一样的，分别求hash值判等

#include <iostream>
#include <string.h>
using namespace std;

typedef unsigned long long ull;
const int N = 1000010;
const int base = 131;

char str[N];
ull h[N],p[N];

ull get(int l,int r)
{
    return h[r] - h[l - 1] * p[r - l + 1];
}

int main()
{
    scanf("%s",str + 1);
    //算每个前缀的哈希值
    int n = strlen(str + 1);

    p[0] = 1;
    for(int i = 1;i <= n;i++)
    {
        h[i] = h[i - 1] * base + str[i] - 'a' + 1;
        p[i] = p[i - 1] * base;
    }

    int m;
    cin>>m;
    while(m--)
    {
        int l,r;
        cin>>l>>r;
        cout<<get(l,r)<<endl;
    }
    return 0;
}
/*
abcabcabc
3
1 3
17426
4 6
17426
7 9
17426
*/

兔子与兔子

由于数据比较大，接收时选择scanf，与上面代码就这不一样。【效率快】

#include <iostream>
#include <string.h>
using namespace std;
typedef unsigned long long ull;
const int N = 1000010;
const int base = 131;
char str[N];
ull h[N],p[N];
ull get(int l,int r)
{
    return h[r] - h[l - 1] * p[r - l + 1];
}
int main()
{
    scanf("%s",str + 1);
    //算每个前缀的哈希值
    int n = strlen(str + 1);
    p[0] = 1;
    for(int i = 1;i <= n;i++)
    {
        h[i] = h[i - 1] * base + str[i] - 'a' + 1;
        p[i] = p[i - 1] * base;
    }
    int m;
    cin>>m;
    while(m--)
    {
        int l1,r1,l2,r2;
        scanf("%d %d %d %d",&l1,&r1,&l2,&r2);
        if(get(l1,r1) == get(l2,r2))
            puts("Yes");
        else
            puts("No");
    }
    return 0;
}

回文子串的最大长度

上海自来水来自海上

左边的正序 == 右边的逆序
首先，回文串分为两大类：长度是奇数abcba，长度是偶数abba。
①技巧
②枚举中点
③二分半径，一个长度，如果一样就扩大长度，否则缩小长度。

技巧：
abcba --> a#b#c#b#a 奇数个数
abba --> a#b#b#a 也变成奇数个数
s个字母 补上 s-1个字母 变成 2s - 1 （奇数个呗）

#include <iostream>
#include <string.h>
#include <algorithm>
using namespace std;
typedef unsigned long long ULL;
const int N = 2000010, base = 131;
char str[N];
ULL hl[N], hr[N], p[N];
ULL get(ULL h[], int l, int r)
{
    return h[r] - h[l - 1] * p[r - l + 1];
}
int main()
{
    int T = 1;
    while (scanf("%s", str + 1), strcmp(str + 1, "END")) //调用这个函数，判断有没有遇到END，如果有就结束。逗号表达式，用逗号隔开的语句，返回值，只看最后一个语句的返回值 **细节**
    {
        int n = strlen(str + 1);
        for (int i = n * 2; i > 0; i -= 2)
        {
            str[i] = str[i / 2];
            str[i - 1] = 'z' + 1;
        }
        n *= 2;
        p[0] = 1;
        for (int i = 1, j = n; i <= n; i ++, j -- )//i,j分别是正序，逆序
        {
            hl[i] = hl[i - 1] * base + str[i] - 'a' + 1;
            hr[i] = hr[i - 1] * base + str[j] - 'a' + 1;
            p[i] = p[i - 1] * base;
        }
        int res = 0;
        for (int i = 1; i <= n; i ++ )
        {
            int l = 0, r = min(i - 1, n - i);
            while (l < r)
            {
                int mid = l + r + 1 >> 1;
                if (get(hl, i - mid, i - 1) != get(hr, n - (i + mid) + 1, n - (i + 1) + 1)) r = mid - 1;//注意端点值的确定，自己举俩例子判断找的对不对
                else l = mid;
            }
            if (str[i - l] <= 'z') res = max(res, l + 1);
            else res = max(res, l);
        }
        printf("Case %d: %d\n", T ++, res);
    }
    return 0;
}

后缀数组

/*
ponoiiipoi

10 i
9 oi
8 poi
7 ipoi
6 iipoi
5 iiipoi
4 oiiipoi
3 noiiipoi
2 onoiiipoi
1 ponoiiipoi

输出字典序最小的……
输出排名为 i 的后缀与排名为 i-1 的后缀，把二者的最长公共前缀的长度记为 Height[i] 
*/ 
#include <iostream>
#include <algorithm>
#include <string.h>
#include <limits.h>
using namespace std;
typedef unsigned long long ULL;
const int N = 300010, base = 131;
int n;
char str[N];
ULL h[N], p[N];
int sa[N];
int get(int l, int r)
{
    return h[r] - h[l - 1] * p[r - l + 1];
}

int get_max_common_prefix(int a, int b)
{
    int l = 0, r = min(n - a + 1, n - b + 1);
    while (l < r)
    {
        int mid = l + r + 1 >> 1;
        if (get(a, a + mid - 1) != get(b, b + mid - 1)) r = mid - 1;
        else l = mid;
    }
    return l;
}

bool cmp(int a, int b)
{
    int l = get_max_common_prefix(a, b);
    int av = a + l > n ? INT_MIN : str[a + l];
    int bv = b + l > n ? INT_MIN : str[b + l];
    return av < bv;
}

int main()
{
    scanf("%s", str + 1);
    n = strlen(str + 1);
    p[0] = 1;
    for (int i = 1; i <= n; i ++ )
    {
        h[i] = h[i - 1] * base + str[i] - 'a' + 1;
        p[i] = p[i - 1] * base;
        sa[i] = i;
    }
    sort(sa + 1, sa + 1 + n, cmp);
    for (int i = 1; i <= n; i ++ ) printf("%d ", sa[i] - 1);
    puts("");
    for (int i = 1; i <= n; i ++ )
        if (i == 1) printf("0 ");
        else printf("%d ", get_max_common_prefix(sa[i - 1], sa[i]));
    puts("");
    
    return 0;
}

所有和前缀和有关的下标都从1开始！