【codeforces 750E】New Year and Old Subsequence

time limit per test3 seconds

memory limit per test256 megabytes

inputstandard input

outputstandard output

A string t is called nice if a string “2017” occurs in t as a subsequence but a string “2016” doesn’t occur in t as a subsequence. For example, strings “203434107” and “9220617” are nice, while strings “20016”, “1234” and “20167” aren’t nice.

The ugliness of a string is the minimum possible number of characters to remove, in order to obtain a nice string. If it’s impossible to make a string nice by removing characters, its ugliness is  - 1.

Limak has a string s of length n, with characters indexed 1 through n. He asks you q queries. In the i-th query you should compute and print the ugliness of a substring (continuous subsequence) of s starting at the index ai and ending at the index bi (inclusive).

Input

The first line of the input contains two integers n and q (4 ≤ n ≤ 200 000, 1 ≤ q ≤ 200 000) — the length of the string s and the number of queries respectively.

The second line contains a string s of length n. Every character is one of digits ‘0’–’9’.

The i-th of next q lines contains two integers ai and bi (1 ≤ ai ≤ bi ≤ n), describing a substring in the i-th query.

Output

For each query print the ugliness of the given substring.

Examples

input

8 3

20166766

1 8

1 7

2 8

output

4

3

-1

input

15 5

012016662091670

3 4

1 14

4 15

1 13

10 15

output

-1

2

1

-1

-1

input

4 2

1234

2 4

1 2

output

-1

-1

Note

In the first sample:

In the first query, ugliness(“20166766”) = 4 because all four sixes must be removed.

In the second query, ugliness(“2016676”) = 3 because all three sixes must be removed.

In the third query, ugliness(“0166766”) =  - 1 because it’s impossible to remove some digits to get a nice string.

In the second sample:

In the second query, ugliness(“01201666209167”) = 2. It’s optimal to remove the first digit ‘2’ and the last digit ‘6’, what gives a string “010166620917”, which is nice.

In the third query, ugliness(“016662091670”) = 1. It’s optimal to remove the last digit ‘6’, what gives a nice string “01666209170”.

【题目链接】:http://codeforces.com/contest/750/problem/E

【题解】

    merge矩阵(dp)+线段树;
    m[i][j]表示从状态i->j转移的花费;
    0表示什么都没有
    1表示出现了2
    2表示出现了20
    3表示出现了201
    4表示出现了2017
    出现了2,20，则遇到6的时候我么可以不用管;
    但是如果出现了201或2017,然后又遇到了6,则我们需要把这个6删掉;
    for (i = 0;i <= 4;i++)//除了遇到2,0,1,6,7这5个特别的数字之外,
        m[i][i] = 0;//遇到的时候状态都不会变;所以不用花费(操作);
    if (ch == '2')
    {
        m[0][0] = 1;//什么都没有->什么都没有,删掉这个2
        m[0][1] = 0;//什么都没有->出现了2,花费变成0
        //注意这里m[1][1] = 0,表示从出现了一个2到出现了一个2可以不用删掉任何东西,因为加上一个2也无妨,下面的解释就省略了,希望大家能看得明白.
    }
    if (ch=='0')
    {
        m[1][1] = 1 ;//出现了一个2->出现了一个2,则把0删掉
        m[1][2] = 0;//从出现一个2->出现了20,因为当前就是0,所以什么都不用加
    }
    if (ch=='1')
    {
        ma[2][2] = 1;//出现了20->出现了20,则把1删掉
        ma[2][3] = 0;//出现了20->出现了201，因为刚好遇到一个1则什么都不加
    }
    if (ch=='7')
    {
        m[3][3] = 1;//出现了201->出现了201,则把遇到的7删掉
        m[3][4] = 0;//出现了201->出现了2017,刚好遇到7，则什么都不做
    }
    if (ch=='6')
    {
        a[3][3] = 1;//出现了201->出现了数字6,则一定要把6删掉,不然无法满足题意
        a[4][4] = 1;//出现了2017->出现了数字6,则也一定要把6删掉.
    }
    线段树加一个合并操作就好;
    那个合并的操作和floyd算法类似;
    最后输出m[0][4];表示从什么都没有然后出现"2017"

【完整代码】

#include <bits/stdc++.h>
using namespace std;
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define LL long long
#define rep1(i,a,b) for (int i = a;i <= b;i++)
#define rep2(i,a,b) for (int i = a;i >= b;i--)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define rei(x) scanf("%d",&x)
#define rel(x) scanf("%I64d",&x)
typedef pair<int,int> pii;
typedef pair<LL,LL> pll;
const int MAXN = 2e5+10;
const int INF = 7e8;
const int dx[9] = {0,1,-1,0,0,-1,-1,1,1};
const int dy[9] = {0,0,0,-1,1,-1,1,-1,1};
const double pi = acos(-1.0);
struct abc
{
    int m[5][5];
    friend abc operator * (abc a,abc b)
    {
        abc d;
        rep1(i,0,4)
            rep1(j,0,4)
            {
                d.m[i][j] = INF;
                rep1(k,0,4)
                    d.m[i][j] = min(d.m[i][j],a.m[i][k]+b.m[k][j]);
            }
        return d;
    }
};
int n,q;
abc a[MAXN*4];
char s[MAXN];
void build(int l,int r,int rt)
{
    if (l==r)
    {
        char ch = s[l];
        rep1(i,0,4)
            rep1(j,0,4)
                a[rt].m[i][j] = (i==j)?0:INF;
        if (ch == '2')
        {
            a[rt].m[0][0] = 1;
            a[rt].m[0][1] = 0;
        }
        if (ch=='0')
        {
            a[rt].m[1][1] = 1;
            a[rt].m[1][2] = 0;
        }
        if (ch=='1')
        {
            a[rt].m[2][2] = 1;
            a[rt].m[2][3] = 0;
        }
        if (ch=='7')
        {
            a[rt].m[3][3] = 1;
            a[rt].m[3][4] = 0;
        }
        if (ch=='6')
        {
            a[rt].m[3][3] = 1;
            a[rt].m[4][4] = 1;
        }
        return;
    }
    int m = (l+r)>>1;
    build(lson);build(rson);
    a[rt] = a[rt<<1]*a[rt<<1|1];
}
abc query(int L,int R,int l,int r,int rt)
{
    if (L<=l && r <= R)
        return a[rt];
    int m = (l+r)>>1;
    abc temp1,temp2;
    bool f1 = 0,f2 = 0;
    if (L <= m)
    {
        temp1 = query(L,R,lson);
        f1 = 1;
    }
    if (m < R)
    {
        temp2 = query(L,R,rson);
        f2 = 1;
    }
    if (f1&&f2)
        return temp1*temp2;
    if (f1)
        return temp1;
    if (f2)
        return temp2;
}
int main()
{
    //freopen("F:\\rush.txt","r",stdin);
    rei(n);rei(q);
    scanf("%s",s+1);
    build(1,n,1);
    rep1(i,1,q)
    {
        int L,R;
        rei(L);rei(R);
        int ans = query(L,R,1,n,1).m[0][4];
        if (ans>=INF)
            puts("-1");
        else
            cout << ans << endl;
    }
    return 0;
}