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  • Light bulbs (树状数组模板题)

    There are N light bulbs indexed from 00 to N1. Initially, all of them are off.

    A FLIP operation switches the state of a contiguous subset of bulbs. FLIP(L, R)means to flip all bulbs x such that LxR. So for example, FLIP(3, 5) means to flip bulbs 3 , 4 and 5, and FLIP(5, 5)means to flip bulb 5.

    Given the value of N and a sequence of M flips, count the number of light bulbs that will be on at the end state.

    InputFile

    The first line of the input gives the number of test cases, TT test cases follow. Each test case starts with a line containing two integers N and M, the number of light bulbs and the number of operations, respectively. Then, there are M more lines, the i-th of which contains the two integers Li and Ri, indicating that the ii-th operation would like to flip all the bulbs from Li to Ri , inclusive.

    1T1000

    1 N1000000

    1 M1000

    0LiRiN1

    OutputFile

    For each test case, output one line containing Case #x: y, where xx is the test case number (starting from 11) and yyis the number of light bulbs that will be on at the end state, as described above.

    样例输入

    2
    10 2
    2 6
    4 8
    6 3
    1 1
    2 3
    3 4
    

    样例输出

    Case #1: 4
    Case #2: 3
    题意:n个灯,m次操作,每次把一个区间的灯反转,最初都是暗的,问最后有多少灯是亮的;
    题解:树状数组,每次调用add()函数把L处加一,R+1处减一,然后最后把每一个区间用排序去重之后计算当前区间处L(只用L就够了)被加了多少次(通过调用ask()函数计算),偶数就代表当前区间的灯都是关的,反之就是开的,然后这个区间长度就是
    (str[i+1]-1)-str[i]+1;
    还有就是记得内存限制;
    最后每一次树状数组清零时是通过保存输入进行清零的,L处减一,R+1处加一;
    总的复杂度是O(t*m*log(n));
    #include <bits/stdc++.h>
    #pragma GCC optimize(3)
    using namespace std;
    const int maxn=2e3+5;
    int str[maxn],str2[maxn],c[1000005],n,m;
    int ask(int x)
    {
        int ans=0;
        for(; x; x-=x&-x)ans+=c[x];
        return ans;
    }
    void add(int x,int y)
    {
        for(; x<=n; x+=x&-x)c[x]+=y;
    }
    template<class T>
    inline void read(T&x)
    {
        T ans=0,f=1;
        char ch=getchar();
        while(ch<'0'||ch>'9')
        {
            if(ch=='-')f=-1;
            ch=getchar();
        }
        while(ch>='0'&&ch<='9')
        {
            ans=ans*10+ch-'0';
            ch=getchar();
        }
        x=ans*f;
    }
    int main()
    {
        int t,l,r,cnt=0,k=0;
        read(t);
        while(t--)
        {
            cnt=0;
            read(n);
            read(m);
            int m2=m;
            while(m2--)
            {
                read(l);read(r);
                ++l,++r;
                add(l,1);
                add(r+1,-1);
                str[++cnt]=l,str2[cnt]=l;
                str[++cnt]=r+1,str2[cnt]=r+1;
            }
            sort(str+1,str+cnt+1);
            int cnt2=0;
            for(int i=1; i<=cnt; ++i)
            {
                if(str[i]!=str[cnt2])
                    str[++cnt2]=str[i];
            }
            int ans=0,flag;
            for(int i=1; i<cnt2; ++i)
            {
                flag=ask(str[i]);
                if((flag&1)==1)
                    ans+=str[i+1]-1-str[i]+1;
            }
            printf("Case #%d: %d
    ",++k,ans);
            for(int i=1; i<=2*m; i+=2)
            {
                add(str2[i],-1);
                add(str2[i+1],1);
            }
        }
        return 0;
    }
    

      

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  • 原文地址:https://www.cnblogs.com/lengsong/p/11523654.html
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