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  • Gym 100463A Crossings (树状数组 逆序对)

    Crossings

    Time Limit: 20 Sec

    Memory Limit: 256 MB

    题目连接

    http://codeforces.com/gym/100463

    Description

    Given a permutation P of {0, 1, ..., n − 1}, we define the crossing number of it as follows. Write the sequence 0, 1, 2, . . . , n − 1 from left to right above the sequence P(0), P(1), . . . , P(n − 1). Draw a straignt line from 0 in the top line to 0 in the bottom line, from 1 to 1, and so on. The crossing number of P is the number of pairs of lines that cross. For example, if n = 5 and P = [1, 3, 0, 2, 4], then the crossing number of P is 3, as shown in the figure below. !""""#""""""""""""&" In this problem a permutation will be specified by a tuple (n, a, b), where n is a prime and a and b are integers (1 ≤ a ≤ n − 1 and 0 ≤ b ≤ n − 1). We call this permutation Perm(n, a, b), and the ith element of it is a ∗ i + b mod n (with i in the range [0, n − 1]). So the example above is specified by Perm(5, 2, 1).

    Input

    There are several test cases in the input file. Each test case is specified by three space-separated numbers n, a, and b on a line. The prime n will be at most 1,000,000. The input is terminated with a line containing three zeros.

    Output

    For each case in the input print out the case number followed by the crossing number of the permutation. Follow the format in the example output.

    Sample Input

    5 2 1 19 12 7 0 0 0

    Sample Output

    Case 1: 3 Case 2: 77

    HINT

     思路:

    很明显的逆序对。。照着公式把每个值算出来,然后直接求逆序对个数就好了。

    注意要开long long 要不会超时。。。因为中间计算公式的时候值是超过了in范围t的,

    不开long long就会陷入死循环

    实现代码:

    //#pragma comment(linker, "/STACK:1024000000,1024000000")
    #include<iostream>
    #include<cstring>
    #include<algorithm>
    #include<cstdio>
    #define ll long long
    using namespace std;
    #define lson l,m,rt<<1
    #define rson m+1,r,rt<<1|1
    #define mid int m = (l + r) >> 1
    const int M = 1e6 + 10;
    const double EPS = 1e-8;
    //inline int sgn(double x) return (x > EPS) - (x < -EPS); //浮点数比较常数优化写法
    int c[M],l[M];
    ll n;
    
    int lowbit(int x){
        return x&(-x);
    }
    
    int getsum(int x){
        int sum = 0;
        while(x>0){
            sum += c[x];
            x -= lowbit(x);
        }
        return sum;
    }
    
    void update(int x,int value){
        while(x<=n){
            c[x] += value;
            x += lowbit(x);
        }
    }
    
    int main()
    {
        ll a,b;
        int cal = 1;
        while(scanf("%lld%lld%lld",&n,&a,&b)!=EOF){
            memset(c,0,sizeof(c));
            if(n==0&&a==0&&b==0) break;
            for(int i = 1;i <= n;i ++){
                l[i] = ((i-1)*a+b)%n+1;
            }
            ll ans = 0;
            for(int i = 1;i <= n;i ++){
                update(l[i],1);
                ans +=i - getsum(l[i]);
            }
    
            printf("Case %d: %lld
    ",cal++,ans);
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/kls123/p/8977485.html
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