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  • Codeforces Round #256 (Div. 2) D. Multiplication Table 二分法

    
    D. Multiplication Table
    time limit per test
    1 second
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    Bizon the Champion isn't just charming, he also is very smart.

    While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number?

    Bizon the Champion always answered correctly and immediately. Can you repeat his success?

    Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.

    Input

    The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).

    Output

    Print the k-th largest number in a n × m multiplication table.

    Sample test(s)
    Input
    2 2 2
    
    Output
    2
    
    Input
    2 3 4
    
    Output
    3
    
    Input
    1 10 5
    
    Output
    5
    
    Note

    A 2 × 3 multiplication table looks like this:

    1 2 3
    2 4 6



    题意:给一个n*m的乘法表找第k大的数。

    思路:二分。对于每一行找比mid小的数的个数加起来假设等于k就找到啦。

    AC代码:
    #include <cstdio>
    #include <iostream>
    using namespace std;
    typedef long long ll;
    
    ll solve(ll x,int n,int m){
        ll res=0;
        for(int i=1;i<=n;i++){
            res+=min((ll)m,x/i);
        }
        return res;
    }
    
    int main(){
        int n,m;
        ll k;
        scanf("%d%d",&n,&m);
        cin>>k;
        ll l=1,r=(ll)n*m+1;
        while(l<r){
            ll mid=(l+r)/2;
            if(solve(mid,n,m)<k)
                l=mid+1;
            else
                r=mid;
        }
        cout<<l<<endl;
        return 0;
    }





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  • 原文地址:https://www.cnblogs.com/bhlsheji/p/4572945.html
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