cf.256.div2.D

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 ann × 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 32 4 6

题意:提供一个n*m的乘法表,输出其中第k大的数

题目链接


挑来挑去就选了这道字比较少的题...,

比赛时想:暴力肯定不行,于是找规律,也没什么进展,最后一次都没提交.....,挺失败的

隔了两天看到tags写着 binary search 就试着写了写

小于等于s有多少个数,可以这样求:

typedef long long ll;

ll ans = 0;

    for(int i = 1; i <= n; i++)
        ans += Min(s, m * i) / i;

蛮好想的

就是二分啊....每次写的都是生不如死,下次再碰到就照着改好了

#include <iostream>
#include <cstdio>

using namespace std;

#define Min(a,b) (a>b?b:a)

typedef long long ll;

ll n, m, k;

ll cal(ll s)
{
    ll ans = 0;
    for(int i = 1; i <= n; i++)
        ans += Min(s, m * i) / i;
    return ans;
}

int main()
{
    cin >> n >> m >> k;
    ll l, r;
    l = 1, r = n * m;
    while(l <= r)
    {
        ll m = (l + r) >> 1;
        ll tmp = cal(m);
        if( k <= tmp )
            r = m - 1;
        else
            l = m + 1;
    }
    cout << l << endl;
    system("pause");
    return 0;
}

哦对,还有就是要用 long long 储存答案,又多错了一次...,这也算是cf的特色了吧,hah