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Codeforces Round #257 (Div. 2)449A - Jzzhu and Chocolate(贪心、数学)

题目链接:http://codeforces.com/problemset/problem/449/A


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A. Jzzhu and Chocolate
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Jzzhu has a big rectangular chocolate bar that consists of n?×?m unit squares. He wants to cut this bar exactly k times. Each cut must meet the following requirements:

  • each cut should be straight (horizontal or vertical);
  • each cut should go along edges of unit squares (it is prohibited to divide any unit chocolate square with cut);
  • each cut should go inside the whole chocolate bar, and all cuts must be distinct.

The picture below shows a possible way to cut a 5?×?6 chocolate for 5 times.

Imagine Jzzhu have made k cuts and the big chocolate is splitted into several pieces. Consider the smallest (by area) piece of the chocolate, Jzzhu wants this piece to be as large as possible. What is the maximum possible area of smallest piece he can get with exactlyk cuts? The area of a chocolate piece is the number of unit squares in it.

Input

A single line contains three integers n,?m,?k (1?≤?n,?m?≤?109; 1?≤?k?≤?2·109).

Output

Output a single integer representing the answer. If it is impossible to cut the big chocolate k times, print -1.

Sample test(s)
input
3 4 1
output
6
input
6 4 2
output
8
input
2 3 4
output
-1
Note

In the first sample, Jzzhu can cut the chocolate following the picture below:

In the second sample the optimal division looks like this:

In the third sample, it‘s impossible to cut a 2?×?3 chocolate 4 times.


题意:给出一个 n * m 大小的chocolate bar,你需要在这个bar上切 k 刀,使得最小的部分面积尽可能大,求出这个被划分后的最小部分面积最大可以为多少。如果这个chocolate bar 不能切成 k 部分,则输出-1。注意,每一刀需要符合3个条件:1、打横切或打竖切; 2、每一刀只能经过unit square(即1*1的单元bar)的边,也就是说不能把一个单元bar损坏,要完整; 3、每一刀只能在整个chocolate bar的里面操作,也就是说,外围的四条边是不允许切的。4、每一刀都是不相同的。

思路转载

 首先要知道什么时候这个大bar不能切成 k 刀。很容易知道是如果k > (n-1)+(m-1) 的情况,因为外围的四条边是不允许操刀的!排除这个不能切的情况后,那么就要根据是从n(打横切)还是从m(打竖切)来进行讨论了。不过由于我们不能一眼看出哪种方案更优,所以两者都要讨论下,我一开始只想到 if 中的两条式子,n/(k+1)的意思表示这 k 刀都打横切,而分母为什么是k+1而不是k,是因为一刀可以把一个区域分成两部分,两刀就三个部分,依次类推。而我们需要求的是面积,就需要用到部分,而不是刀数了。m/(k+1)依此类推。

     不过问题出现了,我根据test10返回的wa结果来想出的^_^。有可能完全打横切或者打竖切都没有切够k刀!那么就需要把剩余的刀数分到打竖切(对应之前完全打横切)或者打横切(对应之前的完全打竖切)中了。也就是代码中else的部分。其实完整的a1表达式是这样的:n/(n-1) * m/(k-(n-1)+1),意思:完全打横切,只能切n-1刀,那么它划分的最小部分的面积就充当1了,至于m/(k-(n-1)+1) 表示 打竖切还能切多少刀,+1是因为是求分成的部分,而不是多少刀,与if中的n/(k+1)中的+1意思是相同的。

     (好开心这道题目排到最少用时的26名,继续努力!  ^_^)

代码如下:

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define LL __int64
int main()
{
	LL n, m, k;
	LL ans1, ans2;
	while(~scanf("%I64d%I64d%I64d",&n,&m,&k))
	{
		if(n-1+m-1 < k)
		{
			printf("-1\n");
			continue;
		}
		if(n >= k+1 || m >= k+1)
		{
			ans1 = n/(k+1)*m;
			ans2 = m/(k+1)*n;
		}
		else
		{
			ans1 = n/(k-(m-1)+1)*1;
			ans2 = m/(k-(n-1)+1)*1;
		}
		LL ans = max(ans1, ans2);
		printf("%I64d\n",ans);
	}
	return 0;
}


Codeforces Round #257 (Div. 2)449A - Jzzhu and Chocolate(贪心、数学)