TopCoder SRM 598 Div1 第1题

Problem Statement
	Fox Ciel has some items. The weight of the i-th (0-based) item is item[i]. She wants to put all items into bins. The capacity of each bin is 300. She can put an arbitrary number of items into a single bin, but the total weight of items in a bin must be less than or equal to 300. You are given the vector <int> item. It is known that the weight of each item is between 100 and 300, inclusive. Return the minimal number of bins required to store all items.
Definition
	Class: BinPacking Method: minBins Parameters: vector <int> Returns: int Method signature: int minBins(vector <int> item) (be sure your method is public)
Constraints
-	item will contain between 1 and 50 elements, inclusive.
-	Each element of item will be between 100 and 300, inclusive.
Examples
0)
	{150, 150, 150, 150, 150} Returns: 3 You have five items and each bin can hold at most two of them. You need at least three bins.
1)
	{130, 140, 150, 160} Returns: 2 For example, you can distribute the items in the following way: Bin 1: 130, 150 Bin 2: 140, 160
2)
	{100, 100, 100, 100, 100, 100, 100, 100, 100} Returns: 3
3)
	{100, 200, 100, 100, 100, 100, 200, 100, 200} Returns: 4
4)
	{157, 142, 167, 133, 135, 157, 143, 160, 141, 123, 162, 159, 165, 137, 138, 152} Returns: 8

 

类型：其他  难度：2.5

题意：给出一组数，表示一组物品的重量，每个物品重量范围[100,300]，现在要将这组物品放到若干个桶中，每个桶最多放重量300的物品，问最少需要多少桶

分析：一开始把题目想简单了，经过几次修改才正确。

1、首先将物品按重量排序，从重量大的遍历，考虑大于200的物品，这些物品必定一个物品占一个桶（因为最轻的物品重量为100，大于200的不能和其他物品放在一个桶里）

2、再遍历剩余的物品，找到当前最重的物品，并找到能和它放在一个桶中的最重的物品

（1）若没有和它能放在一个桶中的，那么这个物品单独占一个桶

（2）若有，那么这两个物品放在一个桶中

3、若当前最重物品重量为100，那么还需要（剩余物品数+2）/ 3 个桶

代码：

#include<string>
#include<cstdio>
#include<vector>
#include<cstring>
#include<map>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<set>
using namespace std;

class BinPacking
{
public:
int minBins(vector <int> item)
{
sort(item.begin(),item.end());

int ans = 0;

vector<int>::iterator it;
while(!item.empty() && item.back()>200)
{
ans++;
item.pop_back();
}
while(!item.empty())
{
int i=item.size()-1,j=i-1;
if(item[i]==100)
{
ans += (item.size()+2)/3;
return ans;
}
for(; j>=0; j--)
{
if(item[i]+item[j]<=300)
break;
}
item.pop_back();
if(j>=0) item.erase(item.begin()+j,item.begin()+j+1);
ans++;
}

return ans;
}
};

int main()
{
int a[] = {100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 193, 160, 124, 178, 105, 150, 140, 117, 219, 126, 153, 183, 212, 179, 140, 103, 195};
vector<int> tmp;
for(int i=0; a[i]>0; i++)
{
tmp.push_back(a[i]);
}
BinPacking t;
cout<<t.minBins(tmp)<<endl;
}