CodeForces - 812C Sagheer and Nubian Market （二分）

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本文解析了Codeforces平台上的C题“Sagheer and Nubian Market”，介绍了该问题的背景、规则及解决思路。具体包括：市场售卖纪念品的特殊计价方式，以及如何在预算内最大化购买数量的同时最小化总花费。

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题目链接：http://codeforces.com/problemset/problem/812/C点击打开链接

On his trip to Luxor and Aswan, Sagheer went to a Nubian market to buy some souvenirs for his friends and relatives. The market has some strange rules. It contains n different items numbered from 1 to n. The i-th item has base cost ai Egyptian pounds. If Sagheer buys kitems with indices x1, x2, ..., xk, then the cost of item xj is axj + xj·k for 1 ≤ j ≤ k. In other words, the cost of an item is equal to its base cost in addition to its index multiplied by the factor k.

Sagheer wants to buy as many souvenirs as possible without paying more than S Egyptian pounds. Note that he cannot buy a souvenir more than once. If there are many ways to maximize the number of souvenirs, he will choose the way that will minimize the total cost. Can you help him with this task?

Input

The first line contains two integers n and S (1 ≤ n ≤ 105 and 1 ≤ S ≤ 109) — the number of souvenirs in the market and Sagheer's budget.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 105) — the base costs of the souvenirs.

Output

On a single line, print two integers k, T — the maximum number of souvenirs Sagheer can buy and the minimum total cost to buy these ksouvenirs.

   Examples
 
     input
   
3 11
2 3 5

     output
   
2 11

     input
   
4 100
1 2 5 6

     output
   
4 54

     input
   
1 7
7

     output
   
0 0

Note

In the first example, he cannot take the three items because they will cost him [5, 9, 14] with total cost 28. If he decides to take only two items, then the costs will be [4, 7, 11]. So he can afford the first and second items.

In the second example, he can buy all items as they will cost him [5, 10, 17, 22].

In the third example, there is only one souvenir in the market which will cost him 8 pounds, so he cannot buy it.

对买物品的个数二分然后判断能买的最大值

#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
#include <stdio.h>
#define maxn 2005
using namespace std;
struct xjy
{
    long long int num;
    long long int index;
    bool operator < (const xjy &r)const
    {
        return num>r.num;
    }
};
vector < xjy > s;
int main()
{
    long long int n,m;
    cin >> n >> m;
    for(int i=1;i<=n;i++)
    {
        xjy mid;
        scanf("%lld",&mid.num);
        mid.index=i;
        s.push_back(mid);
    }

    long long int l=0,r=n;
    long long int ans=0;
    long long int ansnum=0;
    while(l<=r)
    {
        long long int mid=(l+r)>>1;
        long long int midans=0;
        vector < long long int > ss;
        for(int i=0;i<s.size();i++)
            ss.push_back(s[i].num+s[i].index*mid);
        sort(ss.begin(),ss.end());
        for(int i=0;i<mid;i++)
            midans+=ss[i];
        if(midans<=m)
        {
            if(ans<midans)
                ans=midans,ansnum=mid;
            l=mid+1;
        }
        else
        {
            r=mid-1;
        }
    }
    cout << ansnum << " " << ans << endl;
}