poj 3273 Monthly Expense 【二分】

最新推荐文章于 2019-04-20 09:48:00 发布

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最新推荐文章于 2019-04-20 09:48:00 发布

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本文探讨了农民约翰如何通过智能方法优化月度开销预算，将连续N天的开销合理分配到不超过M个连续时间段内，以确保每月开销最小化。通过二分查找算法实现这一目标，文章详细解释了解决方案及其背后的逻辑。

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Monthly Expense

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 19597		Accepted: 7748

Description

Farmer John is an astounding accounting wizard and has realized he might run out of money to run the farm. He has already calculated and recorded the exact amount of money (1 ≤ money_i ≤ 10,000) that he will need to spend each day over the next N (1 ≤ N ≤ 100,000) days.

FJ wants to create a budget for a sequential set of exactly M (1 ≤ M ≤ N) fiscal periods called "fajomonths". Each of these fajomonths contains a set of 1 or more consecutive days. Every day is contained in exactly one fajomonth.

FJ's goal is to arrange the fajomonths so as to minimize the expenses of the fajomonth with the highest spending and thus determine his monthly spending limit.

Input

Line 1: Two space-separated integers: N and M
Lines 2..N+1: Line i+1 contains the number of dollars Farmer John spends on the ith day

Output

Line 1: The smallest possible monthly limit Farmer John can afford to live with.

Sample Input

Sample Output

Hint

If Farmer John schedules the months so that the first two days are a month, the third and fourth are a month, and the last three are their own months, he spends at most $500 in any month. Any other method of scheduling gives a larger minimum monthly limit.

题意：给定连续N天每天要花的钱，一个“fajomonths”由连续的天组成。现在把N天分成不超过M个"fajomonths"，要求所有"fajomonths'里面的最大花费最小化。

二分。。。

AC代码：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <vector>
#define INF 0x3f3f3f
#define eps 1e-8
#define MAXN (100000+1)
#define MAXM (100000)
#define Ri(a) scanf("%d", &a)
#define Rl(a) scanf("%lld", &a)
#define Rf(a) scanf("%lf", &a)
#define Rs(a) scanf("%s", a)
#define Pi(a) printf("%d\n", (a))
#define Pf(a) printf("%.2lf\n", (a))
#define Pl(a) printf("%lld\n", (a))
#define Ps(a) printf("%s\n", (a))
#define W(a) while(a--)
#define CLR(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define LL long long
#define lson o<<1, l, mid
#define rson o<<1|1, mid+1, r
#define ll o<<1
#define rr o<<1|1
using namespace std;
int a[MAXN];
bool judge(int o, int n, int m)
{
    int cnt = 1; LL sum = 0;
    for(int i = 1; i <= n; i++)
    {
        if(sum + a[i] > o)
        {
            cnt++;
            sum = a[i];
        }
        else
            sum += a[i];
    }
    return cnt <= m;
}
int main()
{
    int N, M;
    while(scanf("%d%d", &N, &M) != EOF)
    {
        int l = 0, r = 0;
        for(int i = 1; i <= N; i++)
        {
            Ri(a[i]);
            r += a[i];
            l = max(a[i], l);
        }
        int ans = 0;
        while(l <= r)
        {
            LL mid = (l + r) >> 1;
            if(judge(mid, N, M))
            {
                ans = mid;
                r = mid-1;
            }
            else
                l = mid+1;
        }
        Pi(ans);
    }
    return 0;
}