题意:把连续的n天, 分为连续的m段,使得每段中的花费尽可能的小,求最大的花费。
解题思路:典型的二分, 可行性的判定模拟一下,因为是连续的所以a数组的次序不能打乱(不能排序)。
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 ≤ moneyi ≤ 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
Lines 2.. N+1: Line i+1 contains the number of dollars Farmer John spends on the ith day
Output
Sample Input
7 5 100 400 300 100 500 101 400
Sample Output
500
Hint
Memory: 1088 KB | Time: 32 MS | |
Language: G++ | Result: Accepted |
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cctype>
#include<list>
#include<iostream>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>
using namespace std;
#define FOR(i, s, t) for(int i = (s) ; i <= (t) ; ++i)
#define REP(i, n) for(int i = 0 ; i < (n) ; ++i)
int buf[10];
inline long long read()
{
long long x=0,f=1;
char ch=getchar();
while(ch<'0'||ch>'9')
{
if(ch=='-')f=-1;
ch=getchar();
}
while(ch>='0'&&ch<='9')
{
x=x*10+ch-'0';
ch=getchar();
}
return x*f;
}
inline void writenum(int i)
{
int p = 0;
if(i == 0) p++;
else while(i)
{
buf[p++] = i % 10;
i /= 10;
}
for(int j = p - 1 ; j >= 0 ; --j) putchar('0' + buf[j]);
}
/**************************************************************/
#define MAX_N 100005
const int INF = 0x3f3f3f3f;
int a[MAX_N];
int n, m;
bool f(int x)
{
int cnt = 1;
int sum = 0;
for(int i = 0 ; i < n ; i++)
{
if(a[i] > x)
return false;
if(sum + a[i] <= x)
{
sum += a[i];
}
else
{
cnt++;
// cout<<cnt<<endl;
// cout<<sum<<endl;
sum = a[i];
}
if(cnt > m) return false;
}
return true;
}
int main()
{
while(~scanf("%d%d", &n, &m))
{
for(int i = 0 ; i < n ; i++)
{
a[i] = read();
}
int lb = -1, ub = 100005;
while(ub - lb > 1)
{
int mid = (ub + lb) /2;
if(f(mid)) ub = mid;
else lb = mid;
}
printf("%d\n", ub);
}
return 0;
}