POJ 3273 USACO 2007 Mar Monthly Expense 二分答案

长度为n的序列分成m块是每块数字之和的最大值最小。

二分答案。

如果按给定和的最大值依次分超过了m块，数字就小了。

否则数字就大了。

正确性怎么证都行。。

#include <cstdio>
int main() {
static int d[100005];
int n, m, i, ma, s, l, r, mid, c;
while (scanf("%d%d", &n, &m) != EOF) {
ma = s = 0;
for (i = 1; i <= n; ++i) {
scanf("%d", d + i); s += d[i];
if (d[i] > ma) ma = d[i];
}
l = ma, r = s;
while (l < r) {
s = c = 0;
mid = l + r >> 1;
for (i = 1; i <= n; ++i) {
s += d[i];
if (s > mid) ++c, s = d[i];
}
if (++c > m) l = mid + 1;
else r = mid - 1;
}
printf("%d\n", l);
}
return 0;
}

Monthly Expense

Time Limit: 2000MS Memory Limit: 65536K

Total Submissions: 20927 Accepted: 8198

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

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

7 5

100

400

300

100

500

101

400

Sample Output

500

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.

Source

USACO 2007 March Silver