Intervals
Time Limit: 2000MS
Memory Limit: 65536K
Total Submissions: 20775
Accepted: 7859
Description
You are given n closed, integer intervals [ai, bi] and n integers c1, ..., cn.
Write a program that:
reads the number of intervals, their end points and integers c1, ..., cn from the standard input,
computes the minimal size of a set Z of integers which has at least ci common elements with interval [ai, bi], for each i=1,2,...,n,
writes the answer to the standard output.
Input
The first line of the input contains an integer n (1 <= n <= 50000) -- the number of intervals. The following n lines describe the intervals. The (i+1)-th line of the input contains three integers ai, bi and ci separated by single spaces and such that 0 <=
ai <= bi <= 50000 and 1 <= ci <= bi - ai+1.
Output
The output contains exactly one integer equal to the minimal size of set Z sharing at least ci elements with interval [ai, bi], for each i=1,2,...,n.
Sample Input
5
3 7 3
8 10 3
6 8 1
1 3 1
10 11 1
Sample Output
6
題意:告訴你n個區間,要在第i區間至少取ci個數,問所有區間總共至少去多少個數?
這題的構圖很是巧妙,把每個邊界看成節點,Xi表示0-i有多少個數被選上,則每個區間[li,ri]可以推出X[ri]-X[li-1]>=Ci,即:X[li-1]-X[ri]<=-Ci。
潛在不等式:
1、X[i]-X[i+1]<=0;
2、X[i+1]-X[i]<=0.
本題我多了一個離散化操作。
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