[USACO11NOV]Cow Lineup S

题目背景

【问题描述】

农民约翰雇一个专业摄影师给他的部分牛拍照。由于约翰的牛有好多品种，他喜欢他的照片包含每

个品种的至少一头牛。

约翰的牛都站在一条沿线的不同地方， 每一头牛由一个整数位置 $X_i$ 以及整数品种编号 $ID_i$ 表示。

约翰想拍一张照片，这照片由沿线的奶牛的连续范围组成。照片的成本与规模相当，这就意味着，在一

系列照片中的最大和最小 $X$ 坐标的差距决定了照片的成本。

请帮助约翰计算最小的照片成本，这些照片中有每个不同的品种的至少一头牛，没有两头牛愿意站

在同一个地点的。

【输入格式】

第 $1$ 行：牛的数量 $N$；

第 $2..1+N$ 行：每行包含 2 个以空格分隔的正整数 $X_i$ 和 $ID_i$；意义如题目描述；

【输出格式】

输出共一行，包含每个不同品种 $\rm ID$ 的照片的最低成本。

【输入样例】

6 25 7 26 1 15 1 22 3 20 1 30 1 【输出样例】

4 【输入说明】在不同的坐标点 $25,26,15,22,20,30$ 中有六头牛

【输出说明】在约翰的牛中，从 $X=22$ 到 $X=26$（整个规模为 4）包含了每个的不同品种的 $ID_3，ID_7$ 和 $ID_1$。

【数据规模】

对于 50%的数据： $1≤N≤300$；

对于 100%的数据：$1≤N≤50,000$；$0≤X_i≤1,000,000,000$；$1≤ID_i≤1,000,000$,000；

感谢uid=15936的翻译

题目描述

Farmer John has hired a professional photographer to take a picture of some of his cows. Since FJ's cows represent a variety of different breeds, he would like the photo to contain at least one cow from each distinct breed present in his herd.

FJ's N cows are all standing at various positions along a line, each described by an integer position (i.e., its x coordinate) as well as an integer breed ID. FJ plans to take a photograph of a contiguous range of cows along the line. The cost of this photograph is equal its size -- that is, the difference between the maximum and minimum x coordinates of the cows in the range of the photograph.

Please help FJ by computing the minimum cost of a photograph in which there is at least one cow of each distinct breed appearing in FJ's herd.

依次给出N头牛的位置及种类，要求找出连续一段，使其中包含所有种类的牛，问：这连续的一段最小长度是多少？

输入格式

* Line $1$: The number of cows, $N (1 <= N <= 50,000)$.

* Lines $2..1+N$: Each line contains two space-separated positive integers specifying the x coordinate and breed $\rm ID$ of a single cow. Both numbers are at most $1$ billion.

输出格式

* Line $1$: The smallest cost of a photograph containing each distinct breed $\rm ID$.

样例 #1

样例输入 #1

6 
25 7 
26 1 
15 1 
22 3 
20 1 
30 1

样例输出 #1

4

提示

There are $6$ cows, at positions $25,26,15,22,20,30,$ with respective breed IDs $7,1,1,3,1,1$.

The range from $x=22$ up through $x=26$ (of total size $4$) contains each of the distinct breed IDs $1, 3,$ and $7$ represented in FJ's herd.

感谢 wjcwinmt 提供题目简述