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最新推荐文章于 2024-06-28 09:30:57 发布

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本文探讨了一个有趣的组合数学问题，通过观察不同数量的蚂蚁家族形成各种大小的蚂蚁组合，提出了一种计算特定范围内所有可能组合数量的方法。

Bessie was poking around the ant hill one day watching the ants march to and fro while gathering food. She realized that many of the ants were siblings, indistinguishable from one another. She also realized the sometimes only one ant would go for food, sometimes a few, and sometimes all of them. This made for a large number of different sets of ants!

Being a bit mathematical, Bessie started wondering. Bessie noted that the hive has T (1 <= T <= 1,000) families of ants which she labeled 1..T (A ants altogether). Each family had some number Ni (1 <= Ni <= 100) of ants.

How many groups of sizes S, S+1, ..., B (1 <= S <= B <= A) can be formed?

While observing one group, the set of three ant families was seen as {1, 1, 2, 2, 3}, though rarely in that order. The possible sets of marching ants were:

3 sets with 1 ant: {1} {2} {3}
5 sets with 2 ants: {1,1} {1,2} {1,3} {2,2} {2,3}
5 sets with 3 ants: {1,1,2} {1,1,3} {1,2,2} {1,2,3} {2,2,3}
3 sets with 4 ants: {1,2,2,3} {1,1,2,2} {1,1,2,3}
1 set with 5 ants: {1,1,2,2,3}

Your job is to count the number of possible sets of ants given the data above.

输入

* Line 1: 4 space-separated integers: T, A, S, and B

* Lines 2..A+1: Each line contains a single integer that is an ant type present in the hive

输出

* Line 1: The number of sets of size S..B (inclusive) that can be created. A set like {1,2} is the same as the set {2,1} and should not be double-counted. Print only the LAST SIX DIGITS of this number, with no leading zeroes or spaces

有一天，贝西在蚁丘周围闲逛，看着蚂蚁来回走动，同时采集食物。她意识到许多蚂蚁是兄弟姐妹，彼此无法区分。她还意识到有时只有一只蚂蚁会去觅食，有时是几只，有时是全部。这使得大量不同的蚂蚁组！

有点数学，贝西开始怀疑。 Bessie 指出蜂巢中有 T (1 <= T <= 1,000) 个蚂蚁家族，她将其标记为 1..T（总共 A 蚂蚁）。每个家庭都有一些 Ni (1 <= Ni <= 100) 蚂蚁。

可以形成多少组大小 S, S+1, ..., B (1 <= S <= B <= A)？

在观察一组时，三个蚂蚁家族的集合被视为 {1, 1, 2, 2, 3}，尽管很少按此顺序。可能的行军蚂蚁是：

3 组和 1 只蚂蚁：{1} {2} {3}
5 组 2 只蚂蚁：{1,1} {1,2} {1,3} {2,2} {2,3}
5 组 3 只蚂蚁：{1,1,2} {1,1,3} {1,2,2} {1,2,3} {2,2,3}
3 组 4 只蚂蚁：{1,2,2,3} {1,1,2,2} {1,1,2,3}
1 组 5 只蚂蚁：{1,1,2,2,3}

你的工作是根据上述数据计算可能的蚂蚁组数。

输入

* 第 1 行：4 个空格分隔的整数：T、A、S 和 B

* 第 2..A+1 行：每行包含一个整数，它是蜂巢中存在的蚂蚁类型

输出

* 第 1 行：可创建的大小 S..B（含）的组数。像 {1,2} 这样的集合与集合 {2,1} 相同，不应重复计算。仅打印此数字的最后六位数字，没有前导零或空格