POJ 3046 Ant Counting 题解- 多重集组合数问题（附测试数据）

最新推荐文章于 2020-10-18 23:13:50 发布

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最新推荐文章于 2020-10-18 23:13:50 发布 · 427 阅读

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This blog discusses a problem where Bessie the cow observes ants and wants to calculate the number of unique sets of ants of sizes S to B that can be formed from T families, each having Ni ants (1 <= Ni <= 100). It presents the concept of multiset combinations and provides a dynamic programming solution. The blog includes test data and sample output." 114939264,10538722,GDAL Python教程：创建与操作几何形状,"['GIS', 'Python编程', 'GDAL库', '几何操作', '投影转换']

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Description

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 w