【题解】poj2279Mr. Young's Picture Permutations 杨氏矩阵

最新推荐文章于 2020-10-07 12:45:20 发布

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最新推荐文章于 2020-10-07 12:45:20 发布

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分类专栏：算法竞赛进阶指南 poj 杨氏矩阵文章标签：杨氏矩阵

本文链接：https://blog.youkuaiyun.com/qq_41958841/article/details/82808272

本文介绍了杨氏矩阵及其在排列问题中的应用。给出了杨氏矩阵的递推公式和固定形状杨氏矩阵的钩子公式，帮助计算不同形状的矩阵排列数。

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题目链接

Description

Mr. Young wishes to take a picture of his class. The students will stand in rows with each row no longer than the row behind it and the left ends of the rows aligned. For instance, 12 students could be arranged in rows (from back to front) of 5, 3, 3 and 1 students.
X X X X X

X X X

In addition, Mr. Young wants the students in each row arranged so that heights decrease from left to right. Also, student heights should decrease from the back to the front. Thinking about it, Mr. Young sees that for the 12-student example, there are at least two ways to arrange the students (with 1 as the tallest etc.):
1 2 3 4 5 1 5 8 11 12

6 7 8 2 6 9

9 10 11 3 7 10

12 4

Mr. Young wonders how many different arrangements of the students there might be for a given arrangement of rows. He tries counting