Random Ranking
题意翻译
有一场由 $n$ 个参与者参加的竞赛。每个参与者都会得到一个特定的分数。如果我们对他们以前的表现做一些统计，我们可以或多或少地预测积分榜。
参与者的分数将在区间 $[l_i, r_i]$ 中均匀分布（分数可以是实数）。你能根据这些数据预测积分榜吗？换句话说，你应该告诉每个参与者他在积分榜上取得固定位置的可能性。参赛者在积分榜上以增序排序。因此，得分最高的参与者应当是最后一名。
$n \leq 80$。
允许误差为 $10^{-6}$。
题目描述
Imagine a real contest or exam of $ n $ participants. Every participant will get a particular score. We can predict the standings board more or less, if we do some statistics on their previous performance.
Let's say the score of the participants will be uniformly distributed in interval $ [l_{i},r_{i}] $ (the score can be a real number). Can you predict the standings board according to these data? In other words you should say for each participant the probability that he gets some fixed place in the scoreboard. The participants are sorted by increasing of their scores in the scoreboard. So, the participant with the largest score gets the last place.
输入输出格式
输入格式
The first line contains integer $ n $ ( $ 1<=n<=80 $ ), showing how many participants we have. Each of the next $ n $ lines contains our predictions, the $ i $ -th line contains a pair of integers $ l_{i},r_{i} $ $ (0<=l_{i}<r_{i}<=10^{9}) $ as the distributed interval for participant $ i $ .
Consider the participants numbered from $ 1 $ to $ n $ in some way.
输出格式
Output a distributed matrix $ a $ of order $ n $ . The element $ a_{ij} $ of the matrix is the probability that participant $ i $ has rank $ j $ .
Your answer will considered correct if it has at most $ 10^{-6} $ absolute or relative error.
输入输出样例
输入样例 #1
2
1 6
4 9
输出样例 #1
0.9200000000 0.080
0.080 0.9200000000
输入样例 #2
8
0 2
1 3
2 4
3 5
4 6
5 7
6 8
7 9
输出样例 #2
0.875 0.125 0 0 0 0 0 0
0.125 0.750 0.125 0 0 0 0 0
0 0.125 0.750 0.125 0 0 0 0
0 0 0.125 0.750 0.125 0 0 0
0 0 0 0.125 0.750 0.125 0 0
0 0 0 0 0.125 0.750 0.125 0
0 0 0 0 0 0.125 0.750 0.125
0 0 0 0 0 0 0.125 0.875
说明
The score probability distribution is continuous, which means, there is no possibility for a draw.