BINSTIRL - Binary Stirling Numbers
The Stirling number of the second kind S(n, m) stands for the number of ways to partition a set of n things into m nonempty subsets. For example, there are seven ways to split a four-element set into two parts: {1, 2, 3} u {4}, {1, 2, 4} u {3}, {1, 3, 4} u {2}, {2, 3, 4} u {1}, {1, 2} u {3, 4}, {1, 3} u {2, 4}, {1, 4} u {2, 3}.
There is a recurrence which allows you to compute S(n, m) for all m and n.
S(0, 0) = 1,
S(n, 0) = 0, for n > 0,
S(0, m) = 0, for m > 0,
S(n, m) = m*S(n-1, m) + S(n-1, m-1), for n, m > 0.
Your task is much "easier". Given integers n and m satisfying 1 <= m <= n, compute the parity of S(n, m), i.e. S(n, m) mod 2.
For instance, S(4, 2) mod 2 = 1.
Task
Write a program that:
- reads two positive integers n and m,
- computes S(n, m) mod 2,
- writes the result.
Input
The first line of the input contains exactly one positive integer d equal to the number of data sets, 1 <= d <= 200. The data sets follow.
Line i + 1 contains the i-th data set - exactly two integers ni and mi separated by a single space, 1 < = mi < = ni <= 109.
Output
The output should consist of exactly d lines, one line for each data set. Line i, 1 <= i < = d, should contain 0 or 1, the value of S(ni, mi) mod 2.
Example
Sample input: 1 4 2 Sample output: 1
hide comments
sacsachin:
2020-05-10 21:31:24
AC ... O(1) :) |
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cake_is_a_lie:
2017-03-03 14:06:11
OK, challenge accepted and completed: AC with O(1), without help from teh internets. For me, visual representation was key. Last edit: 2017-03-03 14:07:12 |
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rahulpadhy:
2016-08-24 04:56:14
How to derive the formula of the parity of the stirling numbers of the second kind that works in O(1) time ?
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gautam:
2016-04-26 15:07:54
O(1)...;-) |
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Vishesh Middha:
2015-08-15 14:49:57
providing SIGSEGV error why please explain??
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(Tjandra Satria Gunawan)(曾毅昆):
2015-07-28 05:54:23
Solve this problem without taking help from net? Challenge accepted ;-) |
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Rajat (1307086):
2014-12-28 23:04:26
Challenge for those who do not know Binary Stirling numbers:
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sunil gowda:
2014-12-20 09:51:15
how to do in O(1) time .. anyone knows..
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parijat bhatt:
2014-10-02 17:12:20
@ j1k7_7(JaskamalKainth)
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Anubhav Balodhi :
2014-08-13 17:02:56
Sierpinski Gasket does it all ^_^ |
Added by: | adrian |
Date: | 2004-07-02 |
Time limit: | 3s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All |
Resource: | ACM Central European Programming Contest, Warsaw 2001 |