• [1051] The Rascal Triangle

  • 时间限制: 1000 ms 内存限制: 65535 K
  • 问题描述
  • The Rascal Triangle definition is similar to that of the Pascal Triangle. The rows are numbered from the top starting with 0. Each row n contains n + 1 numbers indexed from 0 to n. Using R(n, m) to indicate the index m item in the index n row:

    R(n, m) = 0 for n < 0 OR m < 0 OR m > n

    The first and last numbers in each row (which are the same in the top row) are 1:

    R(n, 0) = R(n, n) = 1

    The interior values are determined by (UpLeftEntry * UpRightEntry + 1) / UpEntry

    (See the parallelogram in the array below):

    R(n + 1, m + 1) = (R(n, m) * R(n, m + 1) + 1) / R(n – 1, m)

    1

    1 1

    1 2 1

    / \

    1 3 3 1

    \ /

    1 4 5 4 1

    Write a program which computes R(n, m) the mth element of the nth row of the Rascal Triangle.

  • 输入
  • The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line of input consisting of 3 space separated decimal integers. The first integer is data set number, N. The second integer is row number n, and the third integer is the index m within the row of the entry for which you are to find R(n, m) the Rascal Triangle entry (0 ≤ m ≤ n ≤ 50000).
  • 输出
  • For each data set there is one line of output. It contains the data set number, N, followed by a single space which is then followed by the Rascal Triangle entry R(n, m) accurate to the nearest integer value.
  • 样例输入
  • 5
    1 4 0
    2 4 2
    3 45678 12345
    4 12345 9876
    5 34567 11398
    
  • 样例输出
  • 1 1
    2 5
    3 411495886
    4 24383845
    5 264080263
    
  • 提示
  • 来源
  • Greater New York Regional
  • 操作

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