The Rascal Triangle 题解

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Description

The Rascal Triangle definition is similar to that of the Pascal Triangle. The rows are numbered from the top starting with 0. Each rown 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)

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

Input

The first line of input contains a single integer P, ( 1 $\le$ P $\le$ 1000), which is the number of data sets that follow. Each data set is a single line of input consisting of 3 spaces separated decimal integers. The first integer is data set number, N. The second integer is row numbern, 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 $\le$ m $\le$ n $\le$ 50000).

Output

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 theRascal Triangle entry R(n, m) accurate to the nearest integer value.

Sample Input

51 4 02 4 23 45678 123454 12345 98765 34567 11398

Sample Output

1 12 53 4114958864 243838455 264080263

这一题不是像杨辉三家一样去递归，而是有公式：（n-m）*m+1

#include<stdio.h>#include<string.h>int T,i,N,n,m;int main(){    while(~scanf("%d",&T)){        for(i=0;i<T;i++){            scanf("%d %d %d",&N,&n,&m);            printf("%d %d\n",N,1+(n-m)*m);        }    }return 0;}