[UVa] 10105 - Polynomial Coefficients

題目網址: http://goo.gl/4eA5P0

題 意: 求多項式的某一項。


解法: 二項式定理推廣。

TAG: Math

注意:

程式碼:

	/**
	* Tittle: 10105 - Polynomial Coefficients
	* Author: Cheng-Shih, Wong
	* Date: 2015/03/22
	*/
	// include files
	#include <iostream>
	#include <cstdio>
	#include <cstring>
	using namespace std;
	// definitions
	#define FOR(i,a,b) for( int i=(a),_n=(b); i<=_n; ++i )
	#define clr(x,v) memset( x, v, sizeof(x) )
	#define N 15
	// declarations
	int n, k;
	int coef[N];
	int c[N][N];
	int ans;
	// functions
	// main function
	int main( void )
	{
	// init
	clr( c, 0 );
	FOR( i, 0, 12 ) {
	c[i][0] = c[i][i] = 1;
	FOR( j, 1, i-1 ) c[i][j] = c[i-1][j]+c[i-1][j-1];
	}
	// input
	while( scanf( "%d%d", &n, &k )==2 ) {
	FOR( i, 1, k ) scanf( "%d", &coef[i] );
	// solve
	ans = 1;
	FOR( i, 1, k ) {
	ans *= c[n][coef[i]];
	n -= coef[i];
	}
	printf( "%d\n", ans );
	}
	return 0;
	}

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