zoukankan      html  css  js  c++  java
  • Codeforces Round #309 (Div. 2) C. Kyoya and Colored Balls

    Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color ibefore drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen.

    Input

    The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.

    Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).

    The total number of balls doesn't exceed 1000.

    Output

    A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.

    Sample test(s)
    input
    3
    2
    2
    1
    
    output
    3
    
    input
    4
    1
    2
    3
    4
    
    output
    1680
    
    Note

    In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:

    1 2 1 2 3
    1 1 2 2 3
    

    2 1 1 2 3

    这道题让我学会了组合数的计算,因为直接用组合数公式会导致结果不准确,如C(100,50)这样,如果用乘一个数除一个数的方法,那么可能会导致不能整除而会发生误差。

    思路:若前i种颜色的方法总数是f(i),那么第i+1种颜色的方法总数是f(i+1)=f(i)*C(sum(i+1)-1,a[i+1]-1),其中sum(i+1)是前i+1种颜色的个数总和。

    #include<stdio.h>
    #include<string.h>
    #include<iostream>
    #include<string>
    #include<map>
    #include<algorithm>
    using namespace std;
    #define ll __int64
    #define maxn 1000000007
    int a[1600];
    ll c[1050][1060];
    ll sum;
    
    int main()
    {
    	int n,m,i,j,sum1;
    	for(i=1;i<=1000;i++)c[i][0]=1;
    	
    	for(i=1;i<=1000;i++){
    		for(j=1;j<=i;j++){
    			if(i==j)c[i][j]=1;
    			else if(i>j)
    			c[i][j]=(c[i-1][j]+c[i-1][j-1])%maxn;
    		}
    	}
    	
    	while(scanf("%d",&n)!=EOF)
    	{
    		for(i=1;i<=n;i++){
    			scanf("%d",&a[i]);
    		}
    		sum1=a[1];sum=1;
    		for(i=2;i<=n;i++){
    			sum1+=a[i];
    			//printf("%d %d
    ",a[i]-1,sum1-1);
    			sum=(sum*c[sum1-1][a[i]-1])%maxn;
    			//sum=(sum*f(a[i]-1,sum1-1))%maxn;
    			//printf("%lld
    ",sum);
    		}
    		printf("%I64d
    ",sum);
    	}
    	return 0;
    }


  • 相关阅读:
    64位系统下,一个32位的程序究竟可以申请到多少内存,4GB还是更多
    selenium3 + python3
    selenium3 + python
    selenium3 + python
    selenium3+python-多窗口、句柄(handle)
    selenium3 + python
    selenium3 + python
    selenium3 + python 操作浏览器基本方法
    Appium
    Appium
  • 原文地址:https://www.cnblogs.com/herumw/p/9464718.html
Copyright © 2011-2022 走看看