Kyoya and Colored Balls(组合数)

最新推荐文章于 2020-03-19 19:25:27 发布

转载最新推荐文章于 2020-03-19 19:25:27 发布 · 52 阅读

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原文链接：http://www.cnblogs.com/handsomecui/p/5418738.html

本文介绍了一道关于排列组合的问题，即如何计算特定条件下不同颜色球的排列方式数量。问题中涉及了球的颜色、数量及排列限制，并给出了具体的解决思路与代码实现。

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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 i before 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 c_i, the number of balls of the i-th color (1 ≤ c_i ≤ 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.

Examples

input

3 2 2 1

output

input

4 1 2 3 4

output

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

题意：

有k种颜色，每种颜色对应a[i]个球，球的总数不超过1000

要求第i种颜色的最后一个球，其后面接着的必须是第i+1种颜色的球

问一共有多少种排法
对于每一种颜色的求有当前所剩的总位数sum，当前颜色个数a
C(sum - 1, a - 1);
乘上所有的情况就好了；
另外组合数要打表求出；
C[i][j] = C[i - 1][j] + C[i - 1][j - 1];杨辉三角的求法；
代码：

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<iostream>
#define LL __int64
using namespace std;
const int MAXN = 1010;
const LL MOD = 1000000007;
int a[MAXN];
LL C[MAXN][MAXN];
void db(){
    C[0][0] = 1;
    C[1][0] = 1; C[1][1] = 1;
    for(int i = 2; i < MAXN; i++){
        C[i][0] = C[i][i] = 1;
        for(int j = 1; j < i; j++){
            C[i][j] = C[i - 1][j] + C[i - 1][j - 1];
            C[i][j] %= MOD;
        }
    }
}
int main(){
    int k;
    db();
    while(~scanf("%d", &k)){
        LL sum = 0;
        for(int i = 1; i <= k; i++){
            scanf("%d", a + i);
            sum += a[i];
        }
        LL ans = 1;
        for(int i = k; i >= 1; i--){
            ans *= C[sum - 1][a[i] - 1];
            ans %= MOD;
        //    printf("%d %d %d\n", sum - 1, a[i] - 1, C[sum - 1][a[i] - 1]);
            sum -= a[i];
        }
        printf("%I64d\n", ans);
    }
    return 0;
}

转载于:https://www.cnblogs.com/handsomecui/p/5418738.html