Codeforces Round #289 (Div. 2, ACM ICPC Rules) A. Maximum in Table【递推】

A. Maximum in Table

time limit per test 2 seconds

memory limit per test 256 megabytes

input standard input

output standard output

Ann × ntableais defined as follows:

The first row and the first column contain ones, that is:ai, 1 = a1, i = 1for alli = 1, 2, ..., n.
Each of the remaining numbers in the table is equal to the sum of the number above it and the number to the left of it. In other words, the remaining elements are defined by the formulaai, j = ai - 1, j + ai, j - 1.

These conditions define all the values in the table.

You are given a numbern. You need to determine the maximum value in then × ntable defined by the rules above.

Input

The only line of input contains a positive integern(1 ≤ n ≤ 10) — the number of rows and columns of the table.

Output

Print a single line containing a positive integerm— the maximum value in the table.

Sample test(s)

input

output

input

output

Note

In the second test the rows of the table look as follows:

{1, 1, 1, 1, 1}, {1, 2, 3, 4, 5}, {1, 3, 6, 10, 15}, {1, 4, 10, 20, 35}, {1, 5, 15, 35, 70}. 【分析】：第一行全为1，递推求最后一个数。【代码】：

#include <bits/stdc++.h>
using namespace std;

const int INF=0x3f3f3f3f;
#define LL long long

int a[15][15],n,ma;
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
        a[i][1]=a[1][i]=1;
    
    for(int i=2;i<=n;i++)
    {
        for(int j=2;j<=n;j++)
        {
            a[i][j]=a[i-1][j]+a[i][j-1];
        }
    }
    cout<<a[n][n]<<endl;
    return 0;
}

傻逼递推求最大

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