Shortest path counting

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Shortest path counting

1000(ms)

65535(kb)

1008 / 1840

Tags: 动态规划

A chess rook can move horizontally o r vertically to any square in the same row o r in the same column of a chessboard. Find the number of shortest paths by which a rook can move from one corner of a chessboard to the diagonally opposite corner。

输入

a interger number n is row and column of chessboard. 0 < n <=16

输出

the number of shortest paths.

样例输入

4

样例输出

20

@浅夏沫若.code:

#include<iostream>
#include<string>
using namespace std;
struct node
{
 int value=1;
 int path = 1;
}map[20][20];
int main()
{
 int n = 0;
 cin >> n;
 for(int i=1;i<=n;i++)
  for (int j = 1; j <= n; j++)
  {
   if (i == 1 || j == 1)
    map[i][j].value = i * j;
   else
   {
    if (map[i - 1][j].value > map[i][j - 1].value)
    {
     map[i][j].value = map[i][j - 1].value+1;
     map[i][j].path = map[i][j - 1].path;
    }
    else if (map[i - 1][j].value == map[i][j - 1].value)
    {
     map[i][j].value = map[i][j - 1].value + 1;
     map[i][j].path = map[i][j - 1].path+ map[i - 1][j].path;
    }
    else
    {
     map[i][j].value = map[i-1][j].value + 1;
     map[i][j].path = map[i-1][j].path;
    }
   }
  }
 cout << map[n][n].path<<endl;
 return 0;
}