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  • Project Euler Problem 15 Lattice paths

    Lattice paths

    Problem 15

    Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

    How many such routes are there through a 20×20 grid?


    C++:

    #include <iostream>
    #include <cstring>
    
    using namespace std;
    
    const int MAXN = 20;
    
    long grid[MAXN+1][MAXN+1];
    
    long pathcount(int row, int col)
    {
        long count;
    
        if(grid[row][col])
            return grid[row][col];
    
        if(row == 0 && col == 0)
            return 1;
        else if(row == 0)
            count = pathcount(row, col - 1);
        else if(col == 0)
            count = pathcount(row - 1, col);
        else
            count = pathcount(row - 1, col) + pathcount(row, col -1);
    
        grid[row][col] = count;
    
        return count;
    }
    
    int main()
    {
        int n;
    
        memset(grid, 0, sizeof(grid));
    
        while(cin >> n && n <=MAXN) {
            long ans = pathcount(n, n);
    
            cout << ans << endl;
        }
    
        return 0;
    }

    C++:
    #include <iostream>
    
    using namespace std;
    
    const int MAXN = 20;
    
    long grid[MAXN+1][MAXN+1];
    
    int main()
    {
        int n;
    
        while(cin >> n && n <=MAXN) {
            for(int j=0; j<=n; j++)
                grid[0][j] = 1;
            for(int i=1; i<=n; i++) {
                grid[i][0] = 1;
                for(int j=1; j<=n; j++)
                    grid[i][j] = grid[i][j-1] + grid[i-1][j];
            }
    
            cout << grid[n][n] << endl;
        }
    
        return 0;
    }



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  • 原文地址:https://www.cnblogs.com/tigerisland/p/7564018.html
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