Lattice paths

最新推荐文章于 2025-01-04 14:51:54 发布

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本文探讨了一个经典的组合数学问题：在一个20x20的网格中，仅能向右或向下移动，从左上角到达右下角的不同路径数量。通过构建二维数组并使用动态规划的方法，实现了路径计数的高效计算。

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?

这个只要从上到下，一个一个加就好了，非常简单。

def routes():
    grid = [[0] * 21] * 21
    for i in range(0,21):
        grid[0][i] = 1
        grid[i][0] = 1
    for i in range(1,21):
        for j in range(1,21):
            grid[i][j] = grid[i][j-1] + grid[i-1][j]
    return grid[20][20]

print(routes())