ホーム - Project Euler

Problem 15¶

Lattice Paths¶

Starting in the top left corner of a $2 \times 2$ 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 $20 \times 20$ grid?

格子経路¶

2×2 のマス目の左上からスタートした場合, 引き返しなしで右下にいくルートは 6 つある.

では, 20×20 のマス目ではいくつのルートがあるか.

#!r6rs
#!chezscheme

(import (chezscheme))

(define iota-40-20
  (filter
    (lambda (num)
      (< 20 num))
    (iota 41)))

(define iota-20-1
  (cdr (iota 21)))

(define answer-15
  (/ (apply * iota-40-20)
     (apply * iota-20-1)))

(printf "15: ~D~%" answer-15)