题目117：考察使用不同型号的砖块铺满一行的方法
本帖最后由 欧拉计划 于 2016-8-21 02:02 编辑Red, green, and blue tiles
Using a combination of black square tiles and oblong tiles chosen from: red tiles measuring two units, green tiles measuring three units, and blue tiles measuring four units, it is possible to tile a row measuring five units in length in exactly fifteen different ways.
How many ways can a row measuring fifty units in length be tiled?
NOTE: This is related to Problem 116.
题目：
有以下几种长条：红色的 2*1，绿色的 3*1，蓝色的 4*1。
使用黑色方块 1*1 和长条进行组合，想得到 5*1 的矩形，则有 15 种不同的方法：
请问，50*1 的矩形有多少种方法可以形成？
注意：该题与题目116有关。 from math import factorial as f
def P(n,m):
return f(n)//f(m)//f(n-m)
def solve117(n,r=2,g=3,b=4):
total = 0
for i in range(n//r+1):
for j in range(n//g+1):
for k in range(n//b+1):
if i*r+j*g+k*b > n: break
bk = n - i*r - j*g - k*b
total += P(bk+i+j+k,i)*P(bk+j+k, j)*P(bk+k,k)
return total
print(solve117(50))
100808458960497 //100808458960497
#include <iostream>
using namespace std;
long long f;
int a = { 1,2,3,4 };
int main(void)
{
f = 1;
for (int i = 1; i <= 50; ++i)
{
for (int k = 0; k <= 3; ++k)
{
if (i >= a)
f = f] + f] + f] + f];
}
}
cout << f + f + f + f << endl;
return 0;
}
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