欧拉计划31题

计算
/**
* Coin sums
* Problem 31
*
* In England the currency is made up of pound,
* £, and pence, p, and there are eight coins in general circulation:
*     1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
* It is possible to make £2 in the following way:
*     1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
*    
* How many different ways can £2 be made using any number of coins?
*
*/
即求方程： a + 2b + 5c + 10d + 20e + 50f + 100g + 200h = 200
的非负整数解的个数

分析
当b,c,d,e,f,g,h 都为0时1种可能
当c,d,e,f,g,h都为0时有100 + 1种可能,b可能等于1,2,3,...,100
因此可以使用多层循环嵌套，求得结果

int count = 1;
for (int g = 0; g <= 200 / 100; g++){
int tempg = 200 - 100 * g;
for (int f = 0; f <= tempg / 50; f++){
int tempf = tempg - 50 * f;
for (int e = 0; e <= tempf / 20; e++){
int tempe = tempf - 20 * e;
for (int d = 0; d <= tempe / 10; d++){
int tempd = tempe - 10 * d;
for (int c = 0; c <= tempd / 5; c++){
int tempc = tempd - 5 * c;
for (int b = 0; b <= tempc / 2; b++){
System.out.println(b + " " + c + " " + d + " " + e + " " + f);
count++;
}
}
}
}
}
}


return count;


结果为：73682