Number of unique ways that ATM can tender

An atm can only dispense values of $1, $5, $20, and $50. Return the number 
of unique ways that a $ amount of X can be tendered.
($1, $5) is distinct from ($5, $1)

Input: 4 Output: 1
Input: 6 Output: 3
Input: 100 Output: 954515231698

 

这题和Coin Change很像，只不过这题需要考虑顺序的问题。

Solution1:

用递归做。就像斐波那契数列那样。

public int atm(int x) {
    if (x <= 0)
        return x == 0 ? 1 : 0;
     return atm(x - 1) + atm(x - 5) + atm(x - 20) + atm(x - 100);
}

但是这样很多重复的计算，输入太大的话会栈溢出。所以我们可以考虑把中间结果保存起来。

 

Solution2:

public long tellMoneyCombinations(int money) {
	long[] f = new long[money+1];
	f[0] = 1;
	for(int i=1; i<=money; i++) {
		f[i] = f[i-1];
		if(i>=5) f[i]+=f[i-5];
		if(i>=20) f[i]+=f[i-20];
		if(i>=50) f[i]+=f[i-50];
	}
	return f[money];
}