换硬币问题

#define MONEY 100
int COINS;

//递归
//
int findCoinExchange1(int* coins, int coinId, int curMoney) {
	/*钱数刚好兑换完,即这跳路径是满足的情况*/
	if (curMoney == 0) {
		return 1;
	}
	/*curMoney<0为凑不齐的情况;
	 * coinId==COINS表示所给的币值无法凑为要求的币值*/
	if (!coins || curMoney < 0 || coinId == COINS) {
		return 0;
	}

	/*findCoinExchange1(coins, coinId + 1, curMoney)表示不放coinId的情况;
	 *findCoinExchange1(coins, coinId, curMoney - coins[coinId])表示放入coinId的情况 */
	return findCoinExchange1(coins, coinId + 1, curMoney)
			+ findCoinExchange1(coins, coinId, curMoney - coins[coinId]);
}

//非递归
/*	j表示金钱价值
 * ways[j]表示不包含coins[i]时能达到ways[j]的情况,
 * ways[j-coins[i]]表示包含coins[i]时达到ways[j]的情况,
 * 则ways[MONEY]为结果
 * 所以必须声明ways[MONEY+1]
 * */
int findCoinExchange2(int* coins) {
	if (!coins)
		return 0;
	int ways[MONEY + 1] = { 1 };
	for (int i = 0; i < COINS; ++i) {
		for (int j = coins[i]; j <= MONEY; ++j) {
			ways[j] += ways[j - coins[i]];
		}
	}
	return ways[MONEY];
}