34. 丑数(C++版本)

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本文介绍了两种算法来查找第N个丑数，即只包含质因数2、3和5的正整数。基础版本使用循环判断每个数是否为丑数，而高效版本采用动态规划，利用三个指针分别跟踪乘以2、3、5的最小丑数，避免重复计算。

基础版本:

bool IsUglyNum(int64_t data)
{
	int64_t curData = data;
	while (curData % 2 == 0) curData /= 2;
	while (curData % 3 == 0) curData /= 3;
	while (curData % 5 == 0) curData /= 5;
	return 1 == curData ? true : false;
}


int64_t GetUglyNum(int destIdx)
{
	if (destIdx < 0) return -1;

	int64_t destData = 1;
	for (int curIdx = 0, curData = 1; curIdx != destIdx; ++curData)
	{
		if (IsUglyNum(curData))
		{
			++curIdx;
			destData = curData;
		}
	}

	return destData;
}

高效版本：

int64_t MinOfThree(int64_t left, int64_t middle, int last)
{
	int finalData = left < middle ? left : middle;
	finalData = finalData < last ? finalData : last;
	return finalData;
}

int64_t GetUglyNum(int destIdx)
{
	if (destIdx < 0) return -1;

	int64_t* pTempData = new int64_t[destIdx];
	pTempData[0] = 1;

	int64_t* firstBiggerPMultiBy2 = pTempData;
	int64_t* firstBiggerMultiBy3 = pTempData;
	int64_t* firstBiggerMultiBy5 = pTempData;

	for (int curIdx = 1; curIdx != destIdx; ++curIdx)
	{
		int64_t curMaxNum = pTempData[curIdx - 1];

		while (*firstBiggerPMultiBy2 * 2 <= curMaxNum) ++firstBiggerPMultiBy2;
		while (*firstBiggerMultiBy3 * 3 <= curMaxNum) ++firstBiggerMultiBy3;
		while (*firstBiggerMultiBy5 * 5 <= curMaxNum) ++firstBiggerMultiBy5;

		int64_t destNum = MinOfThree(*firstBiggerPMultiBy2 * 2, *firstBiggerMultiBy3 * 3, *firstBiggerMultiBy5 * 5);
		pTempData[curIdx] = destNum;
	}

	int destNum = pTempData[destIdx - 1];
	delete[] pTempData;
	return destNum;
}