《程序员面试宝典-第四版》之递归学习

本文主要是类似杨辉三角阵的两种不同实现算法...

/**
* Problem:
* if m = 1, f(m,n) = n;
* if n = 1, f(m,n) = m;
* if m > 1, n > 1, f(m,n) = f(m-1,n) + f(m,n-1)
*/

#include <iostream>

using namespace std;

#define RECURSION 0
#define NO_RECURSION 1

// !< Recursion version
#if RECURSION
int f(int m, int n)
{
	if (1 == m)
	{
		return n;
	}
	if (1 == n)
	{
		return m;
	}
	return f(m-1,n) + f(m,n-1);
}
#endif

// !< Not recursion version
#if NO_RECURSION
int f(int m, int n)
{
	int a[100][100] = {0};

	for (int i = 0; i != m; ++i)
	{
		a[i][0] = i + 1;        // 第一列每行递增
	}
	for (int i = 0; i != n; ++i)
	{
		a[0][i] = i + 1;        // 第一行每列递增
	}

	for (int i = 1; i != m; ++i)
	{
		for (int j = 1; j != n; ++j)
		{
			a[i][j] = a[i-1][j] + a[i][j-1];					
		}	
	}
	return a[m-1][n-1];
}
#endif

int main()
{
	cout << f(3, 4) << endl;
	return 0;
}