Description
Consider a three-parameter recursive function w(a, b, c):
if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:
1
if a > 20 or b > 20 or c > 20, then w(a, b, c) returns:
w(20, 20, 20)
if a < b and b < c, then w(a, b, c) returns:
w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)
otherwise it returns:
w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)
This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.
题意
现在有一个三元组(a, b, c)，你要对 a、b、c 的大小进行分类讨论从而确定该三元组的值。这个算法很好实现，但是由于递归次数多所以执行时间很长。请你想一个执行时间尽可能短的办法来实现该算法。
Sample
The input for your program will be a series of integer triples, one per line, until the end-of-file flag of -1 -1 -1. Using the above technique, you are to calculate w(a, b, c) efficiently and print the result.
输入格式是三个整数组成的三元组，每个三元组占一行，直到读取到结束标志 -1 -1 -1 。输出格式直接看下面的图，我就不废话了。
Input:
output:
思路
这道题需要解决的是递归中用时过多的问题，想想怎么样能少一点时间？那就是边递归边记录，已经记录的值就可以直接返回，这样就避免了递归时同一条数据的重复递归，这种技巧简称记忆化搜索。
注意边界判断与递归顺序。
我的AC
#include<iostream> using std::cin; using std::cout; using std::endl; int getTripleVal(int , int , int ); //查询给定三元组的值 const int MAX = 21; int w[MAX][MAX][MAX]; //记忆数组 int main(void) { int a, b, c; while (cin >> a >> b >> c) { if ( a == -1 && b == -1 && c == -1) { return 0; } else { int res = getTripleVal(a, b, c); cout << "w(" << a << ", " << b << ", " << c << ")" << " = " << res << endl; } } return 0; }//main int getTripleVal(int a, int b, int c) { if (a <= 0 || b <= 0 || c <= 0) { return w[0][0][0] = 1; } if (a >= MAX || b >= MAX || c >= MAX) { return getTripleVal(MAX-1, MAX-1, MAX-1); } // 在记忆数组中查询 w[a][b][c]的值,实现记忆化搜索 if (w[a][b][c]) { return w[a][b][c]; } //求出结果并保存 if (a < b && b < c) { return w[a][b][c] = getTripleVal(a, b, c-1) + getTripleVal(a, b-1, c-1) - getTripleVal(a, b-1, c); } //求出结果并保存 return w[a][b][c] = getTripleVal(a-1, b, c) + getTripleVal(a-1, b-1, c) + getTripleVal(a-1, b, c-1) - getTripleVal(a-1, b-1, c-1); }//getTripleVal
