[CareerCup][Google Interview] 打印最长序列

1. A
2. Ctrl+A
3. Ctrl+C
4. Ctrl+V

If you can only press the keyboard for N times (with the above four keys), please write a program to produce maximum numbers of A. If possible, please also print out the sequence of keys.

So the input parameter is N (No. of keys that you can press), the output is M (No. of As that you can produce).

这题又是一道经典的DP。打印这种类似最大结果的问题一般都会想到用DP

f[i][4]: 表示有四种方法，f[i][j] = max(f[i-1][k] + 各种操作)

如果要打印每个操作步骤，则要再设一个parent[i][j]数组，记录他的前任操作是哪个，然后递归调用。

#include <iostream>
using namespace std;

int solve(int n)
{
    int f[100][4];

    memset(f, 0, sizeof(f));

    f[0][0] = 1;

    for(int i = 1; i < n; i++)
        for(int j = 0; j < 4; j++)
            for(int k = 0; k < 4; k++)
            {
                if (j == 0) // add A
                {
                    f[i][j] = max(f[i][j], f[i-1][k] + 1);
                }
                else if (j == 1) // ctrl+A
                {
                    f[i][j] = max(f[i][j], f[i-1][k]);
                }
                else if (j == 2) // ctrl+C
                {
                    if (k == 1) // only previous is ctrl+A makes ctrl+C available
                        f[i][j] = max(f[i][j], f[i-1][k]);
                }
                else if (j == 3) //ctrl+V
                {
                    if (k == 2)
                        f[i][j] = max(f[i][j], f[i-1][k] * 2);
                }
            }

    return max(f[n-1][3], f[n-1][0]);
}

int main()
{
    int N = 10;
    cout << solve(N) << endl;
}