[数据结构与算法]4.22--状态机模型

概念：一系列有序的事件
特点：描述的是一些过程，不是类似与背包问题一样是一个结果。
把混沌的状态细化
1、例题：大盗阿福

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1e5+10;
int t,n;
int a[N],f[N][2];
int main()
{
    cin >> t;
    while(t --)
    {
        cin >> n;
        for (int i = 1; i <= n; i ++ ) cin >> a[i];
        f[1][0] = 0, f[1][1] = a[1];
        for (int i = 2; i <= n; i ++ )
        {
            f[i][0] = max(f[i-1][0],f[i-1][1]);
            f[i][1] = f[i-1][0] + a[i];
        }
        cout<<max(f[n][0],f[n][1])<<endl;
    }
    return 0;
}

2、股票买卖IV

f[i,j,0]表示到了第i天，已经进行了j次交易，手中没货的状态
f[i,j,1]表示到了第i天，正在进行第j次交易，手中有货的状态

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1e5+10,M = 110;
int n,k;
int f[N][M][2];
int w[N];
int main()
{
    cin >> n >> k;
    for (int i = 1; i <= n; i ++ ) cin >> w[i];
    memset(f,-0x3f,sizeof f);
    for (int i = 0; i <= n; i ++ ) f[i][0][0] = 0;
    for (int i = 1; i <= n; i ++ )
    {
        for (int j = 1; j <= k; j ++ )
        {
            f[i][j][0] = max(f[i-1][j][0],f[i-1][j][1] + w[i]);
            f[i][j][1] = max(f[i-1][j][1],f[i-1][j-1][0]-w[i]);
        }
    }
    int res = 0;
    for (int i = 0; i <= k; i ++ ) res = max(res,f[n][i][0]);
    cout << res << endl;
    return 0;
}

3、股票买卖v

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1e5+10,inf = 0x3f3f3f3f;
int w[N],f[N][3]; // 0表示手里有货，1表示手里没货的第一天，2表示手里没货的>=2天
int n;
int main()
{
    cin >> n;
    for (int i = 1; i <= n; i ++ ) cin >> w[i];
    
    f[0][0] = f[0][1] = -inf;
    f[0][2] = 0;
    
    for (int i = 1; i <= n; i ++ )
    {
        f[i][0] = max(f[i-1][0],f[i-1][2]-w[i]);
        f[i][1] = f[i-1][0]+w[i];
        f[i][2] = max(f[i-1][2],f[i-1][1]);
    }
    int res = 0;
    for (int i = 1; i <= n; i ++ ) res = max(res,f[i][1]);
    cout<<res<<endl;
    return 0;
}

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