[AcWing 1057] 股票买卖 IV

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点击查看代码

#include<iostream>
#include<cstring>

using namespace std;

const int N = 100010, M = 110;

int n, m;
int w[N];
int f[N][M][2];

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= n; i ++)	scanf("%d", &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 <= m; 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 <= m; i ++)	res = max(res, f[n][i][0]);
	cout << res << endl;
	return 0;
}

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1. 状态表示
   \(f[i][j][0]\) 表示第 \(i\) 天，交易了 \(j\) 次，并且手中不持有股票时的最大值
   \(f[i][j][1]\) 表示第 \(i\) 天，交易了 \(j\) 次，并且手中持有股票时的最大值
2. 状态计算
   \(f[i][j][0] = max(f[i - 1][j][0], f[i - 1][j][1] + w[i])\)
   \(f[i][j][1] = max(f[i - 1][j][1], f[i - 1][j - 1][0] - w[i])\)
3. 状态机模型