Description (leetcode)

You are given an integer array prices where prices[i] is the price of a given stock on the i^th day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Example 1:

Input: k = 2, prices = [2,4,1]

Output: 2

Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.

Example 2:

Input: k = 2, prices = [3,2,6,5,0,3]

Output: 7

Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.

Constraints:

  • 1 <= k <= 100
  • 1 <= prices.length <= 1000
  • 0 <= prices[i] <= 1000

submission

impl Solution {
    pub fn max_profit(k: i32, prices: Vec<i32>) -> i32 {
        // stateful dp
        let k = k as usize;
        let mut dp = vec![(0, i32::MIN); k + 1];
        for price in prices {
            for i in 1..=k {
                // sell the bought stock
                dp[i].0 = dp[i].0.max(dp[i].1 + price);
                // buy a new stock
                dp[i].1 = dp[i].1.max(dp[i - 1].0 - price);
            }
        }
        dp[k].0
    }
}