188. Best Time to Buy and Sell Stock IV

You are given an integer array `prices` where `prices[i]` is the price of a given stock on the `ith` day.

Design an algorithm to find the maximum profit. You may complete at most `k` transactions.

Notice that 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:

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

188. Best Time to Buy and Sell Stock IV
``````struct Solution;

impl Solution {
fn max_profit(k: i32, prices: Vec<i32>) -> i32 {
let n = prices.len();
let mut k = k as usize;
k = k.min(n / 2);
if k == 0 {
return 0;
}
let mut min_costs = vec![std::i32::MAX; k];
let mut max_profits = vec![0; k];
for price in prices {
min_costs = min_costs.min(price);
max_profits = max_profits.max(price - min_costs);
for i in 1..k {
min_costs[i] = min_costs[i].min(price - max_profits[i - 1]);
max_profits[i] = max_profits[i].max(price - min_costs[i]);
}
}
max_profits[k - 1] as i32
}
}

#[test]
fn test() {
let prices = vec![2, 4, 1];
let k = 2;
let res = 2;
assert_eq!(Solution::max_profit(k, prices), res);
let prices = vec![3, 2, 6, 5, 0, 3];
let k = 2;
let res = 7;
assert_eq!(Solution::max_profit(k, prices), res);
}
``````