188-BestTimeToBuyAndSellStockIV.go

package main

// 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, 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

import "fmt"

func maxProfit(k int, prices []int) int {
    costs, profits := make([]int, len(prices)), make([]int, len(prices))
    costs[0] = prices[0]
    min := func (x, y int) int { if x < y { return x; }; return y; }
    max := func (x, y int) int { if x > y { return x; }; return y; }
    for i := 0; i < k; i++ {
        for j := 1; j < len(prices); j++ {
            costs[j] = min(costs[j-1], prices[j] - profits[j])
            profits[j] = max(profits[j-1], prices[j] - costs[j])
        }
    }
    return profits[len(profits)-1]
}

func main() {
    // Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
    fmt.Println(maxProfit(2,[]int{2,4,1})) // 2
    // 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.
    fmt.Println(maxProfit(2,[]int{3,2,6,5,0,3})) // 7
}