Best Time to Buy and Sell Stock IV

Description

Say you have an array for which the i-th element is the price of a given stock on day i.

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

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Example 1:

Input: [2,4,1], k = 2
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.

Example 2:

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

Solution(javascript)

/** DP O(k) space O(kn) time
 * @param {number} k
 * @param {number[]} prices
 * @return {number}
 */
const maxProfit = function (k, prices) {
  k = Math.min(2 * k, prices.length)
  let prevMemo = new Array(k + 2).fill(0)
  for (let index = prices.length - 1; index >= 0; index--) {
    const currentMemo = new Array(k + 2).fill(0)
    for (let count = k; count >= 1; count--) {
      if (count % 2 === 1) {
        currentMemo[count] = Math.max(
          -prices[index] + prevMemo[count + 1],
          prevMemo[count],
        )
      } else {
        currentMemo[count] = Math.max(
          prices[index] + prevMemo[count + 1],
          prevMemo[count],
        )
      }
    }
    prevMemo = currentMemo
  }
  return prevMemo[1]
}