Best Time to Buy and Sell Stock 系列总结

Posted 2022-08-01 珍妮的选择

Best Time to Buy and Sell Stock 系列总结

强烈推荐: ​​Most consistent ways of dealing with the series of stock problems​​, 耐心仔细的全部看完, 收获不小.

Best Time to Buy and Sell Stock 系列有如下题目, 均可用动态规划进行求解, 有通用的递推公式:

• ​​121. Best Time to Buy and Sell Stock*​​
• ​​122. Best Time to Buy and Sell Stock II*​​
• ​​123. Best Time to Buy and Sell Stock III***​​
• ​​188. Best Time to Buy and Sell Stock IV***​​
• ​​309. Best Time to Buy and Sell Stock with Cooldown**​​
• ​​714. Best Time to Buy and Sell Stock with Transaction Fee**​​

通用的递推公式为:

Base cases:
T[-1][k][0] = 0, T[-1][k][1] = -Infinity
T[i][0][0] = 0, T[i][0][1] = -Infinity

Recurrence relations:
T[i][k][0] = max(T[i-1][k][0], T[i-1][k][1] + prices[i]) # sell
T[i][k][1] = max(T[i-1][k][1], T[i-1][k-1][0] - prices[i]) # buy

看 ​​Most consistent ways of dealing with the series of stock problems​​​ 或者 ​​123. Best Time to Buy and Sell Stock III***​​​ 获取关于 ​​T[i][k][*]​​ 的进一步解释.