java - 为什么leetcode的这个题是一个动态规划?

Question

leetcode地址: https://leetcode.com/problems...

我对这个算法慢慢的还是可以想通的, 但是为什么他是动态规划呢? 动态规划不是要话分子问题, 列出递推方程的吗?但是这个题并不能列出递推方程的...还是说我思考的方式不对. 望指点一下这个算法的思想

public class BestTimeToBuyAndSellStockIII
{
    public int maxProfit(int[] prices)
    {
        if(prices.length == 0) return 0;
        int ans = 0;
        int n = prices.length;

        //正向遍历，opt[i]表示 prices[0...i]内做一次交易的最大收益.
        int opt[] = new int[n];
        opt[0] = 0;
        int low = prices[0];
        int curAns = 0;
        for(int i = 1; i < n; i++)
        {
            if(prices[i] < low)
                low = prices[i];
            else if(curAns < prices[i] - low)
                curAns = prices[i] - low;
            opt[i] = curAns;
        }

        //逆向遍历, opt[i]表示 prices[i...n-1]内做一次交易的最大收益.
        int optReverse[] = new int[n];
        optReverse[n - 1] = 0;
        curAns = 0;
        int high = prices[n - 1];
        for(int i = n - 2; i >= 0; i--)
        {
            if(prices[i] > high) high = prices[i];
            else if(curAns < high - prices[i]) curAns = high - prices[i];
            optReverse[i] = curAns;
        }

        //再进行划分，分别计算两个部分
        for(int i = 0; i < n; i++)
        {
            int tmp = opt[i] + optReverse[i];
            if(ans < tmp) ans = tmp;
        }
        return ans;
    }
}

Answer 1

This problem is first decomposed into two problems: forward traversal and reverse traversal.
This step should not be considered dynamic programming.

But the two small problems use dynamic programming algorithm internally.
Each small step is a recursive definition: given the best trading method of the previous K days, what is the best trading method when adding the price of K+1 days.
K is known to rise from 0 to N, so the best trading method for the previous N days is obtained.