188. Best Time to Buy and Sell Stock IV

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).

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

local[i][j] = max(global[i - 1][j - 1] + max(diff, 0), local[i - 1][j] + diff)

global[i][j] = max(local[i][j], global[i - 1][j])，

``````class Solution {
public:
int maxProfit(int k, vector<int> &prices) {
if (prices.empty()) return 0;
if (k >= prices.size()) return solveMaxProfit(prices);
int g[k + 1] = {0};
int l[k + 1] = {0};
for (int i = 0; i < prices.size() - 1; ++i) {
int diff = prices[i + 1] - prices[i];
for (int j = k; j >= 1; --j) {
l[j] = max(g[j - 1] + max(diff, 0), l[j] + diff);
g[j] = max(g[j], l[j]);
}
}
return g[k];
}
int solveMaxProfit(vector<int> &prices) {
int res = 0;
for (int i = 1; i < prices.size(); ++i) {
if (prices[i] - prices[i - 1] > 0) {
res += prices[i] - prices[i - 1];
}
}
return res;
}
};
``````

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