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The Peak-Valley Approach aims to identify opportunities where a buy (at a valley) and a sell (at a peak) transaction yields profit. The idea is to take advantage of every upward trend between valleys and peaks and sum up the differences.
Time Complexity: O(n), where n is the number of prices.
Space Complexity: O(1), no additional space is used.
1#include <vector>
2#include <iostream>
3
4int maxProfit(std::vector<int>& prices) {
5 int profit = 0;
6 for (size_t i = 1; i < prices.size(); ++i) {
7 if (prices[i] > prices[i - 1]) {
8 profit += prices[i] - prices[i - 1];
9 }
10 }
11 return profit;
12}
13
14int main() {
15 std::vector<int> prices = {7,1,5,3,6,4};
16 std::cout << "Max Profit: " << maxProfit(prices) << std::endl;
17 return 0;
18}This C++ solution uses a similar logic to the C solution; it checks pairs of consecutive prices and adds the difference to profit if there is an upward trend. The vector 'prices' allows dynamic sizing suitable for market data use cases.
The simple one-pass greedy approach makes a decision on each day based on whether the price will go up (buy or hold) or down (sell or do nothing). This maximizes profit by keeping solutions simple, efficient and using the greedy approach to sum up all local gains.
Time Complexity: O(n)
Space Complexity: O(1)
1
public class Solution {
public int MaxProfit(int[] prices) {
int profit = 0;
for (int i = 1; i < prices.Length; i++) {
profit += (prices[i] > prices[i - 1]) ? prices[i] - prices[i - 1] : 0;
}
return profit;
}
public static void Main(string[] args) {
Solution sol = new Solution();
int[] prices = {7,1,5,3,6,4};
Console.WriteLine("Max Profit: " + sol.MaxProfit(prices));
}
}The C# implementation closely follows the logic laid out in the approach description: iterating through price data once, summing positive differentials.