Stock Buy Sell to Maximize Profit

The cost of a stock on each day is given in an array, find the max profit that you can make by buying and selling in those days. For example, if the given array is {100, 180, 260, 310, 40, 535, 695}, the maximum profit can earned by buying on day 0, selling on day 3. Again buy on day 4 and sell on day 6. If the given array of prices is sorted in decreasing order, then profit cannot be earned at all.

If we are allowed to buy and sell only once, then we can use following algorithm. Maximum difference between two elements. Here we are allowed to buy and sell multiple times. Following is algorithm for this problem.
1. Find the local minima and store it as starting index. If not exists, return.
2. Find the local maxima. and store it as ending index. If we reach the end, set the end as ending index.
3. Update the solution (Increment count of buy sell pairs)
4. Repeat the above steps if end is not reached.

// Program to find best buying and selling days #include <stdio.h>   // solution structure struct Interval {     int buy;     int sell; };   // This function finds the buy sell schedule for maximum profit void stockBuySell(int price[], int n) {     // Prices must be given for at least two days     if (n == 1)         return;       int count = 0; // count of solution pairs       // solution vector     Interval sol[n/2 + 1];       // Traverse through given price array     int i = 0;     while (i < n-1)     {         // Find Local Minima. Note that the limit is (n-2) as we are         // comparing present element to the next element.         while ((i < n-1) && (price[i+1] <= price[i]))             i++;           // If we reached the end, break as no further solution possible         if (i == n-1)             break;           // Store the index of minima         sol[count].buy = i++;           // Find Local Maxima.  Note that the limit is (n-1) as we are         // comparing to previous element         while ((i < n) && (price[i] >= price[i-1]))             i++;           // Store the index of maxima         sol[count].sell = i-1;           // Increment count of buy/sell pairs         count++;     }       // print solution     if (count == 0)         printf("There is no day when buying the stock will make profit\n");     else     {        for (int i = 0; i < count; i++)           printf("Buy on day: %d\t Sell on day: %d\n", sol[i].buy, sol[i].sell);     }       return; }   // Driver program to test above functions int main() {     // stock prices on consecutive days     int price[] = {100, 180, 260, 310, 40, 535, 695};     int n = sizeof(price)/sizeof(price[0]);       // fucntion call     stockBuySell(price, n);       return 0; }

Output:

Buy on day : 0   Sell on day: 3
Buy on day : 4   Sell on day: 6

Time Complexity: The outer loop runs till i becomes n-1. The inner two loops increment value of i in every iteration. So overall time complexity is O(n)