Dynamic Programming | High-effort vs. Low-effort Tasks Problem - GeeksforGeeks


Dynamic Programming | High-effort vs. Low-effort Tasks Problem - GeeksforGeeks
You are given n days and for each day (di) you could either perform a high effort tasks (hi) or a low effort tasks (li) or no task with the constraint that you can choose a high-effort tasks only if you chose no task on the previous day. Write a program to find the maximum amount of tasks you can perform within these n days.

To find the maximum amount of tasks done till i’th day, we need to compare 2 choices:
  1. Go for high effort tasks on that day, then find the maximum amount of tasks done till (i – 2) th day.
  2. Go for low effort task on that day and find the maximum amount of tasks done till (i – 1) th day.
Let high [1…n] be the input array for high effort task amount on i’th day and low [1…n] be the input array for low effort task amount on ith day.
Let max_task (high [], low [], i) be the function that returns maximum amount of task done till ith day, so it will return max(high[i] + max_task(high, low, (i – 2)), low [i] + max_task (high, low, (i – 1)))
int maxTasks(int high[], int low[], int n)
{
    // If n is less than equal to 0, then no
    // solution exists
    if (n <= 0)
        return 0;
 
    /* Determines which task to choose on day n,
       then returns the maximum till that day */
    return max(high[n-1] + maxTasks(high, low, (n-2)),
              low[n-1] + maxTasks(high, low, (n-1)));
}

int maxTasks(int high[], int low[], int n)
{
    // An array task_dp that stores the maximum
    // task done
    int task_dp[n+1];
 
    // If n = 0, no solution exists
    task_dp[0] = 0;
 
    // If n = 1, high effort task on that day will
    // be the solution
    task_dp[1] = high[0];
 
    // Fill the entire array determining which
    // task to choose on day i
    for (int i = 2; i <= n; i++)
        task_dp[i] = max(high[i-1] + task_dp[i-2],
                         low[i-1] + task_dp[i-1]);
    return task_dp[n];
}
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