Minimum time to finish tasks without skipping two consecutive

Given time taken by n tasks. Find the minimum time needed to finish the tasks such that skipping of tasks is allowed, but can not skip two consecutive tasks.

Examples :

Input : arr[] = {10, 5, 7, 10}
Output : 12
We can skip first and last task and
finish these task in 12 min.

Input : arr[] = {10}
Output : 0
There is only one task and we can
skip it.

Input : arr[] = {10, 30}
Output : 10

Input : arr[] = {10, 5, 2, 4, 8, 6, 7, 10}
Output : 22

Expected Time Complexity is O(n) and extra space is O(1).

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

The given problem has the following recursive property.

Let minTime(i) be minimum time to finish till i’th task. It can be written as minimum of two values.

1. Minimum time if i’th task is included in list, let this time be incl(i)
2. Minimum time if i’th task is excluded from result, let this time be excl(i)
minTime(i) = min(excl(i), incl(i))

Result is minTime(n-1) if there are n tasks and indexes start from 0.

incl(i) can be written as below.

// There are two possibilities
// (a) Previous task is also included
// (b) Previous task is not included
incl(i) = min(incl(i-1), excl(i-1)) +
arr[i] // Since this is inclusive
// arr[i] must be included

excl(i) can be written as below.

// There is only one possibility (Previous task must be
// included as we can't skip consecutive tasks.
excl(i) = incl(i-1)

A simple solution is to make two tables incl[] and excl[] to store times for tasks. Finally return minimum of incl[n-1] and excl[n-1]. This solution requires O(n) time and O(n) space.

If we take a closer look, we can notice that we only need incl and excl of previous job. So we can save space and solve the problem in O(n) time and O(1) space. Below is C++ implementation of the idea.

C++

 // C++ program to find minimum time to finish tasks // such that no two consecutive tasks are skipped. #include using namespace std;    // arr[] represents time taken by n given tasks int minTime(int arr[], int n) {     // Corner Cases     if (n <= 0)         return 0;        // Initialize value for the case when there     // is only one task in task list.     int incl = arr;  // First task is included     int excl = 0;       // First task is exluded        // Process remaining n-1 tasks     for (int i=1; i

PHP



Output :

12
12
22

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Improved By : nitin mittal

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