Given an array arr of N positive elements, the task is to find whether it is possible to convert this array into Geometric Progression (GP) by removing at-most one element. If yes, then find index of the number removing which converts the array into a geometric progression.
Special Cases :
1) If whole array is already in GP, then return any index.
2) If it is not possible to convert array into GP, then print “Not possible”.
Input : arr = [2, 4, 8, 24, 16, 32] Output : 3 Number to remove is arr, i.e., 24 After removing 24 array will be [2, 4, 8, 16, 32] which is a GP with starting value 2 and common ratio 2. Input : arr = [2, 8, 30, 60] Output : Not Possible
We can solve this problem by handling some special cases and then finding the pivot element, removing which makes array a GP. First we will check that our pivot element is first or second element, if not then the multiplier between them will be common ration of our GP, if yes then we found our solution.
Once we get common ratio of GP, we can check array element with this ratio, if this ratio violates at some index, then we skip this element and check from next index whether it is a continuation of previous GP or not.
In below code a method isGP is implemented which checks array to be GP after removing element at index ‘index’. This method is written for special case handling of first, second and last element.
Please see below code for better understanding.
Remove 30 to get geometric progression
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