# Remove minimum elements from either side such that 2*min becomes more than max | Set 2

Given an unsorted array, trim the array such that twice of minimum is greater than the maximum in the trimmed array. Elements should be removed from either end of the array. The number of removals should be minimum.

Examples:

Input: arr[] = {4, 5, 100, 9, 10, 11, 12, 15, 200}
Output: 4
We need to remove 4 elements (4, 5, 100, 200)
so that 2*min becomes more than max.

Input: arr[] = {4, 7, 5, 6}
Output: 0
We don’t need to remove any element as
4*2 > 7

Input: arr[] = {20, 7, 5, 6}
Output: 1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: We have discussed various approaches to solve this problem in O(n3), O(n2 * logn), and O(n2) time in previous article. In this articles, we are going to discuss a O(n * logn) time solution using Sliding Window and Segment Tree concepts.

1. Construct Segment Tree for RangeMinimumQuery and RangeMaximumQuery for the given input array.
2. Take two pointers start and end, and initialize both to 0.
3. While end is less than the length of the input array, do the following:
• Find min and max in the current window using Segment Trees constructed in step 1.
• Check if 2 * min ≤ max, if so then increment start pointer else update max valid length so far, if required
• Increment end
4. length(arr[]) – maxValidLength is the required answer.

Below is the implementation of the above approach:

 `// Java implementation of the approach ` `public` `class` `GFG { ` ` `  `    ``// Function to return the minimum removals ` `    ``// required so that the array satisfy ` `    ``// the given condition ` `    ``public` `int` `removeMinElements(``int``[] a) ` `    ``{ ` `        ``int` `n = a.length; ` ` `  `        ``RangeMinimumQuery rMimQ = ``new` `RangeMinimumQuery(); ` `        ``int``[] minTree = rMimQ.createSegmentTree(a); ` ` `  `        ``RangeMaximumQuery rMaxQ = ``new` `RangeMaximumQuery(); ` `        ``int``[] maxTree = rMaxQ.createSegmentTree(a); ` ` `  `        ``int` `start = ``0``, end = ``0``; ` ` `  `        ``// To store min and max in the current window ` `        ``int` `min, max; ` `        ``int` `maxValidLen = ``0``; ` ` `  `        ``while` `(end < n) { ` `            ``min = rMimQ.rangeMinimumQuery(minTree, ` `                                          ``start, end, n); ` `            ``max = rMaxQ.rangeMaximumQuery(maxTree, ` `                                          ``start, end, n); ` `            ``if` `(``2` `* min <= max) ` `                ``start++; ` `            ``else` `                ``maxValidLen = Math.max(maxValidLen, ` `                                       ``end - start + ``1``); ` `            ``end++; ` `        ``} ` `        ``return` `n - maxValidLen; ` `    ``} ` ` `  `    ``class` `RangeMinimumQuery { ` ` `  `        ``// Creates a new segment tree from ` `        ``// the given input array ` `        ``public` `int``[] createSegmentTree(``int``[] input) ` `        ``{ ` `            ``int` `n = input.length; ` `            ``int` `segTreeSize = ``2` `* getNextPowerOfTwo(n) - ``1``; ` `            ``int``[] segmentTree = ``new` `int``[segTreeSize]; ` ` `  `            ``createSegmentTreeUtil(segmentTree, input, ` `                                  ``0``, n - ``1``, ``0``); ` `            ``return` `segmentTree; ` `        ``} ` ` `  `        ``private` `void` `createSegmentTreeUtil(``int``[] segmentTree, ` `                                           ``int``[] input, ``int` `low, ` `                                           ``int` `high, ``int` `pos) ` `        ``{ ` `            ``if` `(low == high) { ` ` `  `                ``// Its a leaf node ` `                ``segmentTree[pos] = input[low]; ` `                ``return``; ` `            ``} ` ` `  `            ``// Construct left and right subtrees and then ` `            ``// update value for current node ` `            ``int` `mid = (low + high) / ``2``; ` `            ``createSegmentTreeUtil(segmentTree, input, low, ` `                                  ``mid, (``2` `* pos + ``1``)); ` `            ``createSegmentTreeUtil(segmentTree, input, ` `                                  ``mid + ``1``, high, (``2` `* pos + ``2``)); ` `            ``segmentTree[pos] = Math.min(segmentTree[``2` `* pos + ``1``], ` `                                        ``segmentTree[``2` `* pos + ``2``]); ` `        ``} ` ` `  `        ``public` `int` `rangeMinimumQuery(``int``[] segmentTree, ``int` `from, ` `                                     ``int` `to, ``int` `inputSize) ` `        ``{ ` `            ``return` `rangeMinimumQueryUtil(segmentTree, ``0``, ` `                                         ``inputSize - ``1``, from, to, ``0``); ` `        ``} ` ` `  `        ``private` `int` `rangeMinimumQueryUtil(``int``[] segmentTree, ``int` `low, ` `                                        ``int` `high, ``int` `from, ``int` `to, ``int` `pos) ` `        ``{ ` `            ``// Total overlap ` `            ``if` `(from <= low && to >= high) { ` `                ``return` `segmentTree[pos]; ` `            ``} ` ` `  `            ``// No overlap ` `            ``if` `(from > high || to < low) { ` `                ``return` `Integer.MAX_VALUE; ` `            ``} ` ` `  `            ``// Partial overlap ` `            ``int` `mid = (low + high) / ``2``; ` `            ``int` `left = rangeMinimumQueryUtil(segmentTree, low, ` `                                             ``mid, from, to, ` `                                             ``(``2` `* pos + ``1``)); ` `            ``int` `right = rangeMinimumQueryUtil(segmentTree, ` `                                              ``mid + ``1``, high, from, ` `                                              ``to, (``2` `* pos + ``2``)); ` `            ``return` `Math.min(left, right); ` `        ``} ` `    ``} ` ` `  `    ``class` `RangeMaximumQuery { ` ` `  `        ``// Creates a new segment tree from given input array ` `        ``public` `int``[] createSegmentTree(``int``[] input) ` `        ``{ ` `            ``int` `n = input.length; ` `            ``int` `segTreeSize = ``2` `* getNextPowerOfTwo(n) - ``1``; ` `            ``int``[] segmentTree = ``new` `int``[segTreeSize]; ` ` `  `            ``createSegmentTreeUtil(segmentTree, input, ``0``, n - ``1``, ``0``); ` `            ``return` `segmentTree; ` `        ``} ` ` `  `        ``private` `void` `createSegmentTreeUtil(``int``[] segmentTree, ``int``[] input, ` `                                           ``int` `low, ``int` `high, ``int` `pos) ` `        ``{ ` `            ``if` `(low == high) { ` ` `  `                ``// Its a leaf node ` `                ``segmentTree[pos] = input[low]; ` `                ``return``; ` `            ``} ` ` `  `            ``// Construct left and right subtrees and then ` `            ``// update value for current node ` `            ``int` `mid = (low + high) / ``2``; ` `            ``createSegmentTreeUtil(segmentTree, input, low, ` `                                  ``mid, (``2` `* pos + ``1``)); ` `            ``createSegmentTreeUtil(segmentTree, input, ` `                                  ``mid + ``1``, high, (``2` `* pos + ``2``)); ` `            ``segmentTree[pos] = Math.max(segmentTree[``2` `* pos + ``1``], ` `                                        ``segmentTree[``2` `* pos + ``2``]); ` `        ``} ` ` `  `        ``public` `int` `rangeMaximumQuery(``int``[] segmentTree, ` `                                     ``int` `from, ``int` `to, ``int` `inputSize) ` `        ``{ ` `            ``return` `rangeMaximumQueryUtil(segmentTree, ``0``, ` `                                         ``inputSize - ``1``, from, to, ``0``); ` `        ``} ` ` `  `        ``private` `int` `rangeMaximumQueryUtil(``int``[] segmentTree, ``int` `low, ` `                                 ``int` `high, ``int` `from, ``int` `to, ``int` `pos) ` `        ``{ ` `            ``// Total overlap ` `            ``if` `(from <= low && to >= high) { ` `                ``return` `segmentTree[pos]; ` `            ``} ` ` `  `            ``// No overlap ` `            ``if` `(from > high || to < low) { ` `                ``return` `Integer.MIN_VALUE; ` `            ``} ` ` `  `            ``// Partial overlap ` `            ``int` `mid = (low + high) / ``2``; ` `            ``int` `left = rangeMaximumQueryUtil(segmentTree, low, ` `                                             ``mid, from, to, ` `                                             ``(``2` `* pos + ``1``)); ` `            ``int` `right = rangeMaximumQueryUtil(segmentTree, ` `                                              ``mid + ``1``, high, from, ` `                                              ``to, (``2` `* pos + ``2``)); ` `            ``return` `Math.max(left, right); ` `        ``} ` `    ``} ` ` `  `    ``// Function to return the minimum power of 2 ` `    ``// which is greater than n ` `    ``private` `int` `getNextPowerOfTwo(``int` `n) ` `    ``{ ` `        ``int` `logPart = (``int``)Math.ceil(Math.log(n) ` `                                     ``/ Math.log(``2``)); ` `        ``return` `(``int``)Math.pow(``2``, logPart); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int``[] a = { ``4``, ``5``, ``100``, ``9``, ``10``, ``11``, ``12``, ``15``, ``200` `}; ` `        ``GFG gfg = ``new` `GFG(); ` `        ``System.out.println(gfg.removeMinElements(a)); ` `    ``} ` `} `

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to return the minimum removals ` `    ``// required so that the array satisfy ` `    ``// the given condition ` `    ``static` `int` `removeMinElements(``int``[] a) ` `    ``{ ` `        ``int` `n = a.Length; ` ` `  `        ``RangeMinimumQuery rMimQ = ``new` `RangeMinimumQuery(); ` `        ``int``[] minTree = rMimQ.createSegmentTree(a); ` ` `  `        ``RangeMaximumQuery rMaxQ = ``new` `RangeMaximumQuery(); ` `        ``int``[] maxTree = rMaxQ.createSegmentTree(a); ` ` `  `        ``int` `start = 0, end = 0; ` ` `  `        ``// To store min and max in the current window ` `        ``int` `min, max; ` `        ``int` `maxValidLen = 0; ` ` `  `        ``while` `(end < n)  ` `        ``{ ` `            ``min = rMimQ.rangeMinimumQuery(minTree, ` `                                        ``start, end, n); ` `            ``max = rMaxQ.rangeMaximumQuery(maxTree, ` `                                        ``start, end, n); ` `            ``if` `(2 * min <= max) ` `                ``start++; ` `            ``else` `                ``maxValidLen = Math.Max(maxValidLen, ` `                                    ``end - start + 1); ` `            ``end++; ` `        ``} ` `        ``return` `n - maxValidLen; ` `    ``} ` ` `  `    ``class` `RangeMinimumQuery { ` ` `  `        ``// Creates a new segment tree from ` `        ``// the given input array ` `        ``public` `int``[] createSegmentTree(``int``[] input) ` `        ``{ ` `            ``int` `n = input.Length; ` `            ``int` `segTreeSize = 2 * getNextPowerOfTwo(n) - 1; ` `            ``int``[] segmentTree = ``new` `int``[segTreeSize]; ` ` `  `            ``createSegmentTreeUtil(segmentTree, input, ` `                                ``0, n - 1, 0); ` `            ``return` `segmentTree; ` `        ``} ` ` `  `        ``public` `void` `createSegmentTreeUtil(``int``[] segmentTree, ` `                                        ``int``[] input, ``int` `low, ` `                                        ``int` `high, ``int` `pos) ` `        ``{ ` `            ``if` `(low == high) { ` ` `  `                ``// Its a leaf node ` `                ``segmentTree[pos] = input[low]; ` `                ``return``; ` `            ``} ` ` `  `            ``// Construct left and right subtrees and then ` `            ``// update value for current node ` `            ``int` `mid = (low + high) / 2; ` `            ``createSegmentTreeUtil(segmentTree, input, low, ` `                                ``mid, (2 * pos + 1)); ` `            ``createSegmentTreeUtil(segmentTree, input, ` `                                ``mid + 1, high, (2 * pos + 2)); ` `            ``segmentTree[pos] = Math.Min(segmentTree[2 * pos + 1], ` `                                        ``segmentTree[2 * pos + 2]); ` `        ``} ` ` `  `        ``public` `int` `rangeMinimumQuery(``int``[] segmentTree, ``int` `from``, ` `                                    ``int` `to, ``int` `inputSize) ` `        ``{ ` `            ``return` `rangeMinimumQueryUtil(segmentTree, 0, ` `                                        ``inputSize - 1, ``from``, to, 0); ` `        ``} ` ` `  `        ``static` `int` `rangeMinimumQueryUtil(``int``[] segmentTree, ``int` `low, ` `                                        ``int` `high, ``int` `from``, ``int` `to, ``int` `pos) ` `        ``{ ` `            ``// Total overlap ` `            ``if` `(``from` `<= low && to >= high) { ` `                ``return` `segmentTree[pos]; ` `            ``} ` ` `  `            ``// No overlap ` `            ``if` `(``from` `> high || to < low) { ` `                ``return` `int``.MaxValue; ` `            ``} ` ` `  `            ``// Partial overlap ` `            ``int` `mid = (low + high) / 2; ` `            ``int` `left = rangeMinimumQueryUtil(segmentTree, low, ` `                                            ``mid, ``from``, to, ` `                                            ``(2 * pos + 1)); ` `            ``int` `right = rangeMinimumQueryUtil(segmentTree, ` `                                            ``mid + 1, high, ``from``, ` `                                            ``to, (2 * pos + 2)); ` `            ``return` `Math.Min(left, right); ` `        ``} ` `    ``} ` ` `  `    ``class` `RangeMaximumQuery { ` ` `  `        ``// Creates a new segment tree from given input array ` `        ``public` `int``[] createSegmentTree(``int``[] input) ` `        ``{ ` `            ``int` `n = input.Length; ` `            ``int` `segTreeSize = 2 * getNextPowerOfTwo(n) - 1; ` `            ``int``[] segmentTree = ``new` `int``[segTreeSize]; ` ` `  `            ``createSegmentTreeUtil(segmentTree, input, 0, n - 1, 0); ` `            ``return` `segmentTree; ` `        ``} ` ` `  `        ``public` `void` `createSegmentTreeUtil(``int``[] segmentTree, ``int``[] input, ` `                                        ``int` `low, ``int` `high, ``int` `pos) ` `        ``{ ` `            ``if` `(low == high) { ` ` `  `                ``// Its a leaf node ` `                ``segmentTree[pos] = input[low]; ` `                ``return``; ` `            ``} ` ` `  `            ``// Construct left and right subtrees and then ` `            ``// update value for current node ` `            ``int` `mid = (low + high) / 2; ` `            ``createSegmentTreeUtil(segmentTree, input, low, ` `                                ``mid, (2 * pos + 1)); ` `            ``createSegmentTreeUtil(segmentTree, input, ` `                                ``mid + 1, high, (2 * pos + 2)); ` `            ``segmentTree[pos] = Math.Max(segmentTree[2 * pos + 1], ` `                                        ``segmentTree[2 * pos + 2]); ` `        ``} ` ` `  `        ``public` `int` `rangeMaximumQuery(``int``[] segmentTree, ` `                                    ``int` `from``, ``int` `to, ``int` `inputSize) ` `        ``{ ` `            ``return` `rangeMaximumQueryUtil(segmentTree, 0, ` `                                        ``inputSize - 1, ``from``, to, 0); ` `        ``} ` ` `  `        ``public` `int` `rangeMaximumQueryUtil(``int``[] segmentTree, ``int` `low, ` `                                ``int` `high, ``int` `from``, ``int` `to, ``int` `pos) ` `        ``{ ` `            ``// Total overlap ` `            ``if` `(``from` `<= low && to >= high) { ` `                ``return` `segmentTree[pos]; ` `            ``} ` ` `  `            ``// No overlap ` `            ``if` `(``from` `> high || to < low) { ` `                ``return` `int``.MinValue; ` `            ``} ` ` `  `            ``// Partial overlap ` `            ``int` `mid = (low + high) / 2; ` `            ``int` `left = rangeMaximumQueryUtil(segmentTree, low, ` `                                            ``mid, ``from``, to, ` `                                            ``(2 * pos + 1)); ` `            ``int` `right = rangeMaximumQueryUtil(segmentTree, ` `                                            ``mid + 1, high, ``from``, ` `                                            ``to, (2 * pos + 2)); ` `            ``return` `Math.Max(left, right); ` `        ``} ` `    ``} ` ` `  `    ``// Function to return the minimum power of 2 ` `    ``// which is greater than n ` `    ``static` `int` `getNextPowerOfTwo(``int` `n) ` `    ``{ ` `        ``int` `logPart = (``int``)Math.Ceiling(Math.Log(n) ` `                                    ``/ Math.Log(2)); ` `        ``return` `(``int``)Math.Pow(2, logPart); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``int``[] a = { 4, 5, 100, 9, 10, 11, 12, 15, 200 }; ` `        ``Console.WriteLine(removeMinElements(a)); ` `    ``} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:
```4
```

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