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SlidingWindowMedian480.java
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221 lines (195 loc) · 7.25 KB
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/**
* Median is the middle value in an ordered integer list.
* If the size of the list is even, there is no middle value.
* So the median is the mean of the two middle value.
*
* Examples:
* [2,3,4] , the median is 3
* [2,3], the median is (2 + 3) / 2 = 2.5
*
* Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right.
* You can only see the k numbers in the window. Each time the sliding window moves right by one position.
* Your job is to output the median array for each window in the original array.
*
* For example,
* Given nums = [1,3,-1,-3,5,3,6,7], and k = 3.
*
* Window position Median
* --------------- -----
* [1 3 -1] -3 5 3 6 7 1
* 1 [3 -1 -3] 5 3 6 7 -1
* 1 3 [-1 -3 5] 3 6 7 -1
* 1 3 -1 [-3 5 3] 6 7 3
* 1 3 -1 -3 [5 3 6] 7 5
* 1 3 -1 -3 5 [3 6 7] 6
*
* Therefore, return the median sliding window as [1,-1,-1,3,5,6].
*
* Note:
* You may assume k is always valid, ie: 1 ≤ k ≤ input array's size for non-empty array.
*/
import java.util.Arrays;
import java.util.ArrayList;
import java.util.List;
import java.util.Collections;
public class SlidingWindowMedian480 {
public double[] medianSlidingWindow(int[] nums, int k) {
int len = nums.length;
int mid = k / 2;
List<Integer> window = new ArrayList<>();
for (int j = 0; j < k; j++) {
window.add(nums[j]);
}
Collections.sort(window);
if ((k & 1) == 0) {
int lenNew = len - 2 * mid + 1;
double[] returned = new double[lenNew];
for (int i = 0; i < lenNew - 1; i++) {
returned[i] = findMedianFromEven(window, mid);
int idx = window.indexOf(nums[i]);
int newValue = nums[i + k];
updateWindow(window, newValue, idx, k);
}
returned[lenNew - 1] = findMedianFromEven(window, mid);
return returned;
} else {
int lenNew = len - 2 * mid;
double[] returned = new double[lenNew];
for (int i = 0; i < lenNew - 1; i++) {
returned[i] = findMedianFromOdd(window, mid);
int idx = window.indexOf(nums[i]);
int newValue = nums[i + k];
updateWindow(window, newValue, idx, k);
}
returned[lenNew - 1] = findMedianFromOdd(window, mid);
return returned;
}
}
private double findMedianFromEven(List<Integer> window, int mid) {
return ((long)window.get(mid - 1) + (long)window.get(mid)) / 2.0;
}
private double findMedianFromOdd(List<Integer> window, int mid) {
return window.get(mid);
}
private void updateWindow(List<Integer> window, int newValue, int idx, int k) {
while(0 <= idx && idx < k) {
if (idx > 0 && window.get(idx - 1) > newValue) {
window.set(idx, window.get(idx - 1));
idx -= 1;
} else if (idx < k - 1 && window.get(idx + 1) < newValue) {
window.set(idx, window.get(idx + 1));
idx += 1;
} else {
window.set(idx, newValue);
return;
}
}
window.set(idx, newValue);
}
public double[] medianSlidingWindow2(int[] nums, int k) {
Comparator<Pair> comp = new Comparator<Pair>(){
public int compare(Pair p1, Pair p2) {
int diff = Integer.compare(p1.value, p2.value);
if (diff != 0) return diff;
return Integer.compare(p1.index, p2.index);
}
};
TreeSet<Pair> left = new TreeSet<>(comp);
TreeSet<Pair> right = new TreeSet<>(comp);
boolean isOdd = k % 2 == 1;
for (int i=0; i<k; i++) {
addNew(i, nums[i], left, right);
}
int len = nums.length;
double[] res = new double[len - k + 1];
for (int i=0; i<=len-k; i++) {
res[i] = left.size() == right.size() ? ((double) left.last().value + (double) right.first().value) / 2.0 : (double) left.last().value;
if (i == len-k) break;
Pair oldP = new Pair(i, nums[i]);
boolean inLeft = left.remove(oldP);
if (!inLeft) right.remove(oldP);
addNew(i+k, nums[i+k], left, right);
}
return res;
}
private void addNew(int index, int value, TreeSet<Pair> left, TreeSet<Pair> right) {
Pair p = new Pair(index, value);
if (right.size() != 0 && value > right.first().value) {
right.add(p);
} else {
left.add(p);
}
balance(left, right);
}
private void balance(TreeSet<Pair> left, TreeSet<Pair> right) {
while (left.size() > right.size() + 1) {
Pair topLeft = left.pollLast();
right.add(topLeft);
}
while (left.size() < right.size()) {
Pair bottomRight = right.pollFirst();
left.add(bottomRight);
}
}
class Pair {
int index;
int value;
Pair(int i, int v) {
index = i;
value = v;
}
}
public double[] medianSlidingWindow3(int[] nums, int k) {
Comparator<Integer> comp = (i1, i2) -> Integer.compare(i2, i1);
PriorityQueue<Integer> left = new PriorityQueue<>(comp);
PriorityQueue<Integer> right = new PriorityQueue<>();
for (int i=0; i<k; i++) {
if (left.isEmpty() || nums[i] <= left.peek()) {
left.add(nums[i]);
} else {
right.add(nums[i]);
}
if (left.size() < right.size()) {
left.add(right.poll());
} else if (left.size() > right.size() + 1) {
right.add(left.poll());
}
}
int N = nums.length;
double[] res = new double[N-k+1];
for (int i=k; i<=N; i++) {
if (left.size() == right.size() + 1) {
res[i-k] = left.peek() * 1.0;
} else {
res[i-k] = ((long)left.peek() + (long)right.peek()) / 2.0;
}
if (i == N) break;
int toPop = nums[i-k];
int toAdd = nums[i];
if (toAdd <= left.peek()) {
left.add(toAdd);
} else {
right.add(toAdd);
}
if (left.peek() >= toPop) {
left.remove(toPop);
} else {
right.remove(toPop);
}
if (left.size() < right.size()) {
left.add(right.poll());
} else if (left.size() > right.size() + 1) {
right.add(left.poll());
}
}
return res;
}
public static void main(String[] args) {
SlidingWindowMedian480 swm = new SlidingWindowMedian480();
int [] nums = {1, 3, -1, -3, 5, 3, 6, 7};
int [] twos = {2147483647, 2147483647};
System.out.println(Arrays.toString(swm.medianSlidingWindow(nums, 3)));
System.out.println(Arrays.toString(swm.medianSlidingWindow(nums, 4)));
System.out.println(Arrays.toString(swm.medianSlidingWindow(twos, 2)));
}
}