Sunday, January 8, 2017

LeetCode 480 - Sliding Window Median


http://bookshadow.com/weblog/2017/01/08/leetcode-sliding-window-median/
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.
二叉排序树(Binary Search Tree) / 堆(Heap)
维护二叉排序树hiSet与loSet,其中:

  hiSet的最小元素 > loSet的最大元素

  hiSet的大小 - loSet的大小 ∈ [0, 1]

获取中位数:

  若hiSet的大小 > loSet的大小,则返回hiSet.minValue
  
  否则,返回(hiSet.minValue + loSet.maxValue) / 2

新增元素:

  若hiSet为空,或者新元素 > hiSet.minValue,则加入hiSet
  
  否则加入loSet
  
  调整hiSet, loSet

移除元素:

  若hiSet包含目标元素,则从hiSet中移除
  
  否则,从loSet中移除
  
  调整hiSet, loSet

调整元素:

  若loSet的大小 > hiSet的大小,则将loSet的最大值弹出,加入hiSet
  
  否则,若hiSet的大小 - loSet的大小 > 1,则将hiSet的最小值弹出,加入loSet
private Comparator<Point> cmp = new Comparator<Point>(){ public int compare(Point a, Point b) { if (a.getX() != b.getX()) return Double.valueOf(b.getX()).compareTo(Double.valueOf(a.getX())); return Double.valueOf(b.getY()).compareTo(Double.valueOf(a.getY())); } }; private TreeSet<Point> hiSet = new TreeSet<>(cmp); private TreeSet<Point> loSet = new TreeSet<>(cmp); private double getMedian() { if (hiSet.size() > loSet.size()) { return hiSet.last().getX(); } return ((hiSet.last().getX()) + (loSet.first().getX())) / 2; } private void addValue(int val, int i) { Point p = new Point(val, i); if (hiSet.isEmpty() || hiSet.last().getX() < p.getX()) { hiSet.add(p); } else { loSet.add(p); } adjustSet(); } private void removeValue(int val, int i) { Point p = new Point(val, i); if (hiSet.contains(p)) { hiSet.remove(p); } else { loSet.remove(p); } adjustSet(); } private void adjustSet() { if (loSet.size() > hiSet.size()) { hiSet.add(loSet.pollFirst()); } else if (hiSet.size() > loSet.size() + 1) { loSet.add(hiSet.pollLast()); } } public double[] medianSlidingWindow(int[] nums, int k) { double[] ans = new double[nums.length - k + 1]; for (int i = 0; i < nums.length; i++) { if (i >= k) { removeValue(nums[i - k], i - k); } addValue(nums[i], i); if (i >= k - 1) { ans[i - k + 1] = getMedian(); } } return ans; }
https://discuss.leetcode.com/topic/74874/easy-to-understand-o-nlogk-java-solution-using-treemap
TreeMap is used to implement an ordered MultiSet.
In this problem, I use two Ordered MultiSets as Heaps. One heap maintains the lowest 1/2 of the elements, and the other heap maintains the higher 1/2 of elements.
This implementation is faster than the usual implementation that uses 2 PriorityQueues, because unlike PriorityQueue, TreeMap can remove arbitrary element in logarithmic time.

X.
https://discuss.leetcode.com/topic/74724/java-solution-using-two-priorityqueues
Almost the same idea of Find Median from Data Stream https://leetcode.com/problems/find-median-from-data-stream/
  1. Use two Heaps to store numbers. maxHeap for numbers smaller than current median, minHeap for numbers bigger than and equal to current median. A small trick I used is always make size of minHeap equal (when there are even numbers) or 1 element more (when there are odd numbers) than the size of maxHeap. Then it will become very easy to calculate current median.
  2. Keep adding number from the right side of the sliding window and remove number from left side of the sliding window. And keep adding current median to the result.
The documentation says remove(Object) takes linear time.
Then the overall runtime complexity is O(nk).
    PriorityQueue<Integer> minHeap = new PriorityQueue<Integer>();
    PriorityQueue<Integer> maxHeap = new PriorityQueue<Integer>(
        new Comparator<Integer>() {
            public int compare(Integer i1, Integer i2) {
                return i2.compareTo(i1);
            }
        }
    );
 
    public double[] medianSlidingWindow(int[] nums, int k) {
        int n = nums.length - k + 1;
 if (n <= 0) return new double[0];
        double[] result = new double[n];
        
        for (int i = 0; i <= nums.length; i++) {
            if (i >= k) {
         result[i - k] = getMedian();
         remove(nums[i - k]);
            }
            if (i < nums.length) {
         add(nums[i]);
            }
        }
        
        return result;
    }
    
    private void add(int num) {
 if (num < getMedian()) {
     maxHeap.add(num);
 }
 else {
     minHeap.add(num);
 }
 if (maxHeap.size() > minHeap.size()) {
            minHeap.add(maxHeap.poll());
 }
        if (minHeap.size() - maxHeap.size() > 1) {
            maxHeap.add(minHeap.poll());
        }
    }
 
    private void remove(int num) {
 if (num < getMedian()) {
     maxHeap.remove(num);
 }
 else {
     minHeap.remove(num);
 }
 if (maxHeap.size() > minHeap.size()) {
            minHeap.add(maxHeap.poll());
 }
        if (minHeap.size() - maxHeap.size() > 1) {
            maxHeap.add(minHeap.poll());
        }
    }
 
    private double getMedian() {
 if (maxHeap.isEmpty() && minHeap.isEmpty()) return 0;
     
 if (maxHeap.size() == minHeap.size()) {
     return ((double)maxHeap.peek() + (double)minHeap.peek()) / 2.0;
 }
 else {
            return (double)minHeap.peek();
 }
    }



No comments:

Post a Comment

Labels

LeetCode (1243) GeeksforGeeks (1129) Review (896) Algorithm (764) LeetCode - Review (722) to-do (636) Dynamic Programming (340) Classic Algorithm (313) Classic Interview (266) Google Interview (246) Tree (146) POJ (141) Difficult Algorithm (129) LeetCode - Phone (127) EPI (125) Bit Algorithms (120) Different Solutions (117) Math (115) Lintcode (113) Cracking Coding Interview (110) Smart Algorithm (105) DFS (93) Binary Search (92) HackerRank (89) Greedy Algorithm (84) Binary Tree (83) Stack (78) Graph Algorithm (76) Two Pointers (64) BFS (63) LeetCode - Extended (62) Interview Corner (61) List (57) Advanced Data Structure (56) Geometry Algorithm (56) Interval (54) Codility (53) ComProGuide (52) LeetCode Hard (50) Trie (49) Union-Find (48) Binary Search Tree (47) Segment Tree (47) Algorithm Interview (46) USACO (46) Space Optimization (43) Bisection (42) Mathematical Algorithm (42) ACM-ICPC (41) Data Structure (40) Knapsack (40) Matrix (40) Time Complexity (40) Jobdu (39) Priority Queue (39) Recursive Algorithm (39) Sliding Window (39) Backtracking (38) String Algorithm (38) TopCoder (38) Codeforces (36) Introduction to Algorithms (36) Must Known (36) Beauty of Programming (35) Sort (35) Data Structure Design (34) prismoskills (33) Array (32) LeetCode - DP (32) HDU (31) Random (31) Google Code Jam (30) Graph (30) Permutation (30) Puzzles (30) Array O(N) (29) Company-Airbnb (29) Palindrome (29) Company-Zenefits (28) Pre-Sort (28) to-do-must (28) Logic Thinking (27) Microsoft 100 - July (27) Monotonic Stack (27) Queue (27) Binary Indexed Trees (26) Company - LinkedIn (25) Follow Up (25) GeeksQuiz (25) Post-Order Traverse (25) hihocoder (25) Company-Facebook (24) Algorithm Game (22) Hash (22) High Frequency (22) Merge Sort (22) DFS + Review (21) Lintcode - Review (21) O(N) (21) Brain Teaser (20) CareerCup (20) Company - Twitter (20) BST (19) Hard (19) Topological Sort (19) UVA (19) Sweep Line (18) Company-Uber (17) Game Theory (17) Left and Right Array (17) Probabilities (17) Proof (17) Codercareer (16) DP - Tree (16) Heap (16) Iterator (16) Shortest Path (16) String Search (16) Tree Traversal (16) itint5 (16) Difficult (15) KMP (15) Reverse Thinking (15) LeetCode - DFS (14) Number (14) Number Theory (14) Rolling Hash (14) TreeMap (14) Amazon Interview (13) Basic Algorithm (13) Codechef (13) Computational Geometry (13) Euclidean GCD (13) LeetCode - Classic (13) Long Increasing Sequence(LIS) (13) Majority (13) mitbbs (13) Algorithm - How To (12) Combination (12) Fast Power Algorithm (12) LeetCode - Thinking (12) Modify Tree (12) Reconstruct Tree (12) Reservoir Sampling (12) Simulation (12) 尺取法 (12) AOJ (11) Bucket Sort (11) DFS+Backtracking (11) DP - Interval (11) DP-Space Optimization (11) Divide and Conquer (11) Graph DFS (11) LCA (11) Math-Divisible (11) Miscs (11) O(1) Space (11) Prefix Sum (11) Princeton (11) X Sum (11) 挑战程序设计竞赛 (11) Coin Change (10) Company - Microsoft (10) DFS+Cache (10) DP - Bit Masking (10) DP - Digit (10) Facebook Hacker Cup (10) HackerRank Easy (10) Interval Tree (10) Kadane - Extended (10) MinMax (10) SPOJ (10) Theory (10) Tutorialhorizon (10) DP - Probability (9) DP-Multiple Relation (9) Mathblog (9) Max-Min Flow (9) Monotone Queue (9) Quick Sort (9) Stack Overflow (9) Stock (9) System Design (9) Use XOR (9) Book Notes (8) Bottom-Up (8) Company-Amazon (8) DFS+BFS (8) Dijkstra (8) LeetCode - TODO (8) Linked List (8) Longest Common Subsequence(LCS) (8) Prime (8) Quick Select (8) Suffix Tree (8) Summary (8) Tech-Queries (8) Traversal Once (8) TreeSet (8) 穷竭搜索 (8) Algorithm Problem List (7) Expression (7) Facebook Interview (7) Fast Slow Pointers (7) Fibonacci Numbers (7) Game Nim (7) Graph BFS (7) HackerRank Difficult (7) Hackerearth (7) Inversion (7) Kadane’s Algorithm (7) Level Order Traversal (7) One Pass (7) Pruning (7) Radix Sort (7) Tree DP (7) 蓝桥杯 (7) Bit Mask (6) Catalan Number (6) Classic Data Structure Impl (6) DFS+DP (6) DP - Monotone Queue (6) DP-Print Solution (6) Dutch Flag (6) Flood fill (6) How To (6) Interviewstreet (6) Knapsack - MultiplePack (6) Manacher (6) Minimum Spanning Tree (6) Morris Traversal (6) Multiple Data Structures (6) Pre-Sum (6) Programming Pearls (6) Rabin-Karp (6) Randomized Algorithms (6) Sampling (6) Schedule (6) Stream (6) Suffix Array (6) Xpost (6) n00tc0d3r (6) reddit (6) AI (5) Algorithm - Brain Teaser (5) Art Of Programming-July (5) Big Data (5) Brute Force (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Convex Hull (5) Crazyforcode (5) Cycle (5) DP - Knapsack (5) DP-Include vs Exclude (5) Find Rule (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Java (5) Matrix Chain Multiplication (5) Maze (5) Microsoft Interview (5) Quadtrees (5) Quick Partition (5) Quora (5) SPFA(Shortest Path Faster Algorithm) (5) Subarray Sum (5) Sudoku (5) Threaded (5) Word Search (5) jiuzhang (5) 1point3acres (4) Abbreviation (4) Anagram (4) Anagrams (4) Approximate Algorithm (4) Backtracking-Include vs Exclude (4) Brute Force - Enumeration (4) Chess Game (4) Consistent Hash (4) Dequeue (4) Distributed (4) Eulerian Cycle (4) Graph-Classic (4) Greedy (4) HackerRank AI (4) Histogram (4) Kadane Max Sum (4) Knapsack - Mixed (4) Knapsack - Unbounded (4) LeetCode - Recursive (4) MST (4) N Queens (4) Nerd Paradise (4) Parallel Algorithm (4) Practical Algorithm (4) Probability (4) Spell Checker (4) Stock Maximize (4) Subset Sum (4) Subsets (4) Symbol Table (4) Triangle (4) Water Jug (4) algnotes (4) fgdsb (4) to-do-2 (4) 最大化最小值 (4) 树形DP (4) 男人八题 (4) A Star (3) Algorithm Design (3) B Tree (3) Bellman Ford (3) Big Data Algorithm (3) Caterpillar Method (3) Coins (3) Company - Groupon (3) Company - Indeed (3) Cumulative Sum (3) DP-Fill by Length (3) DP-Two Variables (3) Dedup (3) Dropbox (3) Easy (3) Factor (3) Finite Automata (3) Github (3) GoLang (3) Graph - Bipartite (3) Graph Coloring (3) Include vs Exclude (3) Islands (3) Joseph (3) K (3) Knapsack-多重背包 (3) Knight (3) LeetCode - Bit (3) Linked List Merge Sort (3) LogN (3) Master Theorem (3) Median (3) Min Cost Flow (3) Minesweeper (3) Missing Numbers (3) NP Hard (3) Online Algorithm (3) Parentheses (3) Parser (3) Pascal's Triangle (3) Pattern Match (3) Programcreek (3) Project Euler (3) Rectangle (3) Robot (3) Scala (3) SegmentFault (3) Shuffle (3) Sieve of Eratosthenes (3) Skyline (3) Stack - Smart (3) State Machine (3) Strongly Connected Components (3) Subtree (3) TSP (3) Transform Tree (3) Trie + DFS (3) Warshall Floyd (3) With Random Pointer (3) Word Ladder (3) bookkeeping (3) codebytes (3) Activity Selection Problem (2) Advanced Algorithm (2) AnAlgorithmADay (2) Application of Algorithm (2) Array Merge (2) Augmented BST (2) BOJ (2) BT - Path Sum (2) Balanced Binary Search Tree (2) Binary Search - Smart (2) Binomial Coefficient (2) Bit Counting (2) Bit-Difficult (2) Bloom Filter (2) Book Coding Interview (2) Branch and Bound Method (2) Cache (2) Clock (2) Codesays (2) Company - Baidu (2) Company-Snapchat (2) Complete Binary Tree (2) DP - DFS (2) DP - Trie (2) DP-3D Table (2) DP-Classical (2) DP-Output Solution (2) DP-Slide Window Gap (2) DP-i-k-j (2) Distributed Algorithms (2) Divide and Conqure (2) Doubly Linked List (2) Edit Distance (2) Forward && Backward Scan (2) Game (2) GoHired (2) Graham Scan (2) Graph BFS+DFS (2) Graph-Cut Vertices (2) Hamiltonian Cycle (2) Hard Algorithm (2) Huffman Tree (2) In-order Traverse (2) Include or Exclude Last Element (2) Information Retrieval (2) Interview - Linkedin (2) Invariant (2) Jump Game (2) LeetCode - Hard (2) Linked Interview (2) Linked List Sort (2) Longest SubArray (2) Lucene-Solr (2) Math-Remainder Queue (2) Matrix Power (2) Minimum Vertex Cover (2) Negative All Values (2) Number Each Digit (2) Numerical Method (2) O(N) Hard (2) Object Design (2) Order Statistic Tree (2) Parent-Only Tree (2) Peak (2) PreProcess (2) Programming (2) Range Minimum Query (2) Regular Expression (2) Return Multiple Values (2) Reuse Forward Backward (2) Reverse (2) Rosettacode (2) Scan from right (2) Search (2) SimHash (2) Simple Algorithm (2) Sparse Table (2) Spatial Index (2) TV (2) Tile (2) Traversal From End (2) Tree Sum (2) Tree Traversal Return Multiple Values (2) Tree Without Tree Predefined (2) Two Pointers Window (2) Two-End-BFS (2) Word Break (2) Word Graph (2) Word Trie (2) Yahoo Interview (2) Young Tableau (2) 剑指Offer (2) 数位DP (2) 1-X (1) 51Nod (1) ? (1) Akka (1) Algorithm - New (1) Algorithm Series (1) Algorithms Part I (1) All Substrings (1) Analysis of Algorithm (1) Array-Element Index Negative (1) Array-Rearrange (1) Augmented Tree (1) Auxiliary Array (1) Auxiliary Array: Inc&Dec (1) BACK (1) BFS - Priority Queue (1) BFS Hard (1) BK-Tree (1) BZOJ (1) Basic (1) Bayes (1) Beauty of Math (1) Big Integer (1) Big Number (1) Binary (1) Binary String (1) Binary Tree Variant (1) Bipartite (1) Bit-Missing Number (1) BitMap (1) BitMap index (1) BitSet (1) Bug Free Code (1) BuildIt (1) C/C++ (1) CC Interview (1) Calculate Height at Same Recusrion (1) Cartesian tree (1) Check Tree Property (1) Chinese (1) Circular (1) Circular Buffer (1) Clean Code (1) Cloest (1) Clone (1) Code Quality (1) Codesolutiony (1) Company - Alibaba (1) Company - Palantir (1) Company - WalmartLabs (1) Company-Apple (1) Company-Epic (1) Company-Salesforce (1) Company-Yelp (1) Compression Algorithm (1) Concise (1) Concurrency (1) Convert BST to DLL (1) Convert DLL to BST (1) Custom Sort (1) Cyclic Replacement (1) DFS + RL (1) DFS+BFS, Flood Fill (1) DFS-Matrix (1) DI (1) DP Fill Diagonal First (1) DP-Difficult (1) DP-End with 0 or 1 (1) DP-Fill Diagonal First (1) DP-Graph (1) DP-Left and Right Array (1) DP-MaxMin (1) DP-Memoization (1) DP-Node All Possibilities (1) DP-Optimization (1) DP-Preserve Previous Value (1) DP-Print All Solution (1) DP-树形 (1) Database (1) Detect Negative Cycle (1) Diagonal (1) Directed Graph (1) Do Two Things at Same Recusrion (1) Domino (1) Dr Dobb's (1) Duplicate (1) EntryPoint (1) Equal probability (1) External Sort (1) FST (1) Failure Function (1) Fraction (1) Front End Pointers (1) Funny (1) Fuzzy String Search (1) Generating Function (1) Generation (1) Genetic algorithm (1) GeoHash (1) Geometry - Orientation (1) Google APAC (1) Graph But No Graph (1) Graph Transpose (1) Graph Traversal (1) Graph-Coloring (1) Graph-Longest Path (1) Gray Code (1) HOJ (1) Hanoi (1) How Hash (1) How to Test (1) Improve It (1) In Place (1) Inorder-Reverse Inorder Traverse Simultaneously (1) Interpolation search (1) Interview (1) Interview - Facebook (1) Isomorphic (1) JDK8 (1) K Dimensional Tree (1) Knapsack - Fractional (1) Knapsack - ZeroOnePack (1) Knuth Shuffle (1) Kosaraju’s algorithm (1) Kruskal (1) Kth Element (1) Lazy (1) Least Common Ancestor (1) LeetCode - Binary Tree (1) LeetCode - Coding (1) LeetCode - Construction (1) LeetCode - Detail (1) LeetCode - Related (1) LeetCode -P (1) Linked List Reverse (1) Linkedin (1) Linkedin Interview (1) Local MinMax (1) Lock (1) Logic Pattern (1) Longest Common Subsequence (1) Longest Common Substring (1) Longest Prefix Suffix(LPS) (1) Machine Learning (1) Maintain State (1) Manhattan Distance (1) Map && Reverse Map (1) Math - Induction (1) Math-Multiply (1) Math-Sum Of Digits (1) Matrix - O(N+M) (1) Matrix BFS (1) Matrix Exponentiation (1) Matrix Graph (1) Matrix Multiplication (1) Matrix Search (1) Matrix+DP (1) Matrix-Rotate (1) Max Min So Far (1) Memory-Efficient (1) MinHash (1) MinMax Heap (1) Monto Carlo (1) Multi-End BFS (1) Multi-Reverse (1) Multiple DFS (1) Multiple Steps (1) Multiple Tasks (1) Next Element (1) Next Successor (1) O(32N) (1) Offline Algorithm (1) Optimal Play (1) Optimization (1) PAT (1) Parenthesis (1) Partition (1) Path Finding (1) Patience Sort (1) Persistent (1) Pigeon Hole Principle (1) Power Set (1) Pratical Algorithm (1) Probabilistic Data Structure (1) Probability DP (1) Python (1) Queue & Stack (1) RSA (1) Ranking (1) Rddles (1) ReHash (1) Realtime (1) Recurrence Relation (1) Recursion (1) Recursive DFS (1) Recursive to Iterative (1) Red-Black Tree (1) Region (1) Remap (1) Resources (1) Reverse Inorder Traversal (1) Robin (1) Selection (1) Self Balancing BST (1) Similarity (1) Simplify (1) Sort && Binary Search (1) Space Complexity (1) Square (1) Strategy (1) Streaming Algorithm (1) String Algorithm. Symbol Table (1) String DP (1) String Distance (1) SubMatrix (1) Subsequence (1) System of Difference Constraints(差分约束系统) (1) Ternary Search Tree (1) Test (1) Test Cases (1) Thread (1) TimSort (1) Top-Down (1) Tournament (1) Tournament Tree (1) Trade Off (1) Transform Tree in Place (1) Tree Diameter (1) Tree Rotate (1) Trie and Heap (1) Trie vs Hash (1) Trie vs HashMap (1) Triplet (1) Two Data Structures (1) Two Stacks (1) USACO - Classical (1) USACO - Problems (1) UyHiP (1) Valid Tree (1) Vector (1) Virtual Matrix (1) Wiggle Sort (1) Wikipedia (1) ZOJ (1) ZigZag (1) baozitraining (1) codevs (1) cos126 (1) cycl (1) javabeat (1) jum (1) namic Programming (1) sqrt(N) (1) 两次dijkstra (1) 九度 (1) 二进制枚举 (1) 夹逼法 (1) 归一化 (1) 折半枚举 (1) 枚举 (1) 状态压缩DP (1) 英雄会 (1) 逆向思维 (1)

Popular Posts