X3_Binary Search

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§Binary Tree Level Order Traversal

test case:cover different + corner case

  1. only left/right child
  2. full tree
  3. left child, right child, left child, right child…

Follow Up: output the level to level reversely from bottom to up

  1. reverse funtion
  2. add from front

§Intersection of Two Arrays

  1. If non sort-> Hashmap. Ues extra space. O(m+n)
  2. If sort-> Two pointers. O(m+n)
  3. If no extra space / If n>>m, scan the smaller array and find it in larger one via binary search in -> If already sort -> O(m*logn)

Intersection of k arrays? merge 的变种

  1. ​

§Dot Production (FB)

Conduct Dot Product of two large sparse Vectors

  1. find non-zero indexes
  2. intersection
  3. dot product

§Find K-th Smallest Pair Distance

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    int lo = 0;
    int hi = nums[num.length - 1] - nums[0];
    while (lo < hi){
      int mid = lo + ((hi - lo) >>> 1);
      //...
    }

    // count function = number of pairs with distance <= guess
    if (nums[right] - nums[left] > guess)
      continue;
    count += right - left;

    Runtime: N^2*logW

  2. Optimization

    since there may be duplicate ->

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    right = upperBound(nums, left+1, n-1, target);
    count += right - left -1

  3. Optimization II

    Use Map<Integer, Integer> to memorize

    Binary Search -> N logN * logW

§Others

§410. Split Array Largest Sum
§Copy Books, The Painter’s Partition Problem Part II
§expire map

https://www.quora.com/How-can-I-implement-expiry-key-hashmap-in-Java

cannot remove element while using for loop, but can use interator

https://stackoverflow.com/questions/6092642/how-to-remove-a-key-from-hashmap-while-iterating-over-it

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class ExpiringKey implement Comparable<ExpiringKey> {
        V val;
        long expirationTime; // ttl
        K k;
    }
    
    class ExpringMap {
        Map<K, ExpiringKey> m = new HashMap<>();
        PriorityQueue q
        
        V get(Key k) {
            ExpiringKey v = this.m.get(k);
            if (v == null) {
                return null;
            }
            
            if (v.expirationTime < System.currentTimeMillis()) {
                m.remove(k);
                return null;
            }
            
            return v.val;
        }
    
        void put(Key k, V val, long expirationTime) {
            ExpiringKey expiringKey = new ExpiringKey(val, expirationTime);
            this.m.put(k, expiringKey);
            this.q.add(expiringKey); // log(k)
        }
        
        void cleanup() {
        // q.poll() log(k)
            List<K> keys = new ArrayList<>();
            for (ExpiringKey entry : this.m.entrySet()) {
                if (entry.getValue().expirationTime < System.currentTimeMillis()) {
                    keys.add(entry.getKey());
                }
            }
            
            for (K key : keys) // delete
        }
        
        // PriorityQueue<>()   minHeap
    }

optimization: use PriorityQueue

§Trick

  1. search

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    // search in java, return index
    if (index>=0){
      set.add(num);
      l = index;
    }
    else{
      index = -(index+1); //next one who is larger than it
      if (index >= r)
        break;
      l = index;
    }

  2. Difference between >>> and >>

    >>> is unsigned