493. Reverse Pairs(BST, BIT, MergeSort)

Given an array nums, we call (i, j) an important reverse pair if i < j and nums[i] > 2*nums[j].

You need to return the number of important reverse pairs in the given array.

Example1:

Input: [1,3,2,3,1]
Output: 2

Example2:

Input: [2,4,3,5,1]
Output: 3

Note:

1. The length of the given array will not exceed 50,000.
2. All the numbers in the input array are in the range of 32-bit integer.

 

Approach #1: Brute Force.

class Solution {
public:
    int reversePairs(vector<int>& nums) {
        int len = nums.size();
        int count = 0;
        for (int i = 0; i < len; ++i) {
            for (int j = i + 1; j < len; ++j) {
                if (nums[i] > nums[j] * 2LL) count++;
            }
        }
        return count;
    }
};

　　

Approach #2: Binary Search Tree.

class Node {
public:
    int val, count_ge;
    Node *left, *right;
    Node(int val) {
        this->val = val;
        this->count_ge = 1;
        this->left = NULL;
        this->right = NULL;
    }
};


class Solution {
public:
    int reversePairs(vector<int>& nums) {
        int len = nums.size();
        int count = 0;
        Node* head = NULL;
        
        for (int i = 0; i < len; ++i) {
            count += search(head, nums[i] * 2LL + 1);
            head = insert(head, nums[i]);
        }
        
        return count;
    }
    
private:
    int search(Node* head, long long val) {
        if (head == NULL) 
            return 0;
        else if (head->val == val) {
            return head->count_ge;
        } else if (head->val > val) {
            return head->count_ge + search(head->left, val);
        } else {
            return search(head->right, val);
        }
    }
    
    Node* insert(Node* head, int val) {
        if (head == NULL) return new Node(val);
        else if (head->val == val) 
            head->count_ge++;
        else if (head->val < val) {
            head->count_ge++;
            head->right = insert(head->right, val);
        } else {
            head->left = insert(head->left, val);
        }
        return head;
    }
};

　　

Approach #3: Binary Index Tree.

class Solution {
    public int reversePairs(int[] nums) {
        if (nums == null || nums.length <= 1) return 0;
        int n = nums.length;
        int[] nums_copy = nums.clone();
        
        Arrays.sort(nums_copy);
        
        int[] BITS = new int[n+1];
        
        int count = 0;
        
        for (int i = n-1; i >= 0; --i) {
            count += query(BITS, index(nums_copy, 1.0 * nums[i] / 2));
            update(BITS, index(nums_copy, nums[i]));
        }
        
        return count;
    }
    
    private void update(int[] BIT, int index) {
        index = index + 1;
        while (index < BIT.length) {
            BIT[index]++;
            index += index & (-index);
        }
    }
    
    private int query(int[] BIT, int index) {
        int sum = 0;
        while (index > 0) {
            sum += BIT[index];
            index -= index & (-index);
        }
        return sum;
    }
    
    private int index(int[] arr, double val) {
        int lo = 0, hi = arr.length;
        while (lo < hi) {
            int mid = lo + (hi - lo) / 2;
            if (arr[mid] >= val) hi = mid;
            else lo = mid + 1;
        }
        return lo;
    }
}

　　

Approach #4: Mergesort.

class Solution(object):
    def __init__(self):
        self.cnt = 0
        
    def reversePairs(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        def msort(lst):
            L = len(lst)
            if L <= 1:
                return lst
            else:
                return merge(msort(lst[:int(L/2)]), msort(lst[int(L/2):]))
        
        def merge(left, right):
            l, r = 0, 0
            while l < len(left) and r < len(right):
                if left[l] <= 2*right[r]:
                    l += 1
                else:
                    self.cnt += len(left)-l
                    r += 1
            return sorted(left+right)
            
        msort(nums)
        return self.cnt