Given an integer array nums, return the number of reverse pairs in the array.
A reverse pair is a pair (i, j) where 0 <= i < j < nums.length and nums[i] > 2 * nums[j].
Example 1:
Input: nums = [1,3,2,3,1] Output: 2 Explanation: The reverse pairs are: (1, 4) --> nums[1] = 3, nums[4] = 1, 3 > 2 * 1 (3, 4) --> nums[3] = 3, nums[4] = 1, 3 > 2 * 1
Example 2:
Input: nums = [2,4,3,5,1] Output: 3 Explanation: The reverse pairs are: (1, 4) --> nums[1] = 4, nums[4] = 1, 4 > 2 * 1 (2, 4) --> nums[2] = 3, nums[4] = 1, 3 > 2 * 1 (3, 4) --> nums[3] = 3, nums[4] = 1, 5 > 2 * 1
Constraints:
1 <= nums.length <= 5 * 104-231 <= nums[i] <= 231 - 1
Merge Sort or Binary Indexed Tree or Segment Tree.
Merge Sort:
class Solution:
def reversePairs(self, nums: List[int]) -> int:
def merge_sort(nums, left, right):
if left >= right:
return 0
mid = (left + right) >> 1
res = merge_sort(nums, left, mid) + merge_sort(nums, mid + 1, right)
i, j = left, mid + 1
while i <= mid and j <= right:
if nums[i] <= 2 * nums[j]:
i += 1
else:
res += mid - i + 1
j += 1
tmp = []
i, j = left, mid + 1
while i <= mid and j <= right:
if nums[i] <= nums[j]:
tmp.append(nums[i])
i += 1
else:
tmp.append(nums[j])
j += 1
while i <= mid:
tmp.append(nums[i])
i += 1
while j <= right:
tmp.append(nums[j])
j += 1
for i in range(left, right + 1):
nums[i] = tmp[i - left]
return res
return merge_sort(nums, 0, len(nums) - 1)Binary Indexed Tree:
class BinaryIndexedTree:
def __init__(self, n):
self.n = n
self.c = [0] * (n + 1)
@staticmethod
def lowbit(x):
return x & -x
def update(self, x, delta):
while x <= self.n:
self.c[x] += delta
x += BinaryIndexedTree.lowbit(x)
def query(self, x):
s = 0
while x > 0:
s += self.c[x]
x -= BinaryIndexedTree.lowbit(x)
return s
class Solution:
def reversePairs(self, nums: List[int]) -> int:
s = set()
for num in nums:
s.add(num)
s.add(num * 2)
alls = sorted(s)
m = {v: i for i, v in enumerate(alls, 1)}
ans = 0
tree = BinaryIndexedTree(len(m))
for num in nums[::-1]:
ans += tree.query(m[num] - 1)
tree.update(m[num * 2], 1)
return ansSegment Tree:
class Node:
def __init__(self):
self.l = 0
self.r = 0
self.v = 0
class SegmentTree:
def __init__(self, n):
self.tr = [Node() for _ in range(4 * n)]
self.build(1, 1, n)
def build(self, u, l, r):
self.tr[u].l = l
self.tr[u].r = r
if l == r:
return
mid = (l + r) >> 1
self.build(u << 1, l, mid)
self.build(u << 1 | 1, mid + 1, r)
def modify(self, u, x, v):
if self.tr[u].l == x and self.tr[u].r == x:
self.tr[u].v += 1
return
mid = (self.tr[u].l + self.tr[u].r) >> 1
if x <= mid:
self.modify(u << 1, x, v)
else:
self.modify(u << 1 | 1, x, v)
self.pushup(u)
def pushup(self, u):
self.tr[u].v = self.tr[u << 1].v + self.tr[u << 1 | 1].v
def query(self, u, l, r):
if self.tr[u].l >= l and self.tr[u].r <= r:
return self.tr[u].v
mid = (self.tr[u].l + self.tr[u].r) >> 1
v = 0
if l <= mid:
v += self.query(u << 1, l, r)
if r > mid:
v += self.query(u << 1 | 1, l, r)
return v
class Solution:
def reversePairs(self, nums: List[int]) -> int:
s = set()
for num in nums:
s.add(num)
s.add(num * 2)
alls = sorted(s)
m = {v: i for i, v in enumerate(alls, 1)}
tree = SegmentTree(len(m))
ans = 0
for v in nums[::-1]:
x = m[v]
ans += tree.query(1, 1, x - 1)
tree.modify(1, m[v * 2], 1)
return ansMerge Sort:
class Solution {
private static int[] tmp = new int[50010];
public int reversePairs(int[] nums) {
return mergeSort(nums, 0, nums.length - 1);
}
private int mergeSort(int[] nums, int left, int right) {
if (left >= right) {
return 0;
}
int mid = (left + right) >> 1;
int res = mergeSort(nums, left, mid) + mergeSort(nums, mid + 1, right);
int i = left, j = mid + 1, k = 0;
while (i <= mid && j <= right) {
if ((long) nums[i] <= (long) 2 * nums[j]) {
++i;
} else {
res += (mid - i + 1);
++j;
}
}
i = left;
j = mid + 1;
while (i <= mid && j <= right) {
if (nums[i] <= nums[j]) {
tmp[k++] = nums[i++];
} else {
tmp[k++] = nums[j++];
}
}
while (i <= mid) {
tmp[k++] = nums[i++];
}
while (j <= right) {
tmp[k++] = nums[j++];
}
for (i = left; i <= right; ++i) {
nums[i] = tmp[i - left];
}
return res;
}
}Binary Indexed Tree:
class Solution {
public int reversePairs(int[] nums) {
TreeSet<Long> ts = new TreeSet<>();
for (int num : nums) {
ts.add((long) num);
ts.add((long) num * 2);
}
Map<Long, Integer> m = new HashMap<>();
int idx = 0;
for (long num : ts) {
m.put(num, ++idx);
}
BinaryIndexedTree tree = new BinaryIndexedTree(m.size());
int ans = 0;
for (int i = nums.length - 1; i >= 0; --i) {
int x = m.get((long) nums[i]);
ans += tree.query(x - 1);
tree.update(m.get((long) nums[i] * 2), 1);
}
return ans;
}
}
class BinaryIndexedTree {
private int n;
private int[] c;
public BinaryIndexedTree(int n) {
this.n = n;
c = new int[n + 1];
}
public void update(int x, int delta) {
while (x <= n) {
c[x] += delta;
x += lowbit(x);
}
}
public int query(int x) {
int s = 0;
while (x > 0) {
s += c[x];
x -= lowbit(x);
}
return s;
}
public static int lowbit(int x) {
return x & -x;
}
}Segment Tree:
class Solution {
public int reversePairs(int[] nums) {
TreeSet<Long> ts = new TreeSet<>();
for (int num : nums) {
ts.add((long) num);
ts.add((long) num * 2);
}
Map<Long, Integer> m = new HashMap<>();
int idx = 0;
for (long num : ts) {
m.put(num, ++idx);
}
SegmentTree tree = new SegmentTree(m.size());
int ans = 0;
for (int i = nums.length - 1; i >= 0; --i) {
int x = m.get((long) nums[i]);
ans += tree.query(1, 1, x - 1);
tree.modify(1, m.get((long) nums[i] * 2), 1);
}
return ans;
}
}
class Node {
int l;
int r;
int v;
}
class SegmentTree {
private Node[] tr;
public SegmentTree(int n) {
tr = new Node[4 * n];
for (int i = 0; i < tr.length; ++i) {
tr[i] = new Node();
}
build(1, 1, n);
}
public void build(int u, int l, int r) {
tr[u].l = l;
tr[u].r = r;
if (l == r) {
return;
}
int mid = (l + r) >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
}
public void modify(int u, int x, int v) {
if (tr[u].l == x && tr[u].r == x) {
tr[u].v += v;
return;
}
int mid = (tr[u].l + tr[u].r) >> 1;
if (x <= mid) {
modify(u << 1, x, v);
} else {
modify(u << 1 | 1, x, v);
}
pushup(u);
}
public void pushup(int u) {
tr[u].v = tr[u << 1].v + tr[u << 1 | 1].v;
}
public int query(int u, int l, int r) {
if (tr[u].l >= l && tr[u].r <= r) {
return tr[u].v;
}
int mid = (tr[u].l + tr[u].r) >> 1;
int v = 0;
if (l <= mid) {
v += query(u << 1, l, r);
}
if (r > mid) {
v += query(u << 1 | 1, l, r);
}
return v;
}
}Merge Sort:
class Solution {
public:
int reversePairs(vector<int>& nums) {
int n = nums.size();
vector<int> temp(n);
return mergeSort(nums, temp, 0, n - 1);
}
private:
int mergeSort(vector<int>& nums, vector<int>& temp, int l, int r) {
if (l >= r) {
return 0;
}
int m = l + r >> 1;
int count = mergeSort(nums, temp, l, m) + mergeSort(nums, temp, m + 1, r);
int i = l, j = m + 1, k = l;
while (i <= m && j <= r) {
if ((long long)nums[i] <= (long long)2 * nums[j]) {
++i;
} else {
count += (m - i + 1);
++j;
}
}
i = l;
j = m + 1;
while (i <= m || j <= r) {
if (i > m) {
temp[k++] = nums[j++];
} else if (j > r || nums[i] <= nums[j]) {
temp[k++] = nums[i++];
} else {
temp[k++] = nums[j++];
}
}
copy(temp.begin() + l, temp.begin() + r + 1, nums.begin() + l);
return count;
}
};Binary Indexed Tree:
class BinaryIndexedTree {
public:
int n;
vector<int> c;
BinaryIndexedTree(int _n): n(_n), c(_n + 1){}
void update(int x, int delta) {
while (x <= n)
{
c[x] += delta;
x += lowbit(x);
}
}
int query(int x) {
int s = 0;
while (x > 0)
{
s += c[x];
x -= lowbit(x);
}
return s;
}
int lowbit(int x) {
return x & -x;
}
};
class Solution {
public:
int reversePairs(vector<int>& nums) {
set<long long> s;
for (int num : nums)
{
s.insert(num);
s.insert(num * 2ll);
}
unordered_map<long long, int> m;
int idx = 0;
for (long long num : s) m[num] = ++idx;
BinaryIndexedTree* tree = new BinaryIndexedTree(m.size());
int ans = 0;
for (int i = nums.size() - 1; i >= 0; --i)
{
ans += tree->query(m[nums[i]] - 1);
tree->update(m[nums[i] * 2ll], 1);
}
return ans;
}
};Segment Tree:
class Node {
public:
int l;
int r;
int v;
};
class SegmentTree {
public:
vector<Node*> tr;
SegmentTree(int n) {
tr.resize(4 * n);
for (int i = 0; i < tr.size(); ++i) tr[i] = new Node();
build(1, 1, n);
}
void build(int u, int l, int r) {
tr[u]->l = l;
tr[u]->r = r;
if (l == r) return;
int mid = (l + r) >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
}
void modify(int u, int x, int v) {
if (tr[u]->l == x && tr[u]->r == x)
{
tr[u]->v += v;
return;
}
int mid = (tr[u]->l + tr[u]->r) >> 1;
if (x <= mid) modify(u << 1, x, v);
else modify(u << 1 | 1, x, v);
pushup(u);
}
void pushup(int u) {
tr[u]->v = tr[u << 1]->v + tr[u << 1 | 1]->v;
}
int query(int u, int l, int r) {
if (tr[u]->l >= l && tr[u]->r <= r) return tr[u]->v;
int mid = (tr[u]->l + tr[u]->r) >> 1;
int v = 0;
if (l <= mid) v = query(u << 1, l, r);
if (r > mid) v += query(u << 1 | 1, l, r);
return v;
}
};
class Solution {
public:
int reversePairs(vector<int>& nums) {
set<long long> s;
for (int num : nums)
{
s.insert(num);
s.insert(num * 2ll);
}
unordered_map<long long, int> m;
int idx = 0;
for (long long num : s) m[num] = ++idx;
SegmentTree* tree = new SegmentTree(m.size());
int ans = 0;
for (int i = nums.size() - 1; i >= 0; --i)
{
ans += tree->query(1, 1, m[nums[i]] - 1);
tree->modify(1, m[nums[i] * 2ll], 1);
}
return ans;
}
};func reversePairs(nums []int) int {
return mergeSort(nums, 0, len(nums)-1)
}
func mergeSort(nums []int, left, right int) int {
if left >= right {
return 0
}
mid := (left + right) >> 1
res := mergeSort(nums, left, mid) + mergeSort(nums, mid+1, right)
i, j := left, mid+1
for i <= mid && j <= right {
if nums[i] <= 2*nums[j] {
i++
} else {
res += (mid - i + 1)
j++
}
}
i, j = left, mid+1
var tmp []int
for i <= mid && j <= right {
if nums[i] <= nums[j] {
tmp = append(tmp, nums[i])
i++
} else {
tmp = append(tmp, nums[j])
j++
}
}
for i <= mid {
tmp = append(tmp, nums[i])
i++
}
for j <= right {
tmp = append(tmp, nums[j])
j++
}
for i = left; i <= right; i++ {
nums[i] = tmp[i-left]
}
return res
}type BinaryIndexedTree struct {
n int
c []int
}
func newBinaryIndexedTree(n int) *BinaryIndexedTree {
c := make([]int, n+1)
return &BinaryIndexedTree{n, c}
}
func (this *BinaryIndexedTree) lowbit(x int) int {
return x & -x
}
func (this *BinaryIndexedTree) update(x, delta int) {
for x <= this.n {
this.c[x] += delta
x += this.lowbit(x)
}
}
func (this *BinaryIndexedTree) query(x int) int {
s := 0
for x > 0 {
s += this.c[x]
x -= this.lowbit(x)
}
return s
}
func reversePairs(nums []int) int {
s := make(map[int]bool)
for _, num := range nums {
s[num] = true
s[num*2] = true
}
var alls []int
for num := range s {
alls = append(alls, num)
}
sort.Ints(alls)
m := make(map[int]int)
for i, num := range alls {
m[num] = i + 1
}
tree := newBinaryIndexedTree(len(m))
ans := 0
for i := len(nums) - 1; i >= 0; i-- {
ans += tree.query(m[nums[i]] - 1)
tree.update(m[nums[i]*2], 1)
}
return ans
}