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/**

* You are given an integer array nums and you have to return a new counts array.

* The counts array has the property where counts[i] is the number of smaller

* elements to the right of nums[i].

*

* Example:

*

* Given nums = [5, 2, 6, 1]

*

* To the right of 5 there are 2 smaller elements (2 and 1).

* To the right of 2 there is only 1 smaller element (1).

* To the right of 6 there is 1 smaller element (1).

* To the right of 1 there is 0 smaller element.

*

* Return the array [2, 1, 1, 0].

*

*/

public class CountOfSmallerNumbersAfterSelf315 {

// brutal force method, Time Limit Exceeded

public List<Integer> countSmaller(int[] nums) {

List<Integer> res = new ArrayList<>(nums.length);

for (int i=0; i<nums.length; i++) {

int now = nums[i];

int count = 0;

for (int j=i+1; j<nums.length; j++) {

if (nums[j] < now) {

count++;

}

}

res.set(i, count);

}

return res;

}

// another method, Time Limit Exceeded

public List<Integer> countSmaller2(int[] nums) {

if (nums.length == 0) {

return new ArrayList<Integer>();

}

LinkedList<Integer> res = new LinkedList<>();

res.add(0);

ListNode head = new ListNode(nums[nums.length-1]);

for (int i=nums.length-2; i>=0; i--) {

ListNode newNode = new ListNode(nums[i]);

int count = 0;

ListNode temp = head;

if (nums[i] <= temp.val) {

newNode.next = temp;

head = newNode;

res.addFirst(count);

continue;

}

while (temp.next != null && nums[i] > temp.next.val) {

temp = temp.next;

count++;

}

if (temp.next == null) {

temp.next = newNode;

} else {

newNode.next = temp.next;

temp.next = newNode;

}

count++;

res.addFirst(count);

}

return res;

}

public List<Integer> countSmaller3(int[] nums) {

Integer[] count = new Integer[nums.length];

int[][] arr = new int[nums.length][2];

for (int i=0; i<nums.length; i++) {

arr[i][0] = i;

arr[i][1] = nums[i];

count[i] = 0;

}

mergeSort(arr, count, 0, nums.length-1);

return Arrays.asList(count);

}

private void mergeSort(int[][] arr, Integer[] count, int l, int r) {

if (l >= r) return;

int m = (l+r)/2;

mergeSort(arr, count, l, m);

mergeSort(arr, count, m+1, r);

merge(arr, count, l, m, r);

}

private void merge(int[][] arr, Integer[] count, int l, int m, int r) {

int len1 = m - l + 1;

int len2 = r - m;

int[][] L = new int [len1][2];

int[][] R = new int [len2][2];

for (int i=0; i < len1; i++)

L[i] = arr[l + i];

for (int j=0; j < len2; j++)

R[j] = arr[m + 1 + j];

int i = 0;

int j = 0;

int k = l;

while (i < len1 && j < len2) {

if (L[i][1] <= R[j][1]) {

arr[k] = L[i];

count[L[i][0]] += j;

i++;

} else {

arr[k] = R[j];

j++;

}

k++;

}

while (i < len1) {

arr[k] = L[i];

i++;

k++;

}

while (j < len2) {

arr[k] = R[j];

j++;

k++;

}

}

/**

* https://discuss.leetcode.com/topic/31405/9ms-short-java-bst-solution-get-answer-when-building-bst

*/

public List<Integer> countSmaller4(int[] nums) {

Integer[] ans = new Integer[nums.length];

Node root = null;

for (int i = nums.length - 1; i >= 0; i--) {

root = insert(nums[i], root, ans, i, 0);

}

return Arrays.asList(ans);

}

private Node insert(int num, Node node, Integer[] ans, int i, int preSum) {

if (node == null) {

node = new Node(num, 0);

ans[i] = preSum;

} else if (node.val == num) {

node.dup++;

ans[i] = preSum + node.sum;

} else if (node.val > num) {

node.sum++;

node.left = insert(num, node.left, ans, i, preSum);

} else {

node.right = insert(num, node.right, ans, i, preSum + node.dup + node.sum);

}

return node;

}

class Node {

Node left, right;

int val, sum, dup = 1;

public Node(int v, int s) {

val = v;

sum = s;

}

}

/**

* https://discuss.leetcode.com/topic/31173/my-simple-ac-java-binary-search-code

*/

public List<Integer> countSmaller5(int[] nums) {

Integer[] ans = new Integer[nums.length];

List<Integer> sorted = new ArrayList<Integer>();

for (int i = nums.length - 1; i >= 0; i--) {

int index = findIndex(sorted, nums[i]);

ans[i] = index;

sorted.add(index, nums[i]);

}

return Arrays.asList(ans);

}

private int findIndex(List<Integer> sorted, int target) {

if (sorted.size() == 0) return 0;

int start = 0;

int end = sorted.size() - 1;

if (sorted.get(end) < target) return end + 1;

if (sorted.get(start) >= target) return 0;

while (start + 1 < end) {

int mid = start + (end - start) / 2;

if (sorted.get(mid) < target) {

start = mid + 1;

} else {

end = mid;

}

}

if (sorted.get(start) >= target) return start;

return end;

}

public List<Integer> countSmaller6(int[] nums) {

LinkedList<Integer> res = new LinkedList<>();

if (nums == null || nums.length == 0) return res;

int N = nums.length;

int min = Integer.MAX_VALUE;

int max = Integer.MIN_VALUE;

for (int n: nums) {

min = Math.min(min, n);

}

int[] ranks = new int[N];

for (int i = 0; i < N; i++) {

ranks[i] = nums[i] - min + 1;

max = Math.max(ranks[i], max);

}

BinaryIndexedTree bit = new BinaryIndexedTree(max);

for (int i=ranks.length-1; i>=0 ;i--) {

res.addFirst(bit.query(ranks[i] - 1));

bit.update(ranks[i], 1);

}

return res;

}

class BinaryIndexedTree {

int[] tree;

int N;

BinaryIndexedTree(int N) {

this.N = N;

this.tree = new int[N+1];

}

void update(int i, int delta) {

int k = i + 1;

while (k <= this.N) {

this.tree[k] += delta;

k += lowBit(k);

}

}

int query(int i) {

int k = i + 1;

int res = 0;

while (k > 0) {

res += this.tree[k];

k -= lowBit(k);

}

return res;

}

private int lowBit(int x) {

return x & (-x);

}

}

public List<Integer> countSmaller7(int[] nums) {

LinkedList<Integer> res = new LinkedList<>();

if (nums == null || nums.length == 0) return res;

int N = nums.length;

Node root = new Node(nums[N-1]);

res.add(0);

for (int i=N-2; i>=0; i--) {

res.addFirst(insert(root, nums[i]));

}

return res;

}

private int insert(Node root, int val) {

if (root.val == val) {

root.count++;

return root.leftCount;

} else if (root.val > val) {

root.leftCount++;

if (root.left == null) {

root.left = new Node(val);

return 0;

}

return insert(root.left, val);

} else {

if (root.right == null) {

root.right = new Node(val);

return root.count + root.leftCount;

}

return root.count + root.leftCount + insert(root.right, val);

}

}

class Node {

Node left;

Node right;

int val;

int count = 1;

int leftCount = 0;

Node(int v) {

this.val = v;

}

}

}