Huahua’s Tech Road

花花酱 LeetCode 99. Recover Binary Search Tree

By zxi on September 29, 2019

Two elements of a binary search tree (BST) are swapped by mistake.

Recover the tree without changing its structure.

Example 1:

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

   1
  /
 3
  \
   2

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

   3
  /
 1
  \
   2

Example 2:

Input: [3,1,4,null,null,2]

  3
 / \
1   4
   /
  2

Output: [2,1,4,null,null,3]

  2
 / \
1   4
   /
  3

Follow up:

A solution using O(n) space is pretty straight forward.
Could you devise a constant space solution?

Solution: Inorder traversal

Using inorder traversal to find two nodes that have val < prev.val

Time complexity: O(n)
Space complexity: O(h)

C++

// Author: Huahua

class Solution {

public:

void recoverTree(TreeNode *root) {

inorder(root);

swap(first->val, second->val);

}

void inorder(TreeNode* root) {

if (!root) return;

inorder(root->left);

if (prev && prev->val > root->val) {

if (!first) first = prev;

second = root;

}

prev = root;

inorder(root->right);

}

private:

TreeNode* first;

TreeNode* second;

TreeNode* prev;

};

花花酱 LeetCode 96. Unique Binary Search Trees

By zxi on September 29, 2019

Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?

Example:

Input: 3
Output: 5
Explanation:
Given n = 3, there are a total of 5 unique BST's:

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

Solution: DP

dp[i] = sum(dp[j] * dp[i – j – 1]) (0 <= j < i )

root: 1 node
left child: j nodes
right child i – j – 1 nodes

try all possible partitions

ans = dp[n]

Time complexity: O(n^2)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

int numTrees(int n) {

vector<int> dp(n + 1);

dp[0] = 1;

for (int i = 1; i <= n; i++)

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

dp[i] += dp[j] * dp[i - j - 1];

return dp[n];

}

};

花花酱 LeetCode 528. Random Pick with Weight

By zxi on September 29, 2019

Given an array w of positive integers, where w[i] describes the weight of index i, write a function pickIndex which randomly picks an index in proportion to its weight.

Note:

1 <= w.length <= 10000
1 <= w[i] <= 10^5
pickIndex will be called at most 10000 times.

Example 1:

Input: 
["Solution","pickIndex"]
[[[1]],[]]
Output: [null,0]

Example 2:

Input: 
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output: [null,0,1,1,1,0]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution‘s constructor has one argument, the array w. pickIndex has no arguments. Arguments are always wrapped with a list, even if there aren’t any.

Solution: Binary Search

Crate a cumulative weight array, random sample a “weight”, do a binary search to see which bucket that weight falls in.
e.g. w = [2, 3, 1, 4], sum = [2, 5, 6, 10]
sample 3 => index = 1
sample 7 => index = 3

Time complexity: Init: O(n) Pick: O(logn)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

Solution(vector<int> w): sums_(std::move(w)) {

partial_sum(begin(sums_), end(sums_), begin(sums_));

}

int pickIndex() {

int s = rand() % sums_.back();

return upper_bound(begin(sums_), end(sums_), s) - begin(sums_);

}

private:

vector<int> sums_;

};

花花酱 LeetCode 60. Permutation Sequence

By zxi on September 29, 2019

The set [1,2,3,...,n] contains a total of n! unique permutations.

By listing and labeling all of the permutations in order, we get the following sequence for n = 3:

"123"
"132"
"213"
"231"
"312"
"321"

Given n and k, return the k^th permutation sequence.

Note:

Given n will be between 1 and 9 inclusive.
Given k will be between 1 and n! inclusive.

Example 1:

Input: n = 3, k = 3
Output: "213"

Example 2:

Input: n = 4, k = 9
Output: "2314"

Solution: Math

Time complexity: O(n)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

string getPermutation(int n, int k) {

vector<int> num;

vector<int> fact(10, 1);

for (int i = 1; i <= 9; i++) {

num.push_back(i);

fact[i] = fact[i - 1] * i;

}

string s;

k--;

while (n--) {

int d = k / fact[n];

k %= fact[n];

s += ('0' + num[d]);

for (int i = d + 1; i <= 9; i++)

num[i - 1] = num[i];

}

return s;

}

};

花花酱 LeetCode 59. Spiral Matrix II

By zxi on September 29, 2019

Given a positive integer n, generate a square matrix filled with elements from 1 to n² in spiral order.

Example:

Input: 3
Output:
[
 [ 1, 2, 3 ],
 [ 8, 9, 4 ],
 [ 7, 6, 5 ]
]

Solution: Simulation

Time complexity: O(n^2)
Space complexity: O(n^2)

C++

// Author: Huahua

class Solution {

public:

vector<vector<int> > generateMatrix(int n) {

vector<vector<int>> ans(n, vector<int>(n));

int dir = 2, x = 0, y = 0;

int max_x = n - 1, max_y = n - 1;

int min_x = 0, min_y = 1;

int i = 0;

while (++i <= n*n) {

ans[y][x] = i;

switch (dir) {

// up

case 1: if (--y == min_y) { dir = 2; ++min_y; } break;

// right

case 2: if (++x == max_x) { dir = 3; --max_x; } break;

// down

case 3: if (++y == max_y) { dir = 4; --max_y; } break;

// left

case 4: if (--x == min_x) { dir = 1; ++min_x; } break;

}

return ans;

}

};

Huahua's Tech Road

花花酱 LeetCode 99. Recover Binary Search Tree

Solution: Inorder traversal

C++

花花酱 LeetCode 96. Unique Binary Search Trees

Solution: DP

C++

花花酱 LeetCode 528. Random Pick with Weight

Solution: Binary Search

C++

花花酱 LeetCode 60. Permutation Sequence

Solution: Math

C++

花花酱 LeetCode 59. Spiral Matrix II

Solution: Simulation

C++