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wkw ・2 min read

# About

This is a series of Daily Coding Challenge. Each day I show a few solutions written in C++. The questions are from coding practice/contest sites such as HackerRank, LeetCode, Codeforces, Atcoder and etc.

``````/*
Unique Binary Search Trees

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
*/

class Solution {
public:
int numTrees(int n) {
// dp approach to find Catalan Number
vector<int> catalan(n+1);
catalan[0]=catalan[1]=1;
for(int i=2;i<=n;i++){
for(int j=0;j<i;j++){
catalan[i]+=catalan[j]*catalan[i-j-1];
}
}
return catalan[n];
}
};
``````

``````/*
Find the Duplicate Number

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Example 1:

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

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

You must not modify the array (assume the array is read only).
You must use only constant, O(1) extra space.
Your runtime complexity should be less than O(n2).
There is only one duplicate number in the array, but it could be repeated more than once.
*/

class Solution {
public:
int findDuplicate(vector<int>& nums) {
// Floyd's Tortoise and Hare (Cycle Detection)
int fast,slow;
fast=slow=nums[0];
while(1){
// phase 1
// construct a sequence like x, nums[x], nums[nums[x]], nums[nums[nums[x]]], ...
fast=nums[fast];
slow=nums[nums[slow]];
if(fast==slow) break;
}
slow=nums[0];
while(fast!=slow){
// phase 2
// slow starts from entrance point
// fast starts from intersection point
fast=nums[fast];
slow=nums[slow];
}
return slow;
}
};
``````

The source code is available in corresponding repo below. Star and watch for timely updates!