Category Archives: Algorithms

Check if string has all unique characters

Task

Implement an algorithm to determine if a string (of characters from ‘a’ to ‘z’) has all unique characters or not.

Example 1:

var s = "abcde";
returns true;

Example 2:

var s = "abcade";
returns false;

Solution

Solution 1: The brute force solution will be to iterate through all characters and compare with all other characters.

function areCharactersUnique(s) {
    for(let i=0; i < s.length; i++) {
        for(let j=0; j < s.length; j++) {
            if(i == j)
                continue;
            if(s[i] == s[j]) {
                return false;
            }
        }

    }
    return true;
}

var s = "abcade";

console.log(areCharactersUnique(s));

Solution 2: Using an array (or hashMap table) with key equal to the ASCII character code.

function areCharactersUnique(s) {
    var checker = new Array(26);
    for(let i=0; i < s.length; i++) {
        var pos = s[i].charCodeAt(0) - 'a'.charCodeAt(0);
        if(typeof checker[pos] != 'undefined') {
            return false;
        }
        checker[pos] = 1;
    }
    return true;
}

var s = "abcde";

console.log(areCharactersUnique(s));

Let’s make it more challenging and prohibit the use of additional data structures like count array, hash, etc.

Solution 3: Using bitwise operations to store into 32 bit if one of all 26 characters is presented or not.
We have 26 letters (from a to z). Let’s imagine that we could have 26 empty slots that we could set up to true if the character exists, pretty much as if we have a hashTable.
for simplicity I will use only 6 slots (from a to G) instead of all 26 that represent the whole alphabet.
In addition we have to mention that the slots are actually 32 (this is usually the length of an integer in JavaScript but we need only 26)

6 5 4 3 2 1 0
G F E D C B A
false false false false false false false

Given the string: ‘ABCG’ for example we will end up with this matrix.

6 5 4 3 2 1 0
G F E D C B A
true false false false true true true

But this could be stored into 32bit value using bitwise operations. The binary representation of the matrix above will be:  1000111

The solution:

function areCharactersUnique(s) {
    var checker = 0;

    for(let i=0; i < s.length; i++) {
        // Charcode of a is 97 but we want to start with 0
        var val = s[i].charCodeAt(0) - 'a'.charCodeAt(0);
        // & - Sets each bit to 1 if both bits are 1
        // examples: 
        // 1 & 10 = 0
        // 1 & 101 = 1
        if(checker & ( 1 << val)) {
            return false;
        }

        // | - Sets each bit to 1 if one of two bits is 1
        // examples:
        // 1 | 10 = 11
        // 1 | 1 = 1
        checker = checker | ( 1 << val);
    }
    return true;
}

what we just did:
– we started with creating a loop to go through all characters
– we set up an empty value checker to store if the character is used or not (this is the binary representation of the matrix above)
– (line 6) grabbing the value for each letter in the string but removing ‘a’ = 97 so ‘a’ character will be equal to 0 and z = 26
– (line 19) we are setting the position of the character into the checker to true using bitwise shift left (1 << a) and preserving other already set positions using bitwise | ‘or’
– (line 11) using the same technique but with bitwise & ‘and’ we check if the character position is set to true or not.

Here is a step by  step example for ‘ABCG’ character:
– initially checker = 0 // or the binary representation is '00000000...0'
– we are going to insert a using Zero fill left shift. This is basically going to add ‘1’ followed by as many ‘0’ to the right of the checker as the value of ‘a’ is. In this case 0, so schecker = 1 // binary '00000000...1

– next step inserting ‘b’ follows the same procedure: b = 1, (1 << b) = 2 '000000...10' but we also want to preserve whatever was already inserted so we use bitwise ‘|’ ‘or’ which sets each bit to 1 if one of two bits is 1.
so
checker = checker | (1 << b) = 2
or the binary representation will be:
checker = '00000000...1' | (1 << b) = '000000000...11'

and the same for the rest of the characters

var a = 0;
var b = 1;
var c = 2;
var d = 3;
var e = 4;
var f = 5;
var g = 6;

var s = "abcg";
var checker = 0; 

checker = checker | (1 << a);   // 1
checker = checker | (1 << b);   // 11
checker = checker | (1 << c);   // 111
checker = checker | (1 << g);   // 1000111

Let’s modify the problem, and ask to return the index of the first unique character in the string.
For example for string ‘abcac’ the return will be the index of b – ‘1’
This problem is asked in Leetcode

/**
 * @param {string} s
 * @return {number}
 */
var firstUniqChar = function(s) {
    
    let lastSingle = null;
    let hashMap = {};
    for(var i = 0;i < s.length; i ++) {
        var val = s[i];
        hashMap[val] =  hashMap[val] == undefined ? i: 'not-unique';        
    }

    for(let i=0; i < s.length; i++) {
        var key = s[i];
        if(hashMap[key] != 'not-unique') {
            return hashMap[key];
        }
    }
    return -1;

}

 

LRU Cache

Task

Design and implement a data structure for Least Recently Used (LRU) cache. It should support the following operations: get and put.

get(key) – Get the value (will always be positive) of the key if the key exists in the cache, otherwise return -1.
put(key, value) – Set or insert the value if the key is not already present. When the cache reached its capacity, it should invalidate the least recently used item before inserting a new item.

The cache is initialized with a positive capacity.

Follow up:
Could you do both operations in O(1) time complexity?

Example:

LRUCache cache = new LRUCache( 2 /* capacity */ );

cache.put(1, 1);
cache.put(2, 2);
cache.get(1);       // returns 1
cache.put(3, 3);    // evicts key 2
cache.get(2);       // returns -1 (not found)
cache.put(4, 4);    // evicts key 1
cache.get(1);       // returns -1 (not found)
cache.get(3);       // returns 3
cache.get(4);       // returns 4

This problem was taken from Leetcode

Solution

The brute force solution will be to use array, to push every new element at the top, and on ‘get’ to pop out the element and to put it at the top of the array.

A better solution will be to use hashmap where the element retrieval will be O(1) (constant) but the hashmap is not keeping track of the order of the elements. To solve this problem we are going to link elements in the hashnmap table with double linked list, where each element will point to its previous and next sibling.
On every ‘get’ operation we are going to re-link the element and it’s siblings.

When the cache reaches the capacity we are going to remove the least used node from the bottom.

put(1,1) put(2,2) get(1) put(3,3) get(2) put(4,4) get(1) get(3) get(4)
return 1 -1 -1 3 4
result 1 2,1 1,2 3,1 => (2) 3,1 4,3 => (1) 4,3 3,4 4,3

 

class LRUCache {

  constructor(capacity) {
    
        this.head = null;
        this.tail = null;
        this.capacity = capacity;
        this.count = 0;
    this.hashMap  = new Map();    
  }

 
  get(key) {
    var node = this.hashMap.get(key);
    if(node) {
      if(node == this.head) {
        // node is already at the head, just return the value
        return node.val;
      }			
      if(this.tail == node && this.tail.prev) {
        // if the node is at the tail,
        // set tail to the previous node if it exists.
        this.tail = this.tail.prev;
        this.tail.next = null;
      }
      // link neibouring nodes together
      if(node.prev)
        node.prev.next = node.next;
      if(node.next)
        node.next.prev = node.prev;			
      // add the new head node
      node.prev = null;
      node.next = this.head;
      this.head.prev = node;
      this.head = node;

      return node.val;
    }
    return -1;
  }

  put(key, val) {
    this.count ++;
    var newNode = { key, val, prev: null, next: null };

    if(this.head == null) {
      // this.hashMap is empty creating new node
      this.head =  newNode;
      this.tail = newNode;
    }
    else {
      var oldNode = this.hashMap.get(key);
      if(oldNode) {
        // if node with the same key exists, 
        // clear prev and next pointers before deleting the node.
        if(oldNode.next) {
          if(oldNode.prev)
            oldNode.next.prev = oldNode.prev;
          else
            this.head = oldNode.next;
        }
        if(oldNode.prev) {					
          oldNode.prev.next = oldNode.next;
          if(oldNode == this.tail)
            this.tail = oldNode.prev;
        }
        // removing the node
        this.hashMap.delete(key);
        this.count --;				
      }

      // adding the new node and set up the pointers to it's neibouring nodes			
      var currentHead = this.head;
      currentHead.prev = newNode;				
      newNode.next = currentHead;
      this.head = newNode;

      if(this.tail == null)
        this.tail = currentHead;

      if(this.count == this.capacity + 1) {
        // remove last nove if over capacity
        var lastNode = this.tail;
        this.tail = lastNode.prev;
        if(!this.tail) {
          //debugger;
        }
        this.tail.next = null;
        this.hashMap.delete(lastNode.key);
        this.count --;
      }

    }
    this.hashMap.set(key, newNode);
    return null;
  }
}

 

Trapping Rain Water

Task

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.


image was borrowed from leetcode

The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image!

Example:

Input:

 [0,1,0,2,1,0,1,3,2,1,2,1]

Output:

 6

This problem was taken from Leetcode

Solution

 

The brute force approach: for each element we go to the right and find the maximum height of the bar, then we go to the left and do the same.

For any element the maximum amount of the water that could be trapped will be the minimum of left height and right height, minus the height of the bar.

So for the array [0,1,0,2,1,0,1,3,2,1,2,1] we go all the way to the right and calculate the max right value, starting from first element ‘0’ max right will be 0. ‘1’ – max right is ‘1’ and so on.
We repeat the same from last element ‘1’ to the first one.

Then the trapped water for the first column will be:  min(maxRight, maxLeft) – theArrayElement[n]

the array 0 1 0 2 1 0 1 3 2 1 2 1
max right 0 1 1 2 2 2 2 3 3 3 3 3
max left 3 3 3 3 3 3 3 3 2 2 2 1
collected
water
0 0 1 0 1 2 1 0 0 1 0 0

 

The complexity will be O(n2)

/**
 * @param {number[]} height
 * @return {number}
 */
var trap = function(height) {
    if(height.length < 2)
        return 0;

    let findMaxLeft = function(idx, height) {
        let max = 0;
        for(let i =idx;i >= 0; i --) {
            max = Math.max(max, height[i]);
        }
        return max;
    }

    let findMaxRight = function(idx, height) {
        let max = 0;
        for(let i = idx;i < height.length; i ++) {
            max = Math.max(max, height[i]);
        }
        return max;
    }  

    let collectedWater = 0;
    for(let i = 0;i < height.length; i ++) {

        const maxLeft = findMaxLeft(i, height);
        const maxRight = findMaxRight(i, height);

        let min = Math.min(maxLeft, maxRight);
        collectedWater += (min - height[i]);
    }

    return collectedWater;
};

The better solution: find all max left and max right with one loop, then do a second loop for each element in the array, and calculate trapped water.

/**
 * @param {number[]} height
 * @return {number}
 */
var trap = function(height) {
    let maxLeftArray = [], maxRightArray = [];
    let maxLeft = 0, maxRight = 0;
    const ln = height.length;
    let trappedWater = 0;

    for(let i = 0;i < height.length; i ++) {
        maxLeftArray[i] = Math.max(height[i], maxLeft);
        maxLeft = maxLeftArray[i];

        maxRightArray[ln - i - 1] = Math.max(height[ln - i - 1], maxRight);
        maxRight = maxRightArray[ln - i - 1];
    }

    for(let i = 0;i < height.length; i ++) {
        trappedWater += Math.min(maxLeftArray[i], maxRightArray[i]) - height[i];
    }
    return trappedWater;

};
what we just did:

– With one loop find the max left and right bar on each side.
– for any element the maximum amount of the water that could be trapped will be the minimum of left height and right height, minus the height of the bar.

Majority element in array

Task

Given an array of size n, find the majority element. The majority element is the element that appears more than ⌊ n/2 ⌋ times.

You may assume that the array is non-empty and the majority element always exist in the array.

Example 1:

Input:

 [3,2,3]

Output:

 3

Example 2:

Input:

 [2,2,1,1,1,2,2]

Output:

 2

This problem was taken from Leetcode

Solution

The solution:

Create an object (or associative array, depends of the language), iterate through all elements in the array adding them to the newly created object using the element value as a key. If element exists increase the value +1.
Keep track of mostly repeated element and return it at the end.

var arr = [3, 3, 4, 2, 4, 2, 4, 4];


/**
 * @param {number[]} nums
 * @return {number}
 */
var majorityElement = function(nums) {
  var elements = {};
  var majorityElement = nums[0];
  var majorityElementCount = 1;
  for(var i in nums) {
  	var element = nums[i];
  	elements[element] = typeof elements[element] == 'undefined' ? 1 : elements[element] + 1;
  	if(elements[element] > majorityElementCount) {
  		majorityElement = element;
  		majorityElementCount = elements[element];
  	}
  }    
  return majorityElement;
};

console.log(">>", majorityElement(arr));

– Create an object (line 9)
– Iterate through each element in the array feeling up the object with the elements from the array where the element value would be the key of the element (line 14)
– Each time when the element exists, add + 1
– Keep track of mostly repeated element (Lines 16-17)

Could we optimize the code? Slightly. When we add + 1 we could check if the value is already greater than the length of the array / 2 and if se we know that this is the majority element because no other element could have greater value.

...
    if(elements[element] > nums.length / 2) {
        return element;
    }
...

 

Climbing stairs

Task

You are climbing a stair case. It takes n steps to reach to the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.


Example 1:

Input: 2
Output: 2

Explanation:

 There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps


Example 2:

Input: 3
Output: 3

Explanation:

 There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

 

This problem was taken from Leetcode

Solution

The solution:

Let’s look at the possible scenarios:

# of stairsways to climb# of ways to climb
111
21 1
2
2
31 1 1
2 1
1 2
3
41 1 1 1
2 1 1
1 2 1
1 1 2
2 2
5
51 1 1 1 1
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
2 2 1
2 1 2
1 2 2
8
61 1 1 1 1 1
2 1 1 1 1
1 2 1 1 1
1 1 2 1 1
1 1 1 2 1
1 1 1 1 2
2 2 1 1
1 2 2 1
1 1 2 2
2 1 1 2
2 1 2 1
1 2 1 2
2 2 2
13
71 1 1 1 1 1 1
2 1 1 1 1 1
1 2 1 1 1 1
1 1 2 1 1 1
1 1 1 2 1 1
1 1 1 1 2 1
1 1 1 1 1 2
2 2 1 1 1
1 2 2 1 1
1 1 2 2 1
1 1 1 2 2
2 1 2 1 1
2 1 1 2 1
2 1 1 1 2
1 2 1 1 2
1 1 2 1 2
1 2 1 2 1
2 2 2 1
1 2 2 2
2 1 2 2
2 2 1 2
21

If we look at the # of ways to climb, we clearly see that the ways to climb grows in Fibonacci sequence: 1, 2,  3,  5,  8,  13, 21

Then all we need to do is to iterate n times (where n  is the number of stairs) and to find the corresponding Fibonacci number.

Using while loop

  • basically we use temp to store previous Fibonacci number temp = a , initially 1
  • then we calculate the next number a = a + b , initially a = 0 + 1
  • then we set up b = temp which stores the last Fibonacci number in order to be ready for the next iteration. Initially 1.

Looking at the numbers from the first iteration, it is clear that on the second one we will have:
temp = a = 1
a = a + b = 1 + 1 = 2
b = temp = 1

third iteration will produce:
temp = a = 2
a = a + b = 2 + 1 = 3
b = temp = 2
forth iteration:
temp = a = 3
a = a + b = 3 + 2 = 5
b = temp = 3

and so on … a will always return the Fibonacci number for the current n position.

Java Script

/**
 * @param {number} n
 * @return {number}
 */
var climbStairs = function(n) {
    if( n < 4) 
        return n;

    fibonacci = function(n) {

        var a = 1, b = 0, temp, num = 1;

        while(num <= n) {
            temp = a;
            a = a + b;
            b = temp;
            num ++;
        }
        return a;
    }

    return fibonacci(n);
};

Using For loop

This is the easiest to comprehend:

  • we create an array to store the Fibonacci numbers var fn = [1,1] with the first two numbers pre-set so the for loop could generate the next one.
  • created for loop that picks the fn[i - 1] and fn[i - 2] numbers and generate the next one.
  • pushed newly calculated Fibonacci number into an array so we could use to generate next one.
  • keep looping till we reached i < n + 1 which is the  answer.

Java Script

/**
 * @param {number} n
 * @return {number}
 */
var climbStairs = function(n) {
    if( n  < 3)
    return n;
    
    var fn = [1,1];
    for(var i = 2; i < n + 1; i ++) {
        var nextNumber = fn[i - 1] + fn[i - 2]; 
        fn.push(nextNumber);
    }

    return fn[fn.length - 1];
};

 

Third solution: Using recursive function.

Java Script

/**
 * @param {number} n
 * @return {number}
 */
var climbStairs = function(n) {
    if( n < 4) 
        return n;

    fibonacci = function(n) {
        if(n < 2) {
            return n;
        }
        var result = fibonacci(n - 1) + fibonacci(n - 2);        
        return result;
    }

    return fibonacci(n + 1);
};

The idea here is to call fibonacci(n) function to generate the next Fibonacci number.
For n < 2 the function will simply return n 0,1,2.
For n = 3 the function will call itself recursively asking for previous two Fibonacci numbers (2 and 1) and will calculate the next number which is the sum of the previous two, and so on.

Optimize the recursive function to use Memoization.

Memoization is simple technique where we are storing the value of already computed parameter into a HashMap function and quickly retrieve it when we need it.

In our current example since the keys are just a numbers we could store the Fibonacci numbers in a regular array (line 9). Then we simply check if the value already is set up into memo array and return it or call fibonacci function once again.
Then we set up memo array with the next solved Fibonacci number with index n

Java Script

/**
 * @param {number} n
 * @return {number}
 */
var climbStairs = function(n) {
    if( n < 4) 
        return n;

    var memo = [];
    fibonacci = function(n) {
        if(n < 2) {
            return n;
        }
        var a = memo[n - 1] ? memo[n - 1] : fibonacci(n - 1);
        var b = memo[n - 2] ? memo[n - 2] : fibonacci(n - 2);

        return memo[n] = a + b;
    }

    return fibonacci(n + 1);
};

 

You might also want to check Fibonacci sequence generator.