[Helena] Week 9 solutions

clone-graph/yolophg.js

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+// Time Complexity: O(N + E) N = Node + E = Edge
+// Space Complexity: O(N + E)
+
+var cloneGraph = function (node) {
+  // to keep track of all the nodes that have already been copied
+  const map = new Map();
+
+  // helper to perform the deep copy
+  const dfs = (currentNode) => {
+    if (!currentNode) return null;
+
+    // if the node has already been copied, return the copied one
+    if (map.has(currentNode)) return map.get(currentNode);
+
+    // create a new node with the current node's value
+    const newNode = new Node(currentNode.val);
+
+    // store this new node in the map
+    map.set(currentNode, newNode);
+
+    // iterate through each neighbor of the current node
+    for (const neighbor of currentNode.neighbors) {
+      // clone the neighbors and add them to the new node's neighbors
+      newNode.neighbors.push(dfs(neighbor));
+    }
+
+    // return the newly created node
+    return newNode;
+  };
+
+  // start the deep copy from the given node
+  return dfs(node);
+};

combination-sum/yolophg.js

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+// Time Complexity: O(n * target * k)
+// Space Complexity: O(target)
+
+var combinationSum = function (candidates, target) {
+  // initialize dp array to store combinations
+  const dp = Array(target + 1)
+    .fill(null)
+    .map(() => []);
+
+  // sort candidates to ensure uniqueness and optimize processing
+  candidates.sort((a, b) => a - b);
+
+  // one way to make sum 0 (by choosing no elements)
+  dp[0] = [[]];
+
+  // iterate through each candidate
+  for (let num of candidates) {
+    // update dp array for current candidate
+    for (let i = num; i <= target; i++) {
+      for (let combination of dp[i - num]) {
+        dp[i].push([...combination, num]);
+      }
+    }
+  }
+
+  return dp[target];
+};

construct-binary-tree-from-preorder-and-inorder-traversal/yolophg.js

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+// Time Complexity: O(n)
+// Space Complexity: O(n)
+
+var buildTree = function (preorder, inorder) {
+  // build a map for quick lookup of index positions in inorder array
+  // map to store the value -> index relationships
+  let map = new Map();
+  inorder.forEach((value, index) => map.set(value, index));
+
+  // recursive function to construct the binary tree
+  function buildTreeHelper(preStart, preEnd, inStart, inEnd) {
+    // if there are no elements to consider
+    if (preStart > preEnd || inStart > inEnd) return null;
+
+    // the first element in preorder is the root of the current tree
+    let rootValue = preorder[preStart];
+    // create a new root node
+    let root = { val: rootValue, left: null, right: null };
+
+    // find the root in the inorder array to split the tree
+    let inRootIndex = map.get(rootValue);
+    // number of nodes in the left subtree
+    let numsLeft = inRootIndex - inStart;
+
+    // recursively build the left subtree
+    root.left = buildTreeHelper(
+      preStart + 1,
+      preStart + numsLeft,
+      inStart,
+      inRootIndex - 1
+    );
+
+    // recursively build the right subtree
+    root.right = buildTreeHelper(
+      preStart + numsLeft + 1,
+      preEnd,
+      inRootIndex + 1,
+      inEnd
+    );
+
+    return root;
+  }
+
+  // initiate the recursive construction
+  return buildTreeHelper(0, preorder.length - 1, 0, inorder.length - 1);
+};

course-schedule/yolophg.js

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+// Time Complexity: O(numCourses * E) E = Edge
+// Space Complexity: O(numCourses * E)
+
+// initialize an array to keep track of the in-degrees for each course
+let inDegree = new Array(numCourses).fill(0);
+// initialize an adjacency list to represent the graph of courses
+let adjList = new Array(numCourses).fill(0).map(() => []);
+
+// fill the in-degree array and adjacency list based on the prerequisites
+for (let [course, prereq] of prerequisites) {
+  // increment the in-degree of the course
+  inDegree[course]++;
+  // add the course to the adjacency list of the prerequisite
+  adjList[prereq].push(course);
+}
+
+// initialize a queue to keep track of courses with no prerequisites (in-degree of 0)
+let queue = [];
+for (let i = 0; i < numCourses; i++) {
+  if (inDegree[i] === 0) {
+    queue.push(i);
+  }
+}
+
+// initialize a counter to keep track of the number of courses that have been processed
+let count = 0;
+
+// process the courses with no prerequisites
+while (queue.length > 0) {
+  // get a course from the queue
+  let current = queue.shift();
+  // increment the counter as this course can be taken
+  count++;
+
+  // iterate through the adjacency list of the current course
+  for (let neighbor of adjList[current]) {
+    // decrement the in-degree of the neighboring course
+    inDegree[neighbor]--;
+    // if in-degree becomes 0, add it to the queue
+    if (inDegree[neighbor] === 0) {
+      queue.push(neighbor);
+    }
+  }
+}
+
+// if the count of processed courses equals the total number of courses, return true
+return count === numCourses;

design-add-and-search-words-data-structure/yoloophg.js

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+// AddWord Method : Time Complexity: O(L)/Space Complexity: O(L) L = the length of the word being added
+// Search Method : Time Complexity: O(M)/Space Complexity: O(1) M = the length of the word being searched
+// SearchInNode Method : Time Complexity: O(M)/Space Complexity: O(1)
+
+var WordDictionary = function () {
+  this.root = {};
+};
+
+WordDictionary.prototype.addWord = function (word) {
+  // start from the root node
+  let node = this.root;
+  for (let char of word) {
+    if (!node[char]) {
+      // if the character does not exist, create a new node
+      node[char] = {};
+    }
+    // move to the next node
+    node = node[char];
+  }
+  // mark the end of the word
+  node.isEndOfWord = true;
+};
+
+WordDictionary.prototype.search = function (word) {
+  // start searching from the root
+  return this.searchInNode(word, 0, this.root);
+};
+
+WordDictionary.prototype.searchInNode = function (word, index, node) {
+  if (index === word.length) {
+    // if all characters are checked
+    return node.isEndOfWord === true;
+  }
+
+  const char = word[index];
+  if (char === ".") {
+    //iIf the character is '.', check all possible nodes at this part
+    for (let key in node) {
+      if (
+        key !== "isEndOfWord" &&
+        this.searchInNode(word, index + 1, node[key])
+      ) {
+        // if any path matches, return true
+        return true;
+      }
+    }
+    // no path matched
+    return false;
+  } else if (node[char]) {
+    // if the character exists in the trie
+    return this.searchInNode(word, index + 1, node[char]);
+  } else {
+    // character path does not exist
+    return false;
+  }
+};

implement-trie-prefix-tree/yolophg.js

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+// Insert Method : Time Complexity: O(m)/Space Complexity: O(m)
+// Search Method : Time Complexity: O(m)/Space Complexity: O(1)
+// Starts With Method : Time Complexity: O(p)/Space Complexity: O(1)
+
+var Trie = function () {
+  this.trie = {};
+};
+
+// insert a word into the Trie
+Trie.prototype.insert = function (word) {
+  let node = this.trie;
+  for (let char of word) {
+    if (!node[char]) {
+      // create a new node if it doesn't exist
+      node[char] = {};
+    }
+    // move to the next node
+    node = node[char];
+  }
+  // mark the end of the word
+  node.isEnd = true;
+};
+
+// search for a word in the Trie
+Trie.prototype.search = function (word) {
+  let node = this.trie;
+  for (let char of word) {
+    if (!node[char]) {
+      // character not found
+      return false;
+    }
+    // move to the next node
+    node = node[char];
+  }
+  // Ccheck if it's the end of a valid word
+  return node.isEnd === true;
+};
+
+// check if there's any word in the Trie that starts with the given prefix
+Trie.prototype.startsWith = function (prefix) {
+  let node = this.trie;
+  for (let char of prefix) {
+    if (!node[char]) {
+      // prefix not found
+      return false;
+    }
+    // move to the next node
+    node = node[char];
+  }
+  // prefix found
+  return true;
+};

kth-smallest-element-in-a-bst/yolophg.js

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+// Time Complexity: O(n)
+// Space Complexity: O(n)
+
+var kthSmallest = function (root, k) {
+  let stack = [];
+  let current = root;
+  let count = 0;
+
+  while (stack.length > 0 || current !== null) {
+    // go to the leftmost node
+    while (current !== null) {
+      stack.push(current);
+      current = current.left;
+    }
+
+    // pop the node from the stack
+    current = stack.pop();
+    count++;
+
+    // if reached the kth node
+    if (count === k) {
+      return current.val;
+    }
+
+    // go to the right node
+    current = current.right;
+  }
+
+  // if k is out of the range of the number of in the tree
+  return null;
+};

number-of-islands/yolophg.js

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+// Time Complexity: O(m * n) m = rows n = cols
+// Space Complexity: O(m * n)
+
+var numIslands = function (grid) {
+  const m = grid.length;
+  const n = grid[0].length;
+  let numIslands = 0;
+
+  // directions arrays for moving up, down, left, and right
+  const directions = [
+    [-1, 0],
+    [1, 0],
+    [0, -1],
+    [0, 1],
+  ];
+
+  // BFS function
+  function bfs(row, col) {
+    const queue = [[row, col]];
+    // mark as visited
+    grid[row][col] = "0";
+
+    while (queue.length > 0) {
+      const [r, c] = queue.shift();
+
+      for (const [dr, dc] of directions) {
+        const nr = r + dr;
+        const nc = c + dc;
+
+        if (nr >= 0 && nr < m && nc >= 0 && nc < n && grid[nr][nc] === "1") {
+          // mark as visited
+          grid[nr][nc] = "0";
+          queue.push([nr, nc]);
+        }
+      }
+    }
+  }
+
+  // iterate through each cell in the grid
+  for (let i = 0; i < m; i++) {
+    for (let j = 0; j < n; j++) {
+      if (grid[i][j] === "1") {
+        numIslands++;
+        // start BFS to mark all connected land cells
+        bfs(i, j);
+      }
+    }
+  }
+
+  return numIslands;
+};