🚀 Master Dynamic Programming with These JavaScript MCQs! 🧠💻
Question 1:
Which of the following best describes dynamic programming?
a) A method for breaking down a problem into smaller subproblems and solving them recursively.
b) A technique for solving optimization problems by making a sequence of decisions.
c) A way of solving complex problems by dividing them into simpler overlapping subproblems and storing their solutions.
d) A method that always guarantees the most optimal solution for all problem types.
Question 2:
What is an optimal substructure in the context of dynamic programming?
a) A data structure that is used to store optimal solutions.
b) A property where the solution to a problem can be composed of optimal solutions to its subproblems.
c) A way to iterate through subproblems in a bottom-up manner.
d) A technique used to combine solutions to subproblems in a greedy fashion.
Question 3:
In dynamic programming, what does overlapping subproblems refer to?
a) Subproblems that can be solved independently of each other.
b) Subproblems that are repeated multiple times and can benefit from memoization.
c) Subproblems that do not contribute to the final solution.
d) Subproblems that need to be solved using a divide-and-conquer approach.
Question 4:
Which of the following statements about greedy algorithms is true?
a) Greedy algorithms always provide the most optimal solution.
b) Greedy algorithms are less efficient than dynamic programming for all problems.
c) Greedy algorithms make locally optimal choices at each step with the hope of finding a global optimum.
d) Greedy algorithms never overlap in subproblems.
Question 5:
Which of the following is an example of a problem that can be solved using a greedy algorithm?
a) Finding the shortest path in a weighted graph with negative weights.
b) Solving the knapsack problem with fractional items allowed.
c) Computing the edit distance between two strings.
d) Solving the travelling salesman problem optimally.
Question 6:
What is the primary advantage of backtracking when solving problems with restrictive conditions?
a) It guarantees the optimal solution in polynomial time.
b) It allows exploring all possible solutions and backtrack upon reaching an invalid state.
c) It is faster than both dynamic programming and greedy algorithms.
d) It stores the results of subproblems to avoid redundant calculations.
Question 7:
Which of the following problems is most suited for a backtracking approach?
a) Finding the longest common subsequence.
b) Solving a Sudoku puzzle.
c) Calculating the nth Fibonacci number.
d) Finding the minimum spanning tree in a graph.
Question 8:
In dynamic programming, what is memoization?
a) The process of recording the state of the algorithm for debugging purposes.
b) The technique of storing solutions to subproblems to avoid redundant calculations.
c) The method of selecting the most promising subproblem to solve next.
d) The act of combining subproblems in a top-down manner.
Question 9:
Which of the following characteristics is NOT essential for a problem to be solved using dynamic programming?
a) Optimal substructure
b) Overlapping subproblems
c) Greedy choice property
d) Recursive definition of the problem
Question 10:
Which approach would be most appropriate for solving the Hamiltonian Path problem in a graph?
a) Dynamic Programming
b) Greedy Algorithm
c) Backtracking
d) Divide and Conquer
Question 11:
What is the time complexity of the Fibonacci sequence using Dynamic Programming?
A) O(n)
B) O(n^2)
C) O(log n)
D) O(2^n)
Question 12:
Which of the following problems is NOT typically solved using dynamic programming?
A) 0/1 Knapsack Problem
B) Longest Common Subsequence
C) Travelling Salesman Problem
D) Binary Search
Question 13:
In dynamic programming, what is 'memoization'?
A) A technique to store the results of expensive function calls and reuse them when the same inputs occur again
B) The process of finding the most optimal solution
C) A method to split the problem into smaller subproblems
D) A way to combine the solutions of subproblems
Question 14:
What is the main idea behind dynamic programming?
A) To divide the problem into independent, non-overlapping subproblems
B) To divide the problem into overlapping subproblems and solve each subproblem only once
C) To use a greedy approach to solve the problem
D) To use backtracking to solve the problem
Question 15:
Which data structure is commonly used to implement dynamic programming solutions?
A) Stack
B) Queue
C) Array
D) Graph
Question 16:
Consider the problem of finding the nth Fibonacci number. Which of the following JavaScript functions correctly implements a dynamic programming approach using memoization?
a)
function fibonacci(n) {
if (n <= 1) return n;
return fibonacci(n - 1) + fibonacci(n - 2);
}b)
function fibonacci(n) {
const memo = [0, 1];
for (let i = 2; i <= n; i++) {
memo[i] = memo[i - 1] + memo[i - 2];
}
return memo[n];
}c)
function fibonacci(n) {
const memo = {};
function fib(n) {
if (n in memo) return memo[n];
if (n <= 1) return n;
memo[n] = fib(n - 1) + fib(n - 2);
return memo[n];
}
return fib(n);
}d)
function fibonacci(n) {
let a = 0, b = 1, temp;
while (n >= 1) {
temp = a;
a = b;
b = temp + b;
n--;
}
return a;
}Question 17:
Which JavaScript function uses dynamic programming to solve the "longest increasing subsequence" problem?
a)
function lengthOfLIS(nums) {
const dp = new Array(nums.length).fill(1);
for (let i = 1; i < nums.length; i++) {
for (let j = 0; j < i; j++) {
if (nums[i] > nums[j]) {
dp[i] = Math.max(dp[i], dp[j] + 1);
}
}
}
return Math.max(...dp);
}b)
function lengthOfLIS(nums) {
const dp = new Array(nums.length).fill(1);
for (let i = 1; i < nums.length; i++) {
for (let j = 0; j < i; j++) {
if (nums[i] > nums[j]) {
dp[i] = dp[j] + 1;
}
}
}
return Math.max(...dp);
}c)
function lengthOfLIS(nums) {
if (!nums.length) return 0;
const dp = [];
for (let i = 0; i < nums.length; i++) {
dp[i] = 1;
for (let j = 0; j < i; j++) {
if (nums[i] > nums[j] && dp[i] < dp[j] + 1) {
dp[i] = dp[j] + 1;
}
}
}
return Math.max(...dp);
}d)
function lengthOfLIS(nums) {
const memo = new Map();
function lis(index) {
if (memo.has(index)) return memo.get(index);
let maxLength = 1;
for (let i = 0; i < index; i++) {
if (nums[index] > nums[i]) {
maxLength = Math.max(maxLength, lis(i) + 1);
}
}
memo.set(index, maxLength);
return maxLength;
}
let result = 0;
for (let i = 0; i < nums.length; i++) {
result = Math.max(result, lis(i));
}
return result;
}Question 18:
Which JavaScript function implements a greedy algorithm to solve the fractional knapsack problem?
a)
function fractionalKnapsack(weights, values, capacity) {
const n = weights.length;
const items = [];
for (let i = 0; i < n; i++) {
items.push({ weight: weights[i], value: values[i], ratio: values[i] / weights[i] });
}
items.sort((a, b) => b.ratio - a.ratio);
let maxValue = 0;
for (let i = 0; i < n; i++) {
if (capacity >= items[i].weight) {
capacity -= items[i].weight;
maxValue += items[i].value;
} else {
maxValue += items[i].ratio * capacity;
break;
}
}
return maxValue;
}b)
function fractionalKnapsack(weights, values, capacity) {
const n = weights.length;
let maxValue = 0;
weights.sort((a, b) => values[weights.indexOf(b)] / b - values[weights.indexOf(a)] / a);
for (let i = 0; i < n; i++) {
if (capacity >= weights[i]) {
capacity -= weights[i];
maxValue += values[i];
} else {
maxValue += (values[i] / weights[i]) * capacity;
break;
}
}
return maxValue;
}c)
function fractionalKnapsack(weights, values, capacity) {
const items = weights.map((w, i) => ({ weight: w, value: values[i], ratio: values[i] / w }));
items.sort((a, b) => b.ratio - a.ratio);
let maxValue = 0;
for (const item of items) {
if (capacity >= item.weight) {
capacity -= item.weight;
maxValue += item.value;
} else {
maxValue += item.ratio * capacity;
break;
}
}
return maxValue;
}d)
function fractionalKnapsack(weights, values, capacity) {
const n = weights.length;
let maxValue = 0;
for (let i = 0; i < n; i++) {
if (capacity >= weights[i]) {
capacity -= weights[i];
maxValue += values[i];
} else {
maxValue += (values[i] / weights[i]) * capacity;
break;
}
}
return maxValue;
}Question 19:
Which JavaScript function uses backtracking to solve the N-Queens problem?
a)
function solveNQueens(n) {
const board = Array.from({ length: n }, () => Array(n).fill('.'));
const result = [];
function isSafe(row, col) {
for (let i = 0; i < row; i++) {
if (board[i][col] === 'Q') return false;
if (col - (row - i) >= 0 && board[i][col - (row - i)] === 'Q') return false;
if (col + (row - i) < n && board[i][col + (row - i)] === 'Q') return false;
}
return true;
}
function placeQueens(row) {
if (row === n) {
result.push(board.map(row => row.join('')));
return;
}
for (let col = 0; col < n; col++) {
if (isSafe(row, col)) {
board[row][col] = 'Q';
placeQueens(row + 1);
board[row][col] = '.';
}
}
}
placeQueens(0);
return result;
}b)
function solveNQueens(n) {
const result = [];
const board = Array.from({ length: n }, () => Array(n).fill('.'));
function isSafe(board, row, col) {
for (let i = 0; i < row; i++) {
if (board[i][col] === 'Q') return false;
if (col - (row - i) >= 0 && board[i][col - (row - i)] === 'Q') return false;
if (col + (row - i) < n && board[i][col + (row - i)] === 'Q') return false;
}
return true;
}
function solve(board, row) {
if (row === n) {
const solution = board.map(r => r.join(''));
result.push(solution);
return;
}
for (let col = 0; col < n; col++) {
if (isSafe(board, row, col)) {
board[row][col] = 'Q';
solve(board, row + 1);
board[row][col] = '.';
}
}
}
solve(board, 0);
return result;
}c)
function solveNQueens(n) {
const result = [];
const board = Array(n).fill().map(() => Array(n).fill('.'));
function isValid(board, row, col) {
for (let i = 0; i < row; i++) {
if (board[i][col] === 'Q') return false;
if (col - (row - i) >= 0 && board[i][col - (row - i)] === 'Q') return false;
if (col + (row - i) < n && board[i][col + (row - i)] === 'Q') return false;
}
return true;
}
function solve(board, row) {
if (row === n) {
result.push(board.map(r => r.join('')));
return;
}
for (let col = 0; col < n; col++) {
if (isValid(board, row, col)) {
board[row][col] = 'Q';
solve(board, row + 1);
board[row][col] = '.';
}
}
}
solve(board, 0);
return result;
}d)
function solveNQueens(n) {
const result = [];
const board = Array(n).fill().map(() => Array(n).fill('.'));
function isSafe(row, col) {
for (let i = 0; i < row; i++) {
if (board[i][col] === 'Q') return false;
if (col - (row - i) >= 0 && board[i][col - (row - i)] === 'Q') return false;
if (col + (row - i) < n && board[i][col + (row - i)] === 'Q') return false;
}
return true;
}
function placeQueens(row) {
if (row === n) {
result.push(board.map(r => r.join('')));
return;
}
for (let col = 0; col < n; col++) {
if (isSafe(row, col)) {
board[row][col] = 'Q';
placeQueens(row + 1);
board[row][col] = '.';
}
}
}
placeQueens(0);
return result;
}Question 20:
Which JavaScript function uses backtracking to find all subsets of a given set?
a)
function findSubsets(nums) {
const result = [];
function backtrack(start, path) {
result.push([...path]);
for (let i = start; i < nums.length; i++) {
path.push(nums[i]);
backtrack(i + 1, path);
path.pop();
}
}
backtrack(0, []);
return result;
}b)
function findSubsets(nums) {
const result = [];
function backtrack(start, subset) {
result.push(subset);
for (let i = start; i < nums.length; i++) {
backtrack(i + 1, subset.concat(nums[i]));
}
}
backtrack(0, []);
return result;
}c)
function findSubsets(nums) {
const result = [];
function backtrack(path, index) {
result.push([...path]);
for (let i = index; i < nums.length; i++) {
path.push(nums[i]);
backtrack(path, i + 1);
path.pop();
}
}
backtrack([], 0);
return result;
}d)
function findSubsets(nums) {
const result = [];
function backtrack(subset, index) {
result.push([...subset]);
for (let i = index; i < nums.length; i++) {
subset.push(nums[i]);
backtrack(subset, i + 1);
subset.pop();
}
}
backtrack([], 0);
return result;
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