Introduction

In this blog post, we'll share the most commonly asked coding interview questions at IBM. If you don't have months to study for your interviews, you can use AI tools like Chatmagic to generate solutions quickly and efficiently - helping you pass the interviews and get the job offer!

Problem #1: Count Ways to Group Overlapping Ranges

You are given a 2D integer array ranges where ranges[i] = [starti, endi] denotes that all integers between starti and endi (both inclusive) are contained in the ith range. You are to split ranges into two (possibly empty) groups such that: Each range belongs to exactly one group. Any two overlapping ranges must belong to the same group. Two ranges are said to be overlapping if there exists at least one integer that is present in both ranges. For example, [1, 3] and [2, 5] are overlapping because 2 and 3 occur in both ranges. Return the total number of ways to split ranges into two groups. Since the answer may be very large, return it modulo 109 + 7. Example 1: Input: ranges = [[6,10],[5,15]] Output: 2 Explanation: The two ranges are overlapping, so they must be in the same group. Thus, there are two possible ways: - Put both the ranges together in group 1. - Put both the ranges together in group 2. Example 2: Input: ranges = [[1,3],[10,20],[2,5],[4,8]] Output: 4 Explanation: Ranges [1,3], and [2,5] are overlapping. So, they must be in the same group. Again, ranges [2,5] and [4,8] are also overlapping. So, they must also be in the same group. Thus, there are four possible ways to group them: - All the ranges in group 1. - All the ranges in group 2. - Ranges [1,3], [2,5], and [4,8] in group 1 and [10,20] in group 2. - Ranges [1,3], [2,5], and [4,8] in group 2 and [10,20] in group 1. Constraints: 1 <= ranges.length <= 105 ranges[i].length == 2 0 <= starti <= endi <= 109

Topics: Array, Sorting

Problem #2: Minimum Moves to Equal Array Elements

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal. In one move, you can increment n - 1 elements of the array by 1. Example 1: Input: nums = [1,2,3] Output: 3 Explanation: Only three moves are needed (remember each move increments two elements): [1,2,3] => [2,3,3] => [3,4,3] => [4,4,4] Example 2: Input: nums = [1,1,1] Output: 0 Constraints: n == nums.length 1 <= nums.length <= 105 -109 <= nums[i] <= 109 The answer is guaranteed to fit in a 32-bit integer.

Topics: Array, Math

Problem #3: Minimum Operations to Make Columns Strictly Increasing

You are given a m x n matrix grid consisting of non-negative integers. In one operation, you can increment the value of any grid[i][j] by 1. Return the minimum number of operations needed to make all columns of grid strictly increasing. Example 1: Input: grid = [[3,2],[1,3],[3,4],[0,1]] Output: 15 Explanation: To make the 0th column strictly increasing, we can apply 3 operations on grid[1][0], 2 operations on grid[2][0], and 6 operations on grid[3][0]. To make the 1st column strictly increasing, we can apply 4 operations on grid[3][1]. Example 2: Input: grid = [[3,2,1],[2,1,0],[1,2,3]] Output: 12 Explanation: To make the 0th column strictly increasing, we can apply 2 operations on grid[1][0], and 4 operations on grid[2][0]. To make the 1st column strictly increasing, we can apply 2 operations on grid[1][1], and 2 operations on grid[2][1]. To make the 2nd column strictly increasing, we can apply 2 operations on grid[1][2]. Constraints: m == grid.length n == grid[i].length 1 <= m, n <= 50 0 <= grid[i][j] < 2500

Topics: Array, Greedy, Matrix

Problem #4: Integer to Roman

Seven different symbols represent Roman numerals with the following values: Symbol Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000 Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules: If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral. If the value starts with 4 or 9 use the subtractive form representing one symbol subtracted from the following symbol, for example, 4 is 1 (I) less than 5 (V): IV and 9 is 1 (I) less than 10 (X): IX. Only the following subtractive forms are used: 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD) and 900 (CM). Only powers of 10 (I, X, C, M) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (V), 50 (L), or 500 (D) multiple times. If you need to append a symbol 4 times use the subtractive form. Given an integer, convert it to a Roman numeral. Example 1: Input: num = 3749 Output: "MMMDCCXLIX" Explanation: 3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M) 700 = DCC as 500 (D) + 100 (C) + 100 (C) 40 = XL as 10 (X) less of 50 (L) 9 = IX as 1 (I) less of 10 (X) Note: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places Example 2: Input: num = 58 Output: "LVIII" Explanation: 50 = L 8 = VIII Example 3: Input: num = 1994 Output: "MCMXCIV" Explanation: 1000 = M 900 = CM 90 = XC 4 = IV Constraints: 1 <= num <= 3999

Topics: Hash Table, Math, String

Problem #5: Merge Intervals

Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input. Example 1: Input: intervals = [[1,3],[2,6],[8,10],[15,18]] Output: [[1,6],[8,10],[15,18]] Explanation: Since intervals [1,3] and [2,6] overlap, merge them into [1,6]. Example 2: Input: intervals = [[1,4],[4,5]] Output: [[1,5]] Explanation: Intervals [1,4] and [4,5] are considered overlapping. Constraints: 1 <= intervals.length <= 104 intervals[i].length == 2 0 <= starti <= endi <= 104

Topics: Array, Sorting

Problem #6: Count Vowel Strings in Ranges

You are given a 0-indexed array of strings words and a 2D array of integers queries. Each query queries[i] = [li, ri] asks us to find the number of strings present at the indices ranging from li to ri (both inclusive) of words that start and end with a vowel. Return an array ans of size queries.length, where ans[i] is the answer to the ith query. Note that the vowel letters are 'a', 'e', 'i', 'o', and 'u'. Example 1: Input: words = ["aba","bcb","ece","aa","e"], queries = [[0,2],[1,4],[1,1]] Output: [2,3,0] Explanation: The strings starting and ending with a vowel are "aba", "ece", "aa" and "e". The answer to the query [0,2] is 2 (strings "aba" and "ece"). to query [1,4] is 3 (strings "ece", "aa", "e"). to query [1,1] is 0. We return [2,3,0]. Example 2: Input: words = ["a","e","i"], queries = [[0,2],[0,1],[2,2]] Output: [3,2,1] Explanation: Every string satisfies the conditions, so we return [3,2,1]. Constraints: 1 <= words.length <= 105 1 <= words[i].length <= 40 words[i] consists only of lowercase English letters. sum(words[i].length) <= 3 * 105 1 <= queries.length <= 105 0 <= li <= ri < words.length

Topics: Array, String, Prefix Sum

Problem #7: Minimum Absolute Difference

Given an array of distinct integers arr, find all pairs of elements with the minimum absolute difference of any two elements. Return a list of pairs in ascending order(with respect to pairs), each pair [a, b] follows a, b are from arr a < b b - a equals to the minimum absolute difference of any two elements in arr Example 1: Input: arr = [4,2,1,3] Output: [[1,2],[2,3],[3,4]] Explanation: The minimum absolute difference is 1. List all pairs with difference equal to 1 in ascending order. Example 2: Input: arr = [1,3,6,10,15] Output: [[1,3]] Example 3: Input: arr = [3,8,-10,23,19,-4,-14,27] Output: [[-14,-10],[19,23],[23,27]] Constraints: 2 <= arr.length <= 105 -106 <= arr[i] <= 106

Topics: Array, Sorting

Problem #8: Maximum Units on a Truck

You are assigned to put some amount of boxes onto one truck. You are given a 2D array boxTypes, where boxTypes[i] = [numberOfBoxesi, numberOfUnitsPerBoxi]: numberOfBoxesi is the number of boxes of type i. numberOfUnitsPerBoxi is the number of units in each box of the type i. You are also given an integer truckSize, which is the maximum number of boxes that can be put on the truck. You can choose any boxes to put on the truck as long as the number of boxes does not exceed truckSize. Return the maximum total number of units that can be put on the truck. Example 1: Input: boxTypes = [[1,3],[2,2],[3,1]], truckSize = 4 Output: 8 Explanation: There are: - 1 box of the first type that contains 3 units. - 2 boxes of the second type that contain 2 units each. - 3 boxes of the third type that contain 1 unit each. You can take all the boxes of the first and second types, and one box of the third type. The total number of units will be = (1 3) + (2 2) + (1 * 1) = 8. Example 2: Input: boxTypes = [[5,10],[2,5],[4,7],[3,9]], truckSize = 10 Output: 91 Constraints: 1 <= boxTypes.length <= 1000 1 <= numberOfBoxesi, numberOfUnitsPerBoxi <= 1000 1 <= truckSize <= 106

Topics: Array, Greedy, Sorting

Problem #9: Fizz Buzz

Given an integer n, return a string array answer (1-indexed) where: answer[i] == "FizzBuzz" if i is divisible by 3 and 5. answer[i] == "Fizz" if i is divisible by 3. answer[i] == "Buzz" if i is divisible by 5. answer[i] == i (as a string) if none of the above conditions are true. Example 1: Input: n = 3 Output: ["1","2","Fizz"] Example 2: Input: n = 5 Output: ["1","2","Fizz","4","Buzz"] Example 3: Input: n = 15 Output: ["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14","FizzBuzz"] Constraints: 1 <= n <= 104

Topics: Math, String, Simulation

Problem #10: Find Pivot Index

Given an array of integers nums, calculate the pivot index of this array. The pivot index is the index where the sum of all the numbers strictly to the left of the index is equal to the sum of all the numbers strictly to the index's right. If the index is on the left edge of the array, then the left sum is 0 because there are no elements to the left. This also applies to the right edge of the array. Return the leftmost pivot index. If no such index exists, return -1. Example 1: Input: nums = [1,7,3,6,5,6] Output: 3 Explanation: The pivot index is 3. Left sum = nums[0] + nums[1] + nums[2] = 1 + 7 + 3 = 11 Right sum = nums[4] + nums[5] = 5 + 6 = 11 Example 2: Input: nums = [1,2,3] Output: -1 Explanation: There is no index that satisfies the conditions in the problem statement. Example 3: Input: nums = [2,1,-1] Output: 0 Explanation: The pivot index is 0. Left sum = 0 (no elements to the left of index 0) Right sum = nums[1] + nums[2] = 1 + -1 = 0 Constraints: 1 <= nums.length <= 104 -1000 <= nums[i] <= 1000 Note: This question is the same as 1991: https://leetcode.com/problems/find-the-middle-index-in-array/

Topics: Array, Prefix Sum