Problem 1: Plus One
Statement: A large integer is received represented as an array of digits where each digit is an element of the array. The task is to add one to the integer and return the result as an array of digits. Example: [1,2,3] represents 123 and adding one returns [1,2,4].
Step-by-step approach: - Traverse the array from the last digit to the first. - If the current digit is less than 9, add one and return the updated array immediately. - If the digit is 9, set it to 0 and continue to the previous digit handling the carry. - If all digits are 9, after the traversal insert a 1 at the beginning and return, for example [9,9,9] becomes [1,0,0,0].
Complexity: Time O(n) since in the worst case the entire array is traversed. Space O(1) in place except for the final insertion of a digit at the beginning when all are 9.
Example of JavaScript code explained simply: var plusOne = function(digits) { for (let i = digits.length - 1; i >= 0; i--) { if (digits[i] < 9) { digits[i] += 1; return digits; } digits[i] = 0; } digits.unshift(1); return digits; }; This code traverses from the end, adds one if there is no 9, turns 9 into 0 and propagates the carry, and in the case all are 9 adds a 1 at the beginning.
How it works: it starts at the last element, if it is less than 9 it increments and returns the array. If it is 9 it becomes 0 and the loop continues to propagate the carry. If after processing all digits it was not returned earlier, it means they were all 9 and a 1 is inserted at the beginning resulting in one more digit.
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