grid47 Exploring patterns and algorithms
Sep 30, 2024
4 min read
Solution to LeetCode 371: Sum of Two Integers Problem
You are given two integers a and b. Return their sum without using the + or - operators. You must implement the solution using bitwise operations.
Problem
Approach
Steps
Complexity
Input: The input consists of two integers `a` and `b`.
Example: Input: a = 5, b = 7
Constraints:
• -1000 <= a, b <= 1000
Output: Return the sum of `a` and `b` using bitwise operations without using the `+` or `-` operators.
Example: Output: 12
Constraints:
• The output should be the sum of the two integers using bitwise operations.
Goal: The goal is to compute the sum of two integers without using the arithmetic operators `+` or `-`.
Steps:
• 1. Use the bitwise XOR operation (`^`) to add the numbers without carrying over.
• 2. Use the bitwise AND operation (`&`) and shift the result left by one bit to handle the carry.
• 3. Recursively repeat the process until there is no carry left.
Goal: The constraints specify the valid input range for the integers `a` and `b`.
Steps:
• -1000 <= a, b <= 1000
Assumptions:
• The integers `a` and `b` are within the specified range of -1000 to 1000.
• Input: Input: a = 5, b = 7
Output: 12
• Explanation: The sum of 5 and 7 is computed using bitwise operations. The final result is 12.
Approach: The approach uses bitwise operations to add two integers without using `+` or `-`.
Observations:
• Bitwise XOR can add numbers without considering carry.
• Bitwise AND followed by a left shift can handle the carry during addition.
• We can recursively apply the bitwise operations until there is no carry left, which ensures the correct sum.
Steps:
• 1. XOR the two integers to get the sum without carry.
• 2. AND the two integers, shift the result left by one, and add it to the sum.
• 3. Repeat the process until the carry is zero.
Empty Inputs:
• An input where both `a` and `b` are 0 should return 0.
Large Inputs:
• Ensure the solution handles the largest and smallest inputs within the given constraints.
Special Values:
• Consider the behavior when one of the numbers is negative or zero.
Constraints:
• The solution should work efficiently within the constraints, handling up to the maximum and minimum values for `a` and `b`.
intgetSum(int a, int b) {
return b ==0?a: getSum(a^b, (a&b)<<1);
}
1 : Method Declaration
intgetSum(int a, int b) {
This line declares the method `getSum`, which takes two integers `a` and `b`, and returns their sum using bitwise operations.
2 : Recursive Call
return b ==0?a: getSum(a^b, (a&b)<<1);
The function uses recursion to compute the sum. If `b` is zero, it returns `a` as the result. Otherwise, it recursively calls `getSum`, using the XOR of `a` and `b` for the sum and the left-shifted AND of `a` and `b` for the carry.
Best Case: O(1) if the sum is obtained in the first iteration.
Average Case: O(k), where k is the number of bits in the input values (bounded by the size of the integers).
Worst Case: O(k) as each recursive step involves bitwise operations on the integers.
Description: The time complexity is determined by the number of bits in the input integers, as the process continues until there is no carry.
Best Case: O(1) as the solution requires a fixed amount of space for the operations.
Worst Case: O(1) because the space used is constant, regardless of the input size.
Description: The space complexity is constant as the solution does not use additional space proportional to the input size.
