Watch 10 video solutions for Ant on the Boundary, a easy level problem involving Array, Simulation, Prefix Sum. This walkthrough by CodeJulian has 1,344 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
An ant is on a boundary. It sometimes goes left and sometimes right.
You are given an array of non-zero integers nums. The ant starts reading nums from the first element of it to its end. At each step, it moves according to the value of the current element:
nums[i] < 0, it moves left by -nums[i] units.nums[i] > 0, it moves right by nums[i] units.Return the number of times the ant returns to the boundary.
Notes:
|nums[i]| units. In other words, if the ant crosses the boundary during its movement, it does not count.
Example 1:
Input: nums = [2,3,-5] Output: 1 Explanation: After the first step, the ant is 2 steps to the right of the boundary. After the second step, the ant is 5 steps to the right of the boundary. After the third step, the ant is on the boundary. So the answer is 1.
Example 2:
Input: nums = [3,2,-3,-4] Output: 0 Explanation: After the first step, the ant is 3 steps to the right of the boundary. After the second step, the ant is 5 steps to the right of the boundary. After the third step, the ant is 2 steps to the right of the boundary. After the fourth step, the ant is 2 steps to the left of the boundary. The ant never returned to the boundary, so the answer is 0.
Constraints:
1 <= nums.length <= 100-10 <= nums[i] <= 10nums[i] != 0Problem Overview: An ant starts at position 0 on a number line. You receive an array nums where each value represents a movement. After applying each move sequentially, count how many times the ant lands exactly back on position 0.
Approach 1: Cumulative Position Tracking (O(n) time, O(1) space)
This approach directly simulates the ant’s movement using a running prefix sum. Start with a variable position = 0 and iterate through the array. For each step, add the move value to position. Every time position == 0, increment the answer counter. The key insight is that the ant’s location after each move is simply the cumulative sum of all previous moves. Since you only track a single integer and iterate once through the array, the solution runs in O(n) time with O(1) extra space. This pattern commonly appears in problems involving Prefix Sum and Simulation.
Approach 2: Pre-calculation of Positions (O(n) time, O(n) space)
Instead of updating a single running variable, this approach builds an explicit prefix array of positions. Create an array pos where pos[i] stores the ant’s position after the i-th move. Compute each entry using pos[i] = pos[i-1] + nums[i]. After constructing the prefix array, iterate through it and count how many values equal zero. This approach still runs in O(n) time but requires O(n) space to store intermediate positions. It can be useful if you need the full position history for debugging, visualization, or follow-up queries. The technique is a direct application of prefix accumulation on an Array.
Recommended for interviews: Cumulative Position Tracking. Interviewers expect you to recognize that the ant’s location is just a running prefix sum. The brute-style prefix array approach demonstrates understanding, but the constant-space simulation shows stronger problem-solving efficiency.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Cumulative Position Tracking | O(n) | O(1) | Best general solution. Minimal memory and simple single-pass logic. |
| Pre-calculation of Positions | O(n) | O(n) | Useful when you need the full history of positions for debugging or additional queries. |