Reach A Number - Leetcode Solution

The problem "Reach a Number" on Leetcode asks us to find the minimum steps required to reach a target number by starting from zero and performing either of the following two operations:

1. Adding a positive integer to the current number.
2. Subtracting a positive integer from the current number.

For example, if the target number is 5, we can reach this number by starting from zero and adding 1, then adding 2, and finally adding 2 again. This takes three steps in total. Another way to reach 5 would be to start from zero and subtract 1, then subtract 2, and finally add 3. This also takes three steps.

To solve this problem, we need to follow the steps given below:

1. First, we need to determine the direction we want to move in. We can either add or subtract numbers until we reach the target. By doing this, we can reduce the value we want to reach by half. This is because if we can reach a number x in n steps, we can reach the number -x in n+1 steps by changing the sign of one of the steps.

2. Next, we set a goal by adding or subtracting from zero until we reach a number that is greater than or equal to the target. For example, if the target is 5 and we decide to subtract numbers to reach it, we can set our goal at -6. This is because if we can reach -6 in n steps, we can add 1+2+3=6 to reach 5 in n+3 steps.

3. Once we have established our goal, we need to determine the minimum number of steps required to reach it. We can do this by repeatedly adding or subtracting numbers until we reach our goal. We keep track of the number of steps we take and return the minimum number of steps required to reach the target number.

Here's the Python code to implement the above steps:

def reachNumber(target: int) -> int: target = abs(target) curr_sum = 0 i = 0 while curr_sum < target: i += 1 curr_sum += i diff = curr_sum - target if diff % 2 == 0: return i else: if i % 2 == 0: return i + 1 else: return i + 2

The function reachNumber takes an integer target as input and returns the minimum number of steps required to reach the target.

In step 1, we first take the absolute value of the target to simplify the problem. We then set a flag flip to determine the direction we want to move in. If the target is positive, we move towards the right by adding numbers. If the target is negative, we move towards the left by subtracting numbers.

In step 2, we initialize a variable curr_sum to keep track of the sum of the numbers we have added or subtracted so far. We also initialize a variable i to keep track of the number of steps we have taken.

We then enter a loop where we repeatedly add or subtract numbers until the sum curr_sum is greater than or equal to the target. We keep track of the number of steps we take in the variable i.

In step 3, we calculate the difference diff between the sum curr_sum and the target. If diff is even, we can simply return the number of steps i as it is. This is because we can reach the target by flipping the sign of exactly one of the numbers we have added or subtracted so far.

If diff is odd, we need to add or subtract an additional number to reach the target. If i is even, we can do this by subtracting a number that we have already added. This is because flipping the sign of this number will change the sum by twice its value. If i is odd, we need to add a number that we have not yet added. We can do this by adding i+1, as we know that this number will be odd.

Finally, we return the minimum number of steps required to reach the target.

1