20221104 - 754. Reach a Number 到达终点数字（数学）

You are standing at position 0 on an infinite number line. There is a destination at position target.

You can make some number of moves numMoves so that:

• On each move, you can either go left or right.
• During the i-th move (starting from i == 1 to i == numMoves), you take i steps in the chosen direction.

Given the integer target, return the minimum number of moves required (i.e., the minimum numMoves) to reach the destination.

Example 1

Input: target = 2
Output: 3
Explanation:
On the 1st move, we step from 0 to 1 (1 step).
On the 2nd move, we step from 1 to -1 (2 steps).
On the 3rd move, we step from -1 to 2 (3 steps).

Example 2

Input: target = 3
Output: 2
Explanation:
On the 1st move, we step from 0 to 1 (1 step).
On the 2nd move, we step from 1 to 3 (2 steps).

Constraints

• -1e9 <= target <= 1e9
• target != 0

Solution

class Solution {
public:
    int reachNumber(int target) {
        int k = 0;
        target = abs(target); //只需考虑target>0的情况
        while (target > 0) {
            k++;
            target -= k;
        } //找到最小的k使得sigma大于等于target
        return target % 2 == 0 ? k : k + 1 + k % 2; //分delta奇偶讨论
    }
};

题目链接：754. 到达终点数字 - 力扣（LeetCode）