题目

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

On each move, you can either go left or right. During the n-th move (starting from 1), you take n steps.

Return the minimum number of steps required to reach the destination.

Example 1:

  1. Input: target = 3
  2. Output: 2
  3. Explanation:
  4. On the first move we step from 0 to 1.
  5. On the second step we step from 1 to 3.

Example 2:

  1. Input: target = 2
  2. Output: 3
  3. Explanation:
  4. On the first move we step from 0 to 1.
  5. On the second move we step  from 1 to -1.
  6. On the third move we step from -1 to 2.

Note:

target will be a non-zero integer in the range [-10^9, 10^9].

题意

在一根数轴上从0出发，第n步可以向左或向右走n步，问最少需要几步走到指定值。

思路

target正负不影响，为方便取target绝对值。先求出k，使得sum=1+2+…+k恰好大于target，如果sum-target为偶数，说明在1~k这k步中，只要第(sum-target)/2这一步变为向左走，就能正好到达target；如果sum-target为奇数，说明还需要再走1步或2步，使(sum+k+1-target)为偶数或(sum+k+1+k+2-target)为偶数，这样也能在1~k+1或1~k+2中选一步向左走，使得正好走到target。

代码实现

Java

  1. class Solution {
  2.     public int reachNumber(int target) {
  3.         target = Math.abs(target);
  4.         int step = 0, sum = 0;
  5.         while (sum < target) {
  6.             sum += ++step;
  7.         }
  8.         return (sum - target) % 2 == 0 ? step : step % 2 == 0 ? step + 1 : step + 2;
  9.     }
  10. }