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  • Leetcode: Self Crossing

    You are given an array x of n positive numbers. You start at point (0,0) and moves x[0] metres to the north, then x[1] metres to the west, x[2] metres to the south, x[3] metres to the east and so on. In other words, after each move your direction changes counter-clockwise.
    
    Write a one-pass algorithm with O(1) extra space to determine, if your path crosses itself, or not.
    
    Example 1:
    Given x = 
    [2, 1, 1, 2]
    ,
    ┌───┐
    │   │
    └───┼──>
        │
    
    Return true (self crossing)
    Example 2:
    Given x = 
    [1, 2, 3, 4]
    ,
    ┌──────┐
    │      │
    │
    │
    └────────────>
    
    Return false (not self crossing)
    Example 3:
    Given x = 
    [1, 1, 1, 1]
    ,
    ┌───┐
    │   │
    └───┼>
    
    Return true (self crossing)

    4th line may cross with 1st line, and so on: 5th with 2nd, ...etc

    5th line may cross with 1st line, and so on: 6th with 2nd, ...etc

    6th line also may cross with 1st line, and so on: 7th with 2nd, ...etc

    However, if 7th line also cross with 1st line, either of the following cases should definitely happens: 

      a. 7th line cross with 2nd line

      b. 6th line cross with 1st line

      we have covered these cases.

     1 public class Solution {
     2     public boolean isSelfCrossing(int[] x) {
     3         if (x.length <= 3) return false;
     4         for (int i=3; i<x.length; i++) {
     5             //check if 4th line cross with the first line and so on
     6             if (x[i]>=x[i-2] && x[i-1]<=x[i-3]) return true;
     7             
     8             //check if 5th line cross with the first line and so on
     9             if (i >= 4) {
    10                 if (x[i-1]==x[i-3] && x[i]+x[i-4]>=x[i-2]) return true;
    11             }
    12             
    13             //check if 6th line cross with the first line and so on
    14             if (i >= 5) {
    15                 if (x[i-2]>=x[i-4] && x[i]>=x[i-2]-x[i-4] && x[i-1]<=x[i-3] && x[i-1]>=x[i-3]-x[i-5]) return true;
    16             }
    17         }
    18         return false;
    19     }
    20 }
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  • 原文地址:https://www.cnblogs.com/EdwardLiu/p/6092286.html
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