2345. Finding the Number of Visible Mountains

O(nlogn)

```java
class Solution {
    public int visibleMountains(int[][] peaks) {

        int n = peaks.length;
        int[][] x = new int[peaks.length][2];

        // see base of the moutain
        for (int i = 0; i < peaks.length; i++) {
            int px = peaks[i][0];
            int py = peaks[i][1];
            x[i][0] = px - py;
            x[i][1] = px + py;
        }
        // when s are the same, we want this (for case2 using)
        // 1    4
        // 1 2 
        Arrays.sort(x, (a, b) -> a[0] == b[0] ? b[1] - a[1] : a[0] - b[0]);
        
        int count = 0;
        int i = 0;
        while (i < n) {
          int j = i+1;

          // case1: 
          // if j is the last montain, count it
          // if i and j montain, start or end are not the same, means we can see "one montain"
          if (j == n || x[i][0] != x[j][0] || x[i][1] != x[j][1]) { // s != or  e !=
            count++;
          }

          // case2: if i_start i_end includes entire j, skip this j montain
          while (j < n && x[i][0] <= x[j][0] && x[j][1] <= x[i][1]) { // including case, skip: j interval is including in i interval
            j++;
          }
          i = j; // move to j
        }
        return count;
    }
}

/*
[[2,2],[6,3],[5,4]]

0, 4

3,9

1, 9

[[2,2],[5,2],[8,4], [8,4], [8,4], [8,4],[8,4]]

0,  4

  3  ,  7
    4,       12

0    4   
 1     9   
   3   9   



  is  js je  ie
*/
```