A Distance Maximizing Problem

Given an array A of integers, find the maximum of j-i subjected to the constraint of A[i] < A[j].

Idea:

1. Start point should have no left point that is smaller.

2. End point should have no right point that is larger.

3. Scan array once from left to right. Find the current min from left.

4. For the smallest element with index i, find rightest feasible index j such that A[j]>A[i].

5. Search for next current min i, find rightest feasible index j such that A[j]>A[i] starting from the last stop point(We can ignore the right part).

C++:
01 int dist_max(int A[], int n, int &start, int &end)
02 {
03     bool *min_left=new bool [n];
04 
05     int min=A[0];
06     min_left[0]=true;
07     for(int i=1;i<n;i++){
08         if(A[i]<min){
09             min_left[i]=true;
10             min=A[i];
11         }else{
12             min_left[i]=false;
13         }
14     }
15 
16     int max_dist=0;
17     int i=n1;
18     int j=n1;
19     while(i>=0){
20         if(min_left[i]==false){
21             i;
22             continue;
23         }
24         while((A[j]<=A[i])&&(j>i))
25             j;
26         if((ji)>max_dist){
27             max_dist=ji;
28             start=i;
29             end=j;
30         }
31         i;
32     }
33     return max_dist;
34 }
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