03. Maximum Index

The problem can be found at the following link: Question Link

My approach

• It creates two vectors v_min and v_max, each of size n. These vectors will store the minimum and maximum values encountered so far from the left and right sides of the array, respectively.

• The first element of v_min is initialized as arr[0] (the first element of the array), and the last element of v_max is initialized as arr[n - 1] (the last element of the array).

• Two loops are used to populate the v_min and v_max vectors. Starting from the second element (i = 1), the loop calculates the minimum value between the current element and the previous minimum value and stores it in v_min[i]. Similarly, starting from the second-to-last element (n - i - 1), the loop calculates the maximum value between the current element and the next maximum value and stores it in v_max[n - i - 1].

• After populating the v_min and v_max vectors, the code initializes ans (the maximum difference) to 0 and sets i and j to 0.

• A while loop is used to iterate until either i or j reaches the end of the array. The loop checks if the current minimum value (v_min[i]) is less than or equal to the current maximum value (v_max[j]). If true, it updates the maximum difference (ans) if the difference between j and i is greater than the current maximum difference. Then, it increments j to consider the next element. Otherwise, it increments i to consider the next element.

• Finally, when the while loop finishes, the function returns the maximum difference (ans).

Time and Auxiliary Space Complexity

• Time Complexity : O(n) as it performs iterations only up to n.

• Auxiliary Space Complexity : O(n) because we uses two additional arrays, v_min and v_max, of the same size of n.

Code (C++)

class Solution{
public:
  int maxIndexDiff(int arr[], int n) {
      vector<int> v_min(n), v_max(n);
      v_min[0] = arr[0];
      v_max[n - 1] = arr[n - 1];
      for (int i = 1; i < n; i++) {
        v_min[i] = min(v_min[i - 1], arr[i]);
        v_max[n - i - 1] = max(v_max[n - i], arr[n - i - 1]);
      }
      int ans = 0, i = 0, j = 0;
      while (i < n && j < n) {
        if (v_min[i] <= v_max[j]) {
          ans = max(ans, j - i);
          j++;
        } else i++;
      }
      return ans;
    }
};

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