<p>A <strong>ramp</strong> in an integer array <code>nums</code> is a pair <code>(i, j)</code> for which <code>i &lt; j</code> and <code>nums[i] &lt;= nums[j]</code>. The <strong>width</strong> of such a ramp is <code>j - i</code>.</p>

<p>Given an integer array <code>nums</code>, return <em>the maximum width of a <strong>ramp</strong> in </em><code>nums</code>. If there is no <strong>ramp</strong> in <code>nums</code>, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [6,0,8,2,1,5]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The maximum width ramp is achieved at (i, j) = (1, 5): nums[1] = 0 and nums[5] = 5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [9,8,1,0,1,9,4,0,4,1]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The maximum width ramp is achieved at (i, j) = (2, 9): nums[2] = 1 and nums[9] = 1.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:

    int binary_search(vector<int> &v, int target){
        // reverse vector
        int left = 0;
        int right = v.size();
        while(left < right){
            int mid = (left+right) / 2;
            if(v[mid] > target){
                left = mid + 1;
            }
            else{
                right = mid;
            }
        }
        return left;

    }

    int maxWidthRamp(vector<int>& nums) {
        unordered_map<int, int> mp;
        int n = nums.size();
        vector<int> v;
        int prev = 1e9;
        int res = 0;
        for(int i=0; i<n ;i++){
            if(v.size() == 0){
                v.push_back(nums[i]);
                mp[nums[i]] = i;
            }
            else{
                if(nums[i] > v[0]){
                    res = max(res, i);
                }
                else if(nums[i] < v.back()){
                    v.push_back(nums[i]);
                    mp[nums[i]] = i;
                }
                else{
                    int ins = binary_search(v, nums[i]);
                    /*
                    cout << "vector: ";
                    for(auto &ele:v){
                        cout << ele << ' ';
                    }
                    cout << '\n';

                    cout << ins << ' ' << i << '\n';
                    */
                    res = max(res, i - mp[v[ins]]);
                }
            }
        }
        return res;
    }
};
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