Maximum Gap in C++



Suppose we have an array, that is not sorted. We have to find the maximum difference between successive elements in its sorted form. We will return 0 if the array contains less than 2 elements. So if the array is like [12,3,9,1,17], then the output will be 6, as the sorted array will be [1,3,9,12,17] so 5 will be the maximum difference as difference between 3 and 9 is 6.

To solve this, we will follow these steps −

  • minVal := inf, maxCal := -inf

  • n := size of nums

  • if n < 2, then return 0;

  • for i in range 0 to n – 1 −

    • minVal := min of nums[i] and minVal

    • maxVal := max of nums[i] and maxVal

  • gap := celing of maxVal – minVal / n – 1

  • make one array called bucketMax of size n – 1, and fill this with –inf

  • make one array called bucketMin of size n – 1, and fill this with inf

  • for i in range 0 to n – 1 −

    • x := nums[i]

    • if x = minVal or x = maxVal, then skip next part, go for next iteration

    • idx := (nums[i] – minVal) / gap.

    • bucketMax[idx] := max of bucketMax[idx] and nums[i]

    • bucketMin[idx] := min of bucketMin[idx] and nums[i]

  • ret := 0

  • prev := minVal

  • for i in range 0 to n – 1

    • if bucketMax[i] = -inf and bucketMin[i] = inf, then skip next part, go for next iteration

    • ret := max of ret and bucketMin[i] – prev

    • prev := bucketMax[i]

  • return max of ret, maxVal - prev

Example

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
   public:
   int maximumGap(vector<int>& nums) {
      lli minVal = INT_MAX;
      lli maxVal = INT_MIN;
      int n = nums.size();
      if(n < 2) return 0;
      for(int i = 0; i < n; i++){
         minVal = min((lli)nums[i], minVal);
         maxVal = max((lli)nums[i], maxVal);
      }
      int gap = ceil((double)(maxVal - minVal) / (double)(n - 1));
      vector <int> bucketMax(n - 1, INT_MIN);
      vector <int> bucketMin(n - 1, INT_MAX);
      for(int i = 0; i < n; i++){
         int x = nums[i];
         if(x == minVal || x == maxVal) continue;
         int idx = (nums[i] - minVal) / gap;
         bucketMax[idx] = max(bucketMax[idx], nums[i]);
         bucketMin[idx] = min(bucketMin[idx], nums[i]);
      }
      lli ret = 0;
      lli prev = minVal;
      for(int i = 0; i < n - 1; i++){
         if(bucketMax[i] == INT_MIN && bucketMin[i] == INT_MAX) continue;
         ret = max(ret, bucketMin[i] - prev);
         prev = bucketMax[i];
      }
      return max(ret, maxVal - prev);
   }
};
main(){
   Solution ob;
   vector<int> v = {12,3,9,1,17};
   cout << (ob.maximumGap(v));
}

Input

[12,3,9,1,17]

Output

6

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