# Find the largest interval that contains exactly one of the given N integers.

Given an array **arr[]** of **N** distinct integers, the task is to find the maximum elements in an interval **[L, R]** such that the interval contains exactly one of the given **N** integers and **1 ≤ L ≤ R ≤ 10 ^{5}**

Input:arr[] = {5, 10, 200}

Output:99990

All possible intervals are [1, 9], [6, 199] and [11, 100000].

[11, 100000] has the maximum integers i.e. 99990.

Input:arr[] = {15000, 25000, 40000, 70000, 80000}

Output:44999

**Approach:** The idea is to fix the element we want our interval to contain. Now we are interested in how much we can extend our interval to left and right without overlapping with other elements.

So, we first sort our array. Then for a fixed element we determine its ends using previous and next element. We should also take care of corner cases that is when we fix our first and last intervals. This way for every element i, we find the maximum length of the interval.

Below is the implementation of the above approach:

## CPP

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to return the maximum ` `// size of the required interval ` `int` `maxSize(vector<` `int` `>& v, ` `int` `n) ` `{ ` ` ` `// Insert the borders for array ` ` ` `v.push_back(0); ` ` ` `v.push_back(100001); ` ` ` `n += 2; ` ` ` ` ` `// Sort the elements in ascending order ` ` ` `sort(v.begin(), v.end()); ` ` ` ` ` `// To store the maximum size ` ` ` `int` `mx = 0; ` ` ` `for` `(` `int` `i = 1; i < n - 1; i++) { ` ` ` ` ` `// To store the range [L, R] such that ` ` ` `// only v[i] lies within the range ` ` ` `int` `L = v[i - 1] + 1; ` ` ` `int` `R = v[i + 1] - 1; ` ` ` ` ` `// Total integers in the range ` ` ` `int` `cnt = R - L + 1; ` ` ` `mx = max(mx, cnt); ` ` ` `} ` ` ` ` ` `return` `mx; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `vector<` `int` `> v = { 200, 10, 5 }; ` ` ` `int` `n = v.size(); ` ` ` ` ` `cout << maxSize(v, n); ` ` ` ` ` `return` `0; ` `} ` |

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## Python

`# Python3 implementation of the approach ` ` ` `# Function to return the maximum ` `# size of the required interval ` `def` `maxSize(v, n): ` ` ` ` ` `# Insert the borders for array ` ` ` `v.append(` `0` `) ` ` ` `v.append(` `100001` `) ` ` ` `n ` `+` `=` `2` ` ` ` ` `# Sort the elements in ascending order ` ` ` `v ` `=` `sorted` `(v) ` ` ` ` ` `# To store the maximum size ` ` ` `mx ` `=` `0` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `-` `1` `): ` ` ` ` ` `# To store the range [L, R] such that ` ` ` `# only v[i] lies within the range ` ` ` `L ` `=` `v[i ` `-` `1` `] ` `+` `1` ` ` `R ` `=` `v[i ` `+` `1` `] ` `-` `1` ` ` ` ` `# Total integers in the range ` ` ` `cnt ` `=` `R ` `-` `L ` `+` `1` ` ` `mx ` `=` `max` `(mx, cnt) ` ` ` ` ` ` ` `return` `mx ` ` ` ` ` `# Driver code ` `v ` `=` `[ ` `200` `, ` `10` `, ` `5` `] ` `n ` `=` `len` `(v) ` ` ` `print` `(maxSize(v, n)) ` ` ` `# This code is contributed by mohit kumar 29 ` |

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**Output:**

99990

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