Find the nearest value present on the left of every array element

Difficulty Level : Medium
Last Updated : 19 Jan, 2021

Given an array arr[] of size N, the task is for each array element is to find the nearest non-equal value present on its left in the array. If no such element is found, then print -1

Examples:

Input: arr[] = { 2, 1, 5, 8, 3 }
Output: -1 2 2 5 2
Explanation:
[2], it is the only number in this prefix. Hence, answer is -1.
[2, 1], the closest number to 1 is 2
[2, 1, 5], the closest number to 5 is 2
[2, 1, 5, 8], the closest number to 8 is 5
[2, 1, 5, 8, 3], the closest number to 3 is 2
Input: arr[] = {3, 3, 2, 4, 6, 5, 5, 1}
Output: -1 -1 3 3 4 4 4 2
Explanation:
[3], it is the only number in this prefix. Hence, answer is -1.
[3, 3], it is the only number in this prefix. Hence, answer is -1
[3, 3, 2], the closest number to 2 is 3
[3, 3, 2, 4], the closest number to 4 is 3
[3, 3, 2, 4, 6], the closest number to 6 is 4
[3, 3, 2, 4, 6, 5], the closest number to 5 is 4
[3, 3, 2, 4, 6, 5, 5], the closest number to 5 is 4
[3, 3, 2, 4, 6, 5, 5, 1], the closest number to 1 is 2

Naive Approach: The simplest idea is to traverse the given array and for every i^th element, find the closest element on the left side of index i which is not equal to arr[i].
Time Complexity: O(N^2)
Auxiliary Space: O(1)

Efficient Approach:

The idea is to insert the elements of the given array in a Set such that the inserted numbers are sorted and then for an integer, find its position and compare its next value with the previous value, and print the closer value out of the two.
Fullow the steps below to sulve the problem:

Initialize a Set of integers S to store the elements in sorted order.
Traverse the array arr[] using the variable i.
Now, find the nearest value smaller as well as greater than arr[i], say X and Y respectively.
- If X cannot be found, print Y.
- If Y cannot be found, print Z.
- If both X and Y cannot be found, print “-1”.
After that, add arr[i] to the Set S and print X if abs(X – arr[i]) is smaller than abs(Y – arr[i]). Otherwise, print Y.
Repeat the above steps for every element.

Below is the implementation of the above approach:

C++14

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the closest number on
// the left side of x
void printClosest(set<int>& streamNumbers, int x)
{
 
    // Insert the value in set and store
    // its position
    auto it = streamNumbers.insert(x).first;
 
    // If x is the smallest element in set
    if (it == streamNumbers.begin())
    {
        // If count of elements in the set
        // equal to 1
        if (next(it) == streamNumbers.end())
        {
 
            cout << "-1 ";
            return;
        }
 
        // Otherwise, print its
        // immediate greater element
        int rightVal = *next(it);
        cout << rightVal << " ";
        return;
    }
 
    // Store its immediate smaller element
    int leftVal = *prev(it);
 
    // If immediate greater element does not
    // exists print it's immediate
    // smaller element
    if (next(it) == streamNumbers.end()) {
        cout << leftVal << " ";
        return;
    }
 
    // Store the immediate
    // greater element
    int rightVal = *next(it);
 
    // Print the closest number
    if (x - leftVal <= rightVal - x)
        cout << leftVal << " ";
    else
        cout << rightVal << " ";
}
 
// Driver Code
int main()
{
 
    // Given array
    vector<int> arr = { 3, 3, 2, 4, 6, 5, 5, 1 };
 
    // Initialize set
    set<int> streamNumbers;
 
    // Print Answer
    for (int i = 0; i < arr.size(); i++) {
 
        // Function Call
        printClosest(streamNumbers, arr[i]);
    }
 
    return 0;
}

Output

-1 -1 3 3 4 4 4 2

Time Complexity: O(N * log(N))
Auxiliary Space: O(N)

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