Smallest Difference Triplet from Three arrays
Last Updated :
03 Mar, 2025
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Three arrays of same size are given. Find a triplet such that maximum - minimum in that triplet is minimum of all the triplets. A triplet should be selected in a way such that it should have one number from each of the three given arrays.
If there are 2 or more smallest difference triplets, then the one with the smallest sum of its elements should be displayed.
Examples :
Input : arr1[] = {5, 2, 8}
arr2[] = {10, 7, 12}
arr3[] = {9, 14, 6}
Output : 7, 6, 5
Input : arr1[] = {15, 12, 18, 9}
arr2[] = {10, 17, 13, 8}
arr3[] = {14, 16, 11, 5}
Output : 11, 10, 9
[Naive Solution] - Consider Each Triplet - O(n^3) Time and O(1) Space
We consider each an every triplet using three nested loops and find the required smallest difference triplet out of them. Complexity of O(n3).
#include <bits/stdc++.h>
using namespace std;
vector<int> findMinDiffTriplet(vector<int> &a, vector<int> &b, vector<int> &c) {
int n = a.size();
vector<int> res(3);
int minDiff = INT_MAX, minSum = INT_MAX;
// Iterate over all possible triplets
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < n; k++) {
int mx = max({a[i], b[j], c[k]});
int mn = min({a[i], b[j], c[k]});
int diff = mx - mn;
int sum = a[i] + b[j] + c[k];
// Update result if a better triplet is found
if (diff < minDiff || (diff == minDiff && sum < minSum)) {
minDiff = diff;
minSum = sum;
res = {a[i], b[j], c[k]};
}
}
}
}
return res;
}
int main() {
vector<int> arr1 = {5, 2, 8};
vector<int> arr2 = {10, 7, 12};
vector<int> arr3 = {9, 14, 6};
vector<int> res = findMinDiffTriplet(arr1, arr2, arr3);
cout << res[0] << ", " << res[1] << ", " << res[2] << endl;
return 0;
}
import java.util.*;
public class Main {
public static int[] findMinDiffTriplet(int[] a, int[] b, int[] c) {
int n = a.length;
int[] res = new int[3];
int minDiff = Integer.MAX_VALUE, minSum = Integer.MAX_VALUE;
// Iterate over all possible triplets
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < n; k++) {
int mx = Math.max(Math.max(a[i], b[j]), c[k]);
int mn = Math.min(Math.min(a[i], b[j]), c[k]);
int diff = mx - mn;
int sum = a[i] + b[j] + c[k];
// Update result if a better triplet is found
if (diff < minDiff || (diff == minDiff && sum < minSum)) {
minDiff = diff;
minSum = sum;
res[0] = a[i];
res[1] = b[j];
res[2] = c[k];
}
}
}
}
return res;
}
public static void main(String[] args) {
int[] arr1 = {5, 2, 8};
int[] arr2 = {10, 7, 12};
int[] arr3 = {9, 14, 6};
int[] res = findMinDiffTriplet(arr1, arr2, arr3);
System.out.println(res[0] + ", " + res[1] + ", " + res[2]);
}
}
def find_min_diff_triplet(a, b, c):
n = len(a)
res = [0, 0, 0]
min_diff = float('inf')
min_sum = float('inf')
# Iterate over all possible triplets
for i in range(n):
for j in range(n):
for k in range(n):
mx = max(a[i], b[j], c[k])
mn = min(a[i], b[j], c[k])
diff = mx - mn
sum_ = a[i] + b[j] + c[k]
# Update result if a better triplet is found
if diff < min_diff or (diff == min_diff and sum_ < min_sum):
min_diff = diff
min_sum = sum_
res = [a[i], b[j], c[k]]
return res
arr1 = [5, 2, 8]
arr2 = [10, 7, 12]
arr3 = [9, 14, 6]
res = find_min_diff_triplet(arr1, arr2, arr3)
print(res[0], ",", res[1], ",", res[2])
using System;
using System.Linq;
class Program {
static int[] FindMinDiffTriplet(int[] a, int[] b, int[] c) {
int n = a.Length;
int[] res = new int[3];
int minDiff = int.MaxValue, minSum = int.MaxValue;
// Iterate over all possible triplets
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < n; k++) {
int mx = Math.Max(Math.Max(a[i], b[j]), c[k]);
int mn = Math.Min(Math.Min(a[i], b[j]), c[k]);
int diff = mx - mn;
int sum = a[i] + b[j] + c[k];
// Update result if a better triplet is found
if (diff < minDiff || (diff == minDiff && sum < minSum)) {
minDiff = diff;
minSum = sum;
res[0] = a[i];
res[1] = b[j];
res[2] = c[k];
}
}
}
}
return res;
}
static void Main() {
int[] arr1 = {5, 2, 8};
int[] arr2 = {10, 7, 12};
int[] arr3 = {9, 14, 6};
int[] res = FindMinDiffTriplet(arr1, arr2, arr3);
Console.WriteLine(res[0] + ", " + res[1] + ", " + res[2]);
}
}
function findMinDiffTriplet(a, b, c) {
let n = a.length;
let res = [0, 0, 0];
let minDiff = Infinity, minSum = Infinity;
// Iterate over all possible triplets
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
for (let k = 0; k < n; k++) {
let mx = Math.max(a[i], b[j], c[k]);
let mn = Math.min(a[i], b[j], c[k]);
let diff = mx - mn;
let sum = a[i] + b[j] + c[k];
// Update result if a better triplet is found
if (diff < minDiff || (diff === minDiff && sum < minSum)) {
minDiff = diff;
minSum = sum;
res = [a[i], b[j], c[k]];
}
}
}
}
return res;
}
let arr1 = [5, 2, 8];
let arr2 = [10, 7, 12];
let arr3 = [9, 14, 6];
let res = findMinDiffTriplet(arr1, arr2, arr3);
console.log(res[0] + ", " + res[1] + ", " + res[2]);
[Efficient Solution] - Sorting and Three Pointer - O(n Log n) Time and O(1) Space
- Sort the 3 arrays in non-decreasing order.
- Start three pointers from left most elements of three arrays.
- Now find min and max and calculate max-min from these three elements.
- Now increment pointer of minimum element’s array.
- Repeat steps 2, 3, 4, for the new set of pointers until any one pointer reaches to its end.
#include <bits/stdc++.h>
using namespace std;
void smallestTriplet(vector<int>& a, vector<int>& b,
vector<int>& c) {
// Sort three arrays
sort(a.begin(), a.end());
sort(b.begin(), b.end());
sort(c.begin(), c.end());
// Traverse three arrays from beginning
int i = 0, j = 0, k = 0, diff = INT_MAX;
int x, y, z; // Store result
while (i < a.size() && j < b.size() && k < c.size()) {
int lo = min({a[i], b[j], c[k]});
int hi = max({a[i], b[j], c[k]});
if (diff > hi - lo) {
diff = hi - lo;
x = hi, y = a[i] + b[j] + c[k] - (hi + lo), z = lo;
}
if (a[i] == lo) i++;
else if (b[j] == lo) j++;
else k++;
}
cout << x << ", " << y << ", " << z;
}
int main() {
vector<int> a = {5, 2, 8}, b = {10, 7, 12}, c = {9, 14, 6};
smallestTriplet(a, b, c);
}
import java.util.Arrays;
class Main {
public static void smallestTriplet(int[] a, int[] b, int[] c) {
// Sort three arrays
Arrays.sort(a);
Arrays.sort(b);
Arrays.sort(c);
// Traverse three arrays from beginning
int i = 0, j = 0, k = 0, diff = Integer.MAX_VALUE;
int x = 0, y = 0, z = 0; // Store result
while (i < a.length && j < b.length && k < c.length) {
int lo = Math.min(Math.min(a[i], b[j]), c[k]);
int hi = Math.max(Math.max(a[i], b[j]), c[k]);
if (diff > hi - lo) {
diff = hi - lo;
x = hi;
y = a[i] + b[j] + c[k] - (hi + lo);
z = lo;
}
if (a[i] == lo) i++;
else if (b[j] == lo) j++;
else k++;
}
System.out.println(x + ", " + y + ", " + z);
}
public static void main(String[] args) {
int[] a = {5, 2, 8};
int[] b = {10, 7, 12};
int[] c = {9, 14, 6};
smallestTriplet(a, b, c);
}
}
def smallest_triplet(a, b, c):
# Sort three arrays
a.sort()
b.sort()
c.sort()
# Traverse three arrays from beginning
i = j = k = 0
diff = float('inf')
x = y = z = 0 # Store result
while i < len(a) and j < len(b) and k < len(c):
lo = min(a[i], b[j], c[k])
hi = max(a[i], b[j], c[k])
if diff > hi - lo:
diff = hi - lo
x = hi
y = a[i] + b[j] + c[k] - (hi + lo)
z = lo
if a[i] == lo:
i += 1
elif b[j] == lo:
j += 1
else:
k += 1
print(x, ",", y, ",", z)
if __name__ == '__main__':
a = [5, 2, 8]
b = [10, 7, 12]
c = [9, 14, 6]
smallest_triplet(a, b, c)
using System;
using System.Collections.Generic;
using System.Linq;
class Program {
static void SmallestTriplet(List<int> a, List<int> b, List<int> c) {
// Sort three arrays
a.Sort();
b.Sort();
c.Sort();
// Traverse three arrays from beginning
int i = 0, j = 0, k = 0, diff = int.MaxValue;
int x = 0, y = 0, z = 0; // Store result
while (i < a.Count && j < b.Count && k < c.Count) {
int lo = Math.Min(Math.Min(a[i], b[j]), c[k]);
int hi = Math.Max(Math.Max(a[i], b[j]), c[k]);
if (diff > hi - lo) {
diff = hi - lo;
x = hi;
y = a[i] + b[j] + c[k] - (hi + lo);
z = lo;
}
if (a[i] == lo) i++;
else if (b[j] == lo) j++;
else k++;
}
Console.WriteLine(x + ", " + y + ", " + z);
}
static void Main() {
List<int> a = new List<int> { 5, 2, 8 };
List<int> b = new List<int> { 10, 7, 12 };
List<int> c = new List<int> { 9, 14, 6 };
SmallestTriplet(a, b, c);
}
}
function smallestTriplet(a, b, c) {
// Sort three arrays
a.sort((x, y) => x - y);
b.sort((x, y) => x - y);
c.sort((x, y) => x - y);
// Traverse three arrays from beginning
let i = 0, j = 0, k = 0, diff = Infinity;
let x, y, z; // Store result
while (i < a.length && j < b.length && k < c.length) {
let lo = Math.min(a[i], b[j], c[k]);
let hi = Math.max(a[i], b[j], c[k]);
if (diff > hi - lo) {
diff = hi - lo;
x = hi;
y = a[i] + b[j] + c[k] - (hi + lo);
z = lo;
}
if (a[i] === lo) i++;
else if (b[j] === lo) j++;
else k++;
}
console.log(x + ", " + y + ", " + z);
}
const a = [5, 2, 8];
const b = [10, 7, 12];
const c = [9, 14, 6];
smallestTriplet(a, b, c);
Output
7, 6, 5
