Find pair in an array having minimum absolute sum

Given an sorted array of integers, find a pair in it having minimum absolute sum.


For example,

Input:  A = [-6, -5, -3, 0, 2, 4, 9]

Output: Pair is (-5, 4)

(-5, 4) = abs(-5 + 4) = abs(-1) = 1, which is minimum among all pairs.


The idea is to maintain search space by maintaining two indexes (low and high) that initially points to two end-points of the array. Then we loop till low is less than high index and reduce search space arr[low..high] at each iteration of the loop by comparing sum of elements present at index low and high with 0. We increment index low if sum is less than the 0 else we decrement index high is sum is more than the 0. We also maintain the minimum absolute difference among all pairs present at low and high index.


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Pair found (-5, 4)


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Pair found (-5, 4)

The time complexity of above solution is O(n) and auxiliary space used by the program is O(1).

Thanks for reading.

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Mirwise Khan
Mirwise Khan

// Here is my solution

#include “stdio.h”
#include “math.h”

int main(){

int a[] = {-6, -5, -3, 0, 2, 4, 9};
int size = sizeof(a)/sizeof(a[0]);

// Save min as the sum of first two values

int min = abs(a[0] + a[1]);

// The b array is for the final pair answer

int b[2];

// Compare each number with the series of numbers after it

for(int i = 0; i < size; i++){
for(int j = i+1; j abs(a[i]+a[j])){
b[0] = a[i];
b[1] = a[j];
min = abs(a[i]+a[j]);

printf(“\n\n MiNiMUM (%d,%d) = %d”, b[0], b[1], abs(b[0]+b[1]));

Ankur Maheshwari
Ankur Maheshwari

This can be optimized using binary search finding transition from negative to positive. In other cases(all +ves or _-ves) its the return of first two and last two respectively.