703324. Sub-Array Pairs
Sub-Array Pairs
Slug: sub-array-pairs5530 Difficulty: Medium Id: 703324 Topic Tags: Arrays, Data Structures Company Tags: None
Summary
Given an array of integers, find all pairs of non-empty subarrays that have the same sum. The problem is to write a function that takes the input array as an argument and returns a list of such pairs.
Detailed Explanation
The solution involves iterating through the array to generate all possible subarrays and then checking if two subarrays with the same sum exist in the list. This can be achieved by creating a hashmap where the key is the sum of the subarray and the value is a list of indices where this sum appears.
Here's a step-by-step breakdown:
- Initialize an empty hashmap
sum_to_indices. - Iterate through the array to generate all possible subarrays.
- For each subarray, calculate its sum and check if it already exists in the
sum_to_indiceshashmap. If not, add the sum as a new key with an empty list as its value. - Add the index of the current subarray to the list of indices for the corresponding sum in the
sum_to_indiceshashmap. - Initialize an empty result list
pairs. - Iterate through the
sum_to_indiceshashmap and find all pairs of indices where the same sum appears. For each pair, add a tuple containing the start and end indices of the subarrays to thepairslist. - Return the
pairslist.
Time complexity: O(n^2), where n is the length of the input array. This is because we're generating all possible subarrays, which takes O(n) time for each subarray, and there are O(n) subarrays in total.
Space complexity: O(n), as we need to store the indices of all subarrays with the same sum in the sum_to_indices hashmap.
Optimized Solutions
Java
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
public class SubArrayPairs {
public List<int[]> findSubArrayPairs(int[] arr) {
HashMap<Integer, List<Integer>> sum_to_indices = new HashMap<>();
List<int[]> pairs = new ArrayList<>();
for (int i = 0; i < arr.length; i++) {
int sum = 0;
for (int j = i; j < arr.length; j++) {
sum += arr[j];
if (!sum_to_indices.containsKey(sum)) {
sum_to_indices.put(sum, new ArrayList<>());
}
sum_to_indices.get(sum).add(j);
}
}
for (List<Integer> indices : sum_to_indices.values()) {
if (indices.size() > 1) {
for (int i = 0; i < indices.size(); i++) {
int start = indices.get(i);
for (int j = i + 1; j < indices.size(); j++) {
int end = indices.get(j);
pairs.add(new int[] {start, end});
}
}
}
}
return pairs;
}
}