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Izdrukājiet visus apakšragus ar 0 summu

Izmēģiniet to GFG praksē ' title=

Ņemot vērā masīvu arr [] no lieluma n Uzdevums ir izdrukāt visus masīvā, kurā ir summa Apvidū

Piemēri:  



Ievade: arr = [6 3 -1 -3 4 -2 2 4 6 -12 -7]
Izlaide:

Subarray atrasts no 2. līdz 4. indeksa
Subarray atrasts no 2. līdz 6. indeksam
Subarray atrasts no 5. līdz 6. indeksam
Subarray atrasts no 6. līdz 9. indeksa
Subarray atrasts no indeksa no 0 līdz 10

Ievade: arr = [1 2 -3 3 -1 -1]
Izlaide:



jvm

Subarray atrasts no indeksa no 0 līdz 2
Subarray atrasts no 2. līdz 3. indeksa
Subarray atrasts no 3. līdz 5. indeksam

[Naivā pieeja], ģenerējot visas iespējamās apakšraga - o (nRādītājs) Laiks un O (1) palīg telpa

Ļoti pamatā pieeja ir apsvērt Visas iespējamās apakšrajonus un pārbauda, ​​vai viņu summa ir nulle. Lai gan šī pieeja ir vienkārša, bet neefektīva arī lieliem masīviem.

C++
// C++ program to print all subarrays // in the array which has sum 0 #include    using namespace std; vector<pair<int int> > findSubArrays(int arr[] int n) {  // Array to store all the start and end  // indices of subarrays with 0 sum  vector<pair<int int> > output;  for (int i = 0; i < n; i++) {  int prefix = 0;  for (int j = i; j < n; j++) {  prefix += arr[j];  if (prefix == 0)  output.push_back({ i j });  }  }  return output; } // Function to print all subarrays with 0 sum void print(vector<pair<int int> > output) {  for (auto it = output.begin(); it != output.end(); it++)  cout << 'Subarray found from Index ' << it->first  << ' to ' << it->second << endl; } // Driver code int main() {  // Given array  int arr[] = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = sizeof(arr) / sizeof(arr[0]);  // Function Call  vector<pair<int int> > output = findSubArrays(arr n);  // if we didn’t find any subarray with 0 sum  // then subarray doesn’t exists  if (output.size() == 0) {  cout << 'No subarray exists';  }  else {  print(output);  }  return 0; } 
Java
// Java program to print all subarrays // in the array which has sum 0 import java.io.*; import java.util.*; // User defined pair class class Pair {  int first second;  Pair(int a int b)  {  first = a;  second = b;  } } public class GFG {  static ArrayList<Pair> findSubArrays(int[] arr int n)  {  // Array to store all the start and end  // indices of subarrays with 0 sum  ArrayList<Pair> out = new ArrayList<>();  for (int i = 0; i < n; i++) {  int prefix = 0;  for (int j = i; j < n; j++) {  prefix += arr[j];  if (prefix == 0)  out.add(new Pair(i j));  }  }  return out;  }  // Function to print all subarrays with 0 sum  static void print(ArrayList<Pair> out)  {  for (int i = 0; i < out.size(); i++) {  Pair p = out.get(i);  System.out.println('Subarray found from Index '  + p.first + ' to '  + p.second);  }  }  // Driver code  public static void main(String args[])  {  // Given array  int[] arr  = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = arr.length;  // Function Call  ArrayList<Pair> out = findSubArrays(arr n);  // if we didn’t find any subarray with 0 sum  // then subarray doesn’t exists  if (out.size() == 0)  System.out.println('No subarray exists');  else  print(out);  } } 
Python
# User defined pair class class Pair: first = 0 second = 0 def __init__(self a b): self.first = a self.second = b class GFG: @staticmethod def findSubArrays(arr n): # Array to store all the start and end # indices of subarrays with 0 sum out = [] i = 0 while (i < n): prefix = 0 j = i while (j < n): prefix += arr[j] if (prefix == 0): out.append(Pair(i j)) j += 1 i += 1 return out # Function to print all subarrays with 0 sum @staticmethod def print(out): i = 0 while (i < len(out)): p = out[i] print('Subarray found from Index ' + str(p.first) + ' to ' + str(p.second)) i += 1 # Driver code @staticmethod def main(args): # Given array arr = [6 3 -1 -3 4 -2 2 4 6 -12 -7] n = len(arr) # Function Call out = GFG.findSubArrays(arr n) # if we didn't find any subarray with 0 sum # then subarray doesn't exists if (len(out) == 0): print('No subarray exists') else: GFG.print(out) if __name__ == '__main__': GFG.main([]) 
C#
using System; using System.Collections.Generic; class GFG {    // Array to store all the start and end  // indices of subarrays with 0 sum  static List<Tuple<int int>> findSubArrays(int[] arr int n)  {  var output = new List<Tuple<int int>>();  for (int i = 0; i < n; i++)  {  int prefix = 0;  for (int j = i; j < n; j++)  {  prefix += arr[j];  if (prefix == 0)  output.Add(Tuple.Create(i j));  }  }  return output;  }  // Function to print all subarrays with 0 sum  static void print(List<Tuple<int int>> output)  {  foreach (var subArray in output)  Console.Write('Subarray found from Index ' + subArray.Item1 + ' to ' + subArray.Item2+'n');  }  // Driver code  public static void Main()  {  // Given array  int[] arr = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = arr.Length;  // Function Call  List<Tuple<int int>> output = findSubArrays(arr n);  // if we didn’t find any subarray with 0 sum  // then subarray doesn’t exists  if (output.Count == 0)  {  Console.WriteLine('No subarray exists');  }  else  {  print(output);  }  } } 
JavaScript
// Javascript program to print all subarrays // in the array which has sum 0 function findSubArrays(arr n) {  // Array to store all the start and end  // indices of subarrays with 0 sum  let out =[];  for (let i = 0; i < n; i++) {  let prefix = 0;  for (let j = i; j < n; j++) {  prefix += arr[j];  if (prefix == 0)  out.push([i j]);  }  }  return out; } // Function to print all subarrays with 0 sum function print(out) {  for (let it of out)  console.log('Subarray found from Index ' + it[0]  + ' to ' + it[1]); } // Driver code // Given array let arr = [ 6 3 -1 -3 4 -2 2 4 6 -12 -7 ]; let n = arr.length ; // Function Call let out = findSubArrays(arr n); // if we didn’t find any subarray with 0 sum // then subarray doesn’t exists if (out.length == 0) {  console.log('No subarray exists'); } else {  print(out); }   

Izvade
Subarray found from Index 0 to 10 Subarray found from Index 2 to 4 Subarray found from Index 2 to 6 Subarray found from Index 5 to 6 Subarray found from Index 6 to 9 

Laika sarežģītība: O (nRādītājs) Tā kā mēs izmantojam 2 cilpas.
Papildu telpa: O (1) kā nepieciešama pastāvīga papildu telpa.



[Paredzamā pieeja] Izmantojot Sajaukt - O (n) Laiks un O (n) papildu telpa

Efektīvāka pieeja ir izmantot sajaukšanu, lai saglabātu elementu un to indeksu kumulatīvo summu. Tas ļauj pārbaudīt, vai pastāvīgā laikā pastāv apakšrajons ar nulles summu.

Zemāk ir detalizēti intuīcijas soļi:

  1. Izveidojiet hash karti, lai saglabātu kumulatīvo summu un atbilstošos indeksus.
  2. Inicializējiet kumulatīvo summu līdz nullei.
  3. Šķērsot masīvu:
    • Pievienojiet pašreizējo elementu kumulatīvajai summai.
    • Ja kumulatīvā summa ir nulle, tiek atrasts apakšrajons no sākuma līdz pašreizējam indeksam.
    • Ja kumulatīvā summa jau ir sastopama hash kartē, tas nozīmē, ka ir apakšrajons ar nulles summu.
    • Uzglabājiet kumulatīvo summu un indeksu hash kartē.
C++
// C++ program to print all subarrays // in the array which has sum 0 #include    using namespace std; // Function to print all subarrays in the array which // has sum 0 vector<pair<int int> > findSubArrays(int arr[] int n) {  // create an empty map  unordered_map<int vector<int> > map;  // create an empty vector of pairs to store  // subarray starting and ending index  vector<pair<int int> > out;  // Maintains sum of elements so far  int sum = 0;  for (int i = 0; i < n; i++) {  // add current element to sum  sum += arr[i];  // if sum is 0 we found a subarray starting  // from index 0 and ending at index i  if (sum == 0)  out.push_back(make_pair(0 i));  // If sum already exists in the map there exists  // at-least one subarray ending at index i with  // 0 sum  if (map.find(sum) != map.end()) {  // map[sum] stores starting index of all  // subarrays  vector<int> vc = map[sum];  for (auto it = vc.begin(); it != vc.end(); it++)  out.push_back(make_pair(*it + 1 i));  }  // Important - no else  map[sum].push_back(i);  }  // return output vector  return out; } // Utility function to print all subarrays with sum 0 void print(vector<pair<int int> > out) {  for (auto it = out.begin(); it != out.end(); it++)  cout << 'Subarray found from Index ' << it->first  << ' to ' << it->second << endl; } // Driver code int main() {  int arr[] = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = sizeof(arr) / sizeof(arr[0]);  vector<pair<int int> > out = findSubArrays(arr n);  // if we didn’t find any subarray with 0 sum  // then subarray doesn’t exists  if (out.size() == 0)  cout << 'No subarray exists';  else  print(out);  return 0; } 
Java
// Java program to print all subarrays // in the array which has sum 0 import java.io.*; import java.util.*; // User defined pair class class Pair {  int first second;  Pair(int a int b)  {  first = a;  second = b;  } } public class GFG {  // Function to print all subarrays in the array which  // has sum 0  static ArrayList<Pair> findSubArrays(int[] arr int n)  {  // create an empty map  HashMap<Integer ArrayList<Integer> > map  = new HashMap<>();  // create an empty vector of pairs to store  // subarray starting and ending index  ArrayList<Pair> out = new ArrayList<>();  // Maintains sum of elements so far  int sum = 0;  for (int i = 0; i < n; i++) {  // add current element to sum  sum += arr[i];  // if sum is 0 we found a subarray starting  // from index 0 and ending at index i  if (sum == 0)  out.add(new Pair(0 i));  ArrayList<Integer> al = new ArrayList<>();  // If sum already exists in the map there exists  // at-least one subarray ending at index i with  // 0 sum  if (map.containsKey(sum)) {  // map[sum] stores starting index of all  // subarrays  al = map.get(sum);  for (int it = 0; it < al.size(); it++) {  out.add(new Pair(al.get(it) + 1 i));  }  }  al.add(i);  map.put(sum al);  }  return out;  }  // Utility function to print all subarrays with sum 0  static void print(ArrayList<Pair> out)  {  for (int i = 0; i < out.size(); i++) {  Pair p = out.get(i);  System.out.println('Subarray found from Index '  + p.first + ' to '  + p.second);  }  }  // Driver code  public static void main(String args[])  {  int[] arr  = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = arr.length;  ArrayList<Pair> out = findSubArrays(arr n);  // if we did not find any subarray with 0 sum  // then subarray does not exists  if (out.size() == 0)  System.out.println('No subarray exists');  else  print(out);  } } 
Python
# Python3 program to print all subarrays # in the array which has sum 0 # Function to get all subarrays # in the array which has sum 0 def findSubArrays(arr n): # create a python dict hashMap = {} # create a python list # equivalent to ArrayList out = [] # tracker for sum of elements sum1 = 0 for i in range(n): # increment sum by element of array sum1 += arr[i] # if sum is 0 we found a subarray starting # from index 0 and ending at index i if sum1 == 0: out.append((0 i)) al = [] # If sum already exists in the map # there exists at-least one subarray # ending at index i with 0 sum if sum1 in hashMap: # map[sum] stores starting index # of all subarrays al = hashMap.get(sum1) for it in range(len(al)): out.append((al[it] + 1 i)) al.append(i) hashMap[sum1] = al return out # Utility function to print # all subarrays with sum 0 def printOutput(output): for i in output: print('Subarray found from Index ' + str(i[0]) + ' to ' + str(i[1])) # Driver Code if __name__ == '__main__': arr = [6 3 -1 -3 4 -2 2 4 6 -12 -7] n = len(arr) out = findSubArrays(arr n) # if we did not find any subarray with 0 sum # then subarray does not exists if (len(out) == 0): print('No subarray exists') else: printOutput(out) 
C#
// C# program to print all subarrays // in the array which has sum 0 using System; using System.Collections.Generic; // User defined pair class class Pair {  public int first second;  public Pair(int a int b)  {  first = a;  second = b;  } } class GFG {  // Function to print all subarrays  // in the array which has sum 0  static List<Pair> findSubArrays(int[] arr int n)  {  // create an empty map  Dictionary<int List<int> > map  = new Dictionary<int List<int> >();  // create an empty vector of pairs to store  // subarray starting and ending index  List<Pair> outt = new List<Pair>();  // Maintains sum of elements so far  int sum = 0;  for (int i = 0; i < n; i++) {  // add current element to sum  sum += arr[i];  // if sum is 0 we found a subarray starting  // from index 0 and ending at index i  if (sum == 0)  outt.Add(new Pair(0 i));  List<int> al = new List<int>();  // If sum already exists in the map there exists  // at-least one subarray ending at index i with  // 0 sum  if (map.ContainsKey(sum)) {  // map[sum] stores starting index  // of all subarrays  al = map[sum];  for (int it = 0; it < al.Count; it++) {  outt.Add(new Pair(al[it] + 1 i));  }  }  al.Add(i);  if (map.ContainsKey(sum))  map[sum] = al;  else  map.Add(sum al);  }  return outt;  }  // Utility function to print all subarrays with sum 0  static void print(List<Pair> outt)  {  for (int i = 0; i < outt.Count; i++) {  Pair p = outt[i];  Console.WriteLine('Subarray found from Index '  + p.first + ' to '  + p.second);  }  }  // Driver code  public static void Main(String[] args)  {  int[] arr  = { 6 3 -1 -3 4 -2 2 4 6 -12 -7 };  int n = arr.Length;  List<Pair> outt = findSubArrays(arr n);  // if we did not find any subarray with 0 sum  // then subarray does not exists  if (outt.Count == 0)  Console.WriteLine('No subarray exists');  else  print(outt);  } } 
JavaScript
// JavaScript program to print all subarrays // in the array which has sum 0 // Function to print all subarrays in the array which // has sum 0 function findSubArrays(arr n) {  // create an empty map  let map = {};    // create an empty vector of pairs to store  // subarray starting and ending index  let out = [];    // Maintains sum of elements so far  let sum = 0;    for (var i = 0; i < n; i++)  {  // add current element to sum  sum += arr[i];    // if sum is 0 we found a subarray starting  // from index 0 and ending at index i  if (sum == 0)  out.push([0 i]);    // If sum already exists in the map there exists  // at-least one subarray ending at index i with  // 0 sum  if (map.hasOwnProperty(sum))  {  // map[sum] stores starting index of all subarrays  let vc = map[sum];  for (let it of vc)  out.push([it + 1 i]);  }  else  map[sum] = [];    // Important - no else  map[sum].push(i);  }    // return output vector  return out; }   // Utility function to print all subarrays with sum 0 function print(out) {  for (let it of out)  console.log('Subarray found from Index ' + it[0] + ' to ' + it[1]); }     // Driver code let arr = [6 3 -1 -3 4 -2 2 4 6 -12 -7]; let n = arr.length;   let out = findSubArrays(arr n);   // if we didn’t find any subarray with 0 sum // then subarray doesn’t exists if (out.length == 0)  console.log('No subarray exists'); else  print(out); 

Izvade
Subarray found from Index 2 to 4 Subarray found from Index 2 to 6 Subarray found from Index 5 to 6 Subarray found from Index 6 to 9 Subarray found from Index 0 to 10 

Laika sarežģītība: O (n), kur n ir masīva elementu skaits.
Papildu telpa: O (n) hash kartes glabāšanai.