### Problem :

Given an array of positive integer and given value X, find Contiguous sub array whose sum is equal to X.

**For example: **

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arr[]={14, 12, 70, 15, 99, 65, 21, 90}; X =97. Sum found between index 1 to 3 Elements are 12, 17 and 15 |

### Solution:

#### Solution 1:

Check all sub arrays and if current sum is equal to X, return. This will require two loops and if currentSum is greater than X tben try another sub array.

**Java code:**

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static void findSubArraySumEqualToX(int arr[], int X) { int currentSum; for (int i = 0; i < arr.length; i++) { currentSum = arr[i]; // try all subarrays starting with 'i' for (int j = i + 1; j <= arr.length; j++) { if (currentSum == X) { int endIndexForContArray = j - 1; System.out.println("Sum found between indexes " + i + " and " + endIndexForContArray); for (int k = i; k <= endIndexForContArray; k++) { System.out.print(arr[k]+" "); } return; } if (currentSum > X || j == arr.length) break; currentSum = currentSum + arr[j]; } } System.out.println("No subarray found"); return; } |

Time Complexity : O(N^2)

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**Solution 2: **

Lets say array is arr[] and given sum is X.

- Iterate over array arr[].
- If currentSum is less than X then add current element to currentSum.
- If currentSum is greater than X , it means we need to remove starting elements to make currentSum less than X.
- If CurrentSum is equal to X, we got the continuous sub array, print it.

**Java Code:**

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public static void findSubArraySumEqualToXOptimized(int arr[], int X) { int currentSum = arr[0]; int start = 0; for (int i = 1; i <= arr.length; i++) { // If currentSum is more than the sum, start removing starting elements unless you get currentSum is less than X while (currentSum > X && start < i - 1) { currentSum = currentSum - arr[start]; start++; } // If currentSum becomes equal to sum, then print the index if (currentSum == X) { int endIndexForContArray = i - 1; System.out.println("Sum found between indexes " + start + " and " + endIndexForContArray); System.out.println("Printing Array values : "); for (int j = start; j <= endIndexForContArray; j++) { System.out.print(arr[j]+" "); } return; } // Add this element to currentSum if (i < arr.length) currentSum = currentSum + arr[i]; } |

**Time Complexity : O(N)**

### Java program to find the Contiguous Subarray with Sum to a Given Value in an array :

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package org.arpit.java2blog; public class FindSumSubArrayMain { public static void main(String[] args) { int arr[] = { 15, 2, 4, 8, 9, 5, 10, 23 }; findSubArraySumEqualToX(arr, 33); System.out.println("n======================"); findSubArraySumEqualToXOptimized(arr, 33); } static void findSubArraySumEqualToX(int arr[], int X) { int currentSum; for (int i = 0; i < arr.length; i++) { currentSum = arr[i]; // try all subarrays starting with 'i' for (int j = i + 1; j <= arr.length; j++) { if (currentSum == X) { int endIndexForContArray = j - 1; System.out.println("Sum found between indexes " + i + " and " + endIndexForContArray); for (int k = i; k <= endIndexForContArray; k++) { System.out.print(arr[k]+" "); } return; } if (currentSum > X || j == arr.length) break; currentSum = currentSum + arr[j]; } } System.out.println("No subarray found"); return; } public static void findSubArraySumEqualToXOptimized(int arr[], int X) { int currentSum = arr[0]; int start = 0; for (int i = 1; i <= arr.length; i++) { // If currentSum is more than the sum, start removing starting elements unless you get currentSum is less than X while (currentSum > X && start < i - 1) { currentSum = currentSum - arr[start]; start++; } // If currentSum becomes equal to sum, then print the index if (currentSum == X) { int endIndexForContArray = i - 1; System.out.println("Sum found between indexes " + start + " and " + endIndexForContArray); System.out.println("Printing Array values : "); for (int j = start; j <= endIndexForContArray; j++) { System.out.print(arr[j]+" "); } return; } // Add this element to currentSum if (i < arr.length) currentSum = currentSum + arr[i]; } } } |

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Sum found between indexes 6 and 7 10 23 ====================== Sum found between indexes 6 and 7 Printing Array values : 10 23 |