Merge pull request #979 from parikhitritgithub/dev

Adding the Solution of a problem 523

Author: ajay-dhangar

dsa-solutions/lc-solutions/0500-0599/0523-continuous-subarray-sum.md

@@ -0,0 +1,211 @@
+---
+id: continuous-subarray-sum
+title: continuous-subarray-sum
+sidebar_label: 0523 continuous subarray sum
+tags:
+  - prefix sum + hashmap
+  - LeetCode
+  - Java
+  - Python
+  - C++
+description: This is a solution to the Continuous Subarray Sum problem on LeetCode
+---
+
+## Problem Description
+
+Given an integer array `nums` and an integer `k` return `true` if `nums` has a good subarray or `false` otherwise A good subarray is a subarray where
+
+- Its length is at least two and
+- The sum of the elements of the subarray is a multiple of `k`
+
+Note that:
+- A subarray is a contiguous part of the array
+- An integer `x` is a multiple of `k` if there exists an integer `n` such that `$x = n * k$` 0 is always a multiple of `k`
+
+### Examples
+
+**Example 1:**
+
+
+
+## Problem Description
+
+Given an integer array nums and an integer k return true if nums has a good subarray or false otherwise
+A good subarray is a subarray where:
+
+ - its length is at least two and
+ - the sum of the elements of the subarray is a multiple of k
+Note that:
+ - A subarray is a contiguous part of the array
+ - An integer x is a multiple of k if there exists an integer n such that $x = n * k$ 0 is always a multiple of k
+
+### Examples
+
+**Example 1:**
+
+```
+
+Input: nums : [23,2,4,6,7], k : 6
+Output: true
+Explanation: [2, 4] is a continuous subarray of size 2 whose elements sum up to 6
+
+```
+
+**Example 2:**
+
+
+```
+Input: root : nums : [23,2,6,4,7], k : 6
+Output: true
+Explanation: [23, 2, 6, 4, 7] is an continuous subarray of size 5 whose elements sum up to 42
+42 is a multiple of 6 because 42 = 7 * 6 and 7 is an integer
+```
+
+**Example 3:**
+
+
+```
+Input: nums : [23,2,6,4,7], k : 13
+Output: false
+```
+
+
+### Constraints
+
+-  $1 \leq \text{nums.length} \leq  105$
+
+
+---
+
+## Solution for  Continuous Subarray Sum Problem
+
+### Intuition
+This is a prefix sum's problem Due to LC
+
+    A good subarray is a subarray where:
+    its length is at least two and
+    the sum of the elements of the subarray is a multiple of k
+
+modulo k there are 0,1,...k-1 totally k possible for prefix sum (mod k)
+For this constraint $1 \leq \text{nums.length} \leq  105$ an $O(n^2)$ solution may lead to TLE
+
+
+A hash map with care on prefix sum mod k to use is however a tip  The array version is used when `k<n` combining the hash map version that will be the faster than other solutions
+
+Thanks to the comments of @Sergei proposing to use unordered_set a combination of bitset with unordered_set is implemented which outperforms all other solutions with the elapsed time 86ms
+
+
+### Approach
+
+
+   - First try uses array version for` mod_k(k)`
+   - 2nd approach uses `unordered_map<int, vector<int>>` instead of an array which is accepted by LC
+   - Since the computation uses `mod_k[prefix].front()`, a simple hash table `unordered_map<int, int> mod_k`is sufficient for this need
+   - An acceptable version using array version when $k<n$ otherwise hash map which is a combination of both different data structures
+   - Let prefix denote the current prefix sum modulo k The very crucial part is the following:
+
+
+
+
+#### Code in Different Languages
+
+<Tabs>
+  <TabItem value="Python" label="Python">
+  <SolutionAuthor name="@parikhitkurmi"/>
+    
+   ```python
+//python
+
+   class Solution:
+    def checkSubarraySum(self, nums: List[int], k: int) -> bool:
+        n=len(nums)
+        if n<2: return False
+        mod_k={}
+        prefix=0
+        mod_k[0]=-1
+        for i, x in enumerate(nums):
+            prefix+=x
+            prefix%=k
+            if prefix in mod_k:
+                if i>mod_k[prefix]+1:
+                    return True
+            else:
+                mod_k[prefix]=i
+        return False
+```
+  </TabItem>
+  <TabItem value="Java" label="Java">
+  <SolutionAuthor name="@parikhitkurmi"/>
+
+   ```java
+//java
+
+   class Solution {
+    public boolean checkSubarraySum(int[] nums, int k) {
+        int n = nums.length, prefSum = 0;
+        Map<Integer, Integer> firstOcc = new HashMap<>();
+        firstOcc.put(0, 0);
+
+        for (int i = 0; i < n; i++) {
+            prefSum = (prefSum + nums[i]) % k;
+            if (firstOcc.containsKey(prefSum)) {
+                if (i + 1 - firstOcc.get(prefSum) >= 2) {
+                    return true;
+                }
+            } else {
+                firstOcc.put(prefSum, i + 1);
+            }
+        }
+
+        return false;
+    }
+}
+
+```
+</TabItem>
+<TabItem value="C++" label="C++">
+<SolutionAuthor name="@parikhitkurmi"/>
+
+   ```cpp
+//cpp
+
+   class Solution {
+public:
+    bool checkSubarraySum(vector<int>& nums, int k) {
+        map<int , int> mp ; 
+        mp[0] = 0 ;
+        int sum = 0 ; 
+        for(int i = 0 ; i< nums.size() ; i++ ) {
+            sum += nums[i] ;
+            int rem = sum%k ;
+
+            if(mp.find(rem)==mp.end()){
+                mp[rem] = i+1 ; 
+                
+            }else if (mp[rem]  <  i ) {
+                return true ;
+
+            }
+
+
+        } 
+         return false ;
+        
+    }
+};
+
+```
+
+  </TabItem>
+</Tabs>
+
+
+
+
+
+## References
+
+- **LeetCode Problem:** [Continuous Subarray Sum](https://leetcode.com/problems/continuous-subarray-sum/)
+- **Solution Link:** [Continuous Subarray Sum](https://leetcode.com/problems/continuous-subarray-sum/submissions/1281964300/)
+- **Authors GeeksforGeeks Profile:** [parikhit kurmi](https://www.geeksforgeeks.org/user/sololeveler673/)
+- **Authors Leetcode:** [parikhit kurmi](https://leetcode.com/u/parikhitkurmi14/)