From bbd7092ef8911c4ff85a7d427853a50b3f774d87 Mon Sep 17 00:00:00 2001
From: Hameed Mulani <hameedmulani2001@gmail.com>
Date: Sat, 8 Oct 2022 00:39:42 +0530
Subject: [PATCH] SubArray Sum added by Hameed Mulani

---
 Arrays/subArraySum.cpp | 119 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 119 insertions(+)
 create mode 100644 Arrays/subArraySum.cpp

diff --git a/Arrays/subArraySum.cpp b/Arrays/subArraySum.cpp
new file mode 100644
index 0000000..3a1b7e4
--- /dev/null
+++ b/Arrays/subArraySum.cpp
@@ -0,0 +1,119 @@
+#include <bits/stdc++.h>
+using namespace std;
+// 1.
+// Prblem : Print largest subarray sum of a given array
+// Brute force approach T(n) = O(n^3) 
+// space Complexity is O(1)
+
+int subArraySum_1(int *arr, int n){
+    // largest Sum 
+    int largestSum = 0; 
+    for(int i = 0; i<n; i++){ 
+        for(int j = i; j<n; j++){
+
+            // Individual subarray sum 
+            int subarraySum = 0;
+            for(int k = i; k<=j; k++){
+                subarraySum += arr[k];
+            }
+            // Put a check is subarraySum > largest sum 
+            largestSum = max(subarraySum, largestSum);
+        }
+    }
+    return largestSum;
+}
+
+// Finding out the larget sum of subarray
+// Brute Force
+int main(){
+
+    int arr[] = {-2,3,4,-1,5,-12,6,1,3};
+    int n = sizeof(arr)/sizeof(int);
+
+    cout<<"Max Sum: "<< subArraySum_1(arr, n);
+
+    return 0;
+}
+
+
+// 2.
+#include <bits/stdc++.h>
+using namespace std;
+
+// Problem : Print largest subarray sum of a given array
+// Algotithm approach T(n) = Inner Loops O(n^2) + prefix loop:O(n) = O(n^2) 
+// space Complexity is O(1)
+
+int subArraySum_2(int *arr, int n){
+    int prifix[n] = {0};
+    prifix[0] = arr[0];
+    for(int i = 1; i<n; i++){
+        prifix[i] = prifix[i-1] + arr[i];
+    }
+    // largest Sum 
+    int largestSum = 0; 
+    for(int i = 0; i<n; i++){ 
+        for(int j = i; j<n; j++){
+            
+            int subarraySum = i>0? prifix[j] - prifix[i-1] : prifix[j]; 
+            // false condition : if i = 0 then 0 to J sum i.e exact = J // 0 1 2 5 6
+            //         i=0     j=4 i.e sum = 6
+
+            // Put a check is subarraySum > largest sum 
+            largestSum = max(subarraySum, largestSum);
+        }
+    }
+    return largestSum;
+}
+
+// Finding out the larget sum of subarray
+int main(){
+
+    int arr[] = {-2,3,4,-1,5,-12,6,1,3};
+    int n = sizeof(arr)/sizeof(int);
+
+    cout<<"Max Sum: "<< subArraySum_2(arr, n);
+
+    return 0;
+}
+
+
+// 3.
+#include <bits/stdc++.h>
+using namespace std;
+
+// Problem : Print largest subarray sum of a given array
+// Algotithm: Kadane's Algorithm [T(n) = O(n) Optimal Solution]
+// Space Complexity is O(1)
+
+int kadanes_algo(int *arr, int n){
+  // initial current_sum and max sum
+  int cur_sum = 0;
+  int max_sum = 0; 
+    for(int i = 0; i<n; i++){ 
+        cur_sum += arr[i];
+        if(cur_sum < 0){
+            cur_sum = 0;
+        }
+        max_sum = max(cur_sum,max_sum);
+    }
+    return max_sum;
+}
+
+
+// apprach is
+//          [-2, 3, 4, -1, 5, -12, 6, 1, 3, 2]
+//                      at idx 3 (7+-1 = 6 >0) = 6
+//                           at idx 6 (11+-12 = -1<0) = 0
+// cs =      0  3   7   6  11  0   6   7  10  12
+// ms =      0  3   7   7  11  11  11  11  11  12 = 12
+// Finding out the larget sum of subarray
+int main(){
+
+    int arr[] = {-2,3,4,-1,5,-12,6,1,3};
+    int n = sizeof(arr)/sizeof(int);
+
+    cout<<"Max Sum: "<< kadanes_algo(arr, n);
+
+    return 0;
+}
\ No newline at end of file