Correcting a spelling mistake (#19845)

* Correcting a spelling mistake

* Formatting and adding missing code

* Removing extra code

* Update index.md

guide/english/algorithms/search-algorithms/binary-search/index.md

@@ -85,7 +85,7 @@ The two base cases for recursion would be:
 * Item is found
 
 The Power of Binary Search in Data Systems (B+ trees):
-Binary Search Trees are very powerful because of their O(log n) search times, second to the hashmap data structure which uses a hasing key to search for data in O(1). It is important to understand how the log n run time comes from the height of a binary search tree. If each node splits into two nodes, (binary), then the depth of the tree is log n (base 2).. In order to improve this speed in Data System, we use B+ trees because they have a larger branching factor, and therefore more height. I hope this short article helps expand your mind about how binary search is used in practical systems.
+Binary Search Trees are very powerful because of their O(log n) search times, second to the hashmap data structure which uses a hashing key to search for data in O(1). It is important to understand how the log n run time comes from the height of a binary search tree. If each node splits into two nodes, (binary), then the depth of the tree is log n (base 2).. In order to improve this speed in Data System, we use B+ trees because they have a larger branching factor, and therefore more height. I hope this short article helps expand your mind about how binary search is used in practical systems.
 
 The code for recursive binary search is shown below:
 
@@ -165,7 +165,7 @@ end
 ```C
 int binarySearch(int a[], int l, int r, int x) {
    if (r >= l){
-        int mid = l + (r - l)/2; 
+        int mid = (l + (r - l))/2;
         if (a[mid] == x)
             return mid;
         if (arr[mid] > x)
@@ -181,7 +181,7 @@ int binarySearch(int a[], int l, int r, int x) {
 ```Python
 def binary_search(arr, l, r, target):
     if r >= l:
-        mid = l + (r - l)/2
+        mid = (l + (r - l))/2
         if arr[mid] == target:
             return mid
         elif arr[mid] > target:
@@ -197,12 +197,13 @@ def binary_search(arr, l, r, target):
 
 Recursive approach!
 
-```C++ - Recursive approach
+```C++ -
+// Recursive approach in C++
 int binarySearch(int arr[], int start, int end, int x)
 {
    if (end >= start)
    {
-        int mid = start + (end - start)/2; 
+        int mid = (start + (end - start))/2;
         if (arr[mid] == x)
             return mid;
 
@@ -222,7 +223,7 @@ int binarySearch(int arr[], int start, int end, int x)
 {
     while (start <= end)
     {
-        int mid = start + (end - start)/2; 
+        int mid = (start + (end - start))/2;
         if (arr[mid] == x)
             return mid;
         if (arr[mid] < x)
@@ -274,14 +275,18 @@ int binarySearch(int[] arr, int start, int end, int element)
 // Recursive Approach in Java
 int binarySearch(int[] arr, int start,int end , int element)
 {
-    int mid = ( start + end ) / 2;
-    if(arr[mid] ==  element)
-        return mid;
-    if(arr[mid] < element)
-        return binarySearch( arr , mid + 1 , end , element );
-    else
-        return binarySearch( arr, start, mid - 1 , element);
-}
+    if(start <= end)
+    {
+        int mid = ( start + end ) / 2;
+        if(arr[mid] ==  element)
+                return mid;
+        if(arr[mid] < element)
+                return binarySearch( arr , mid + 1 , end , element );
+        else
+                return binarySearch( arr, start, mid - 1 , element);
+     }
+     return -1;
+ }
 
 ```
 

guide/english/c/arrays-and-strings/index.md

@@ -118,12 +118,12 @@ void copy_string(char [] first_string, char [] second_string)
 ```C
 strcat(first, second);
 ```
-Here is an example of manual implementation of fuction strcat:
+Here is an example of manual implementation of function strcat:
 
 void string_concatenate(char [] s1, char [] s2)
 {
     int i = strlen(s1), j;
-    for(int j = 0; s2[j]; j++, i += 1)
+    for(j = 0; s2[j]; j++, i += 1)
     {
         s1[i] = s2[j];
     }
@@ -140,7 +140,7 @@ int string_length(char [] string)
 {
     int i;
     
-    for(int i = 0; string[i]; i++);
+    for(i = 0; string[i]; i++);
     
     return i;
 }

guide/english/c/structured-data-types/index.md

@@ -53,7 +53,7 @@ point img_dim = { .y = 480, .x = 640 };
 ```
 
 ## Unions vs Structures
-Unions are declared in the same was as structs, but are different because only one item within the union can be used at any time.
+Unions are declared in the same way as structs, but are different because only one item within the union can be used at any time.
 
 ```C
 typedef union{
@@ -83,6 +83,6 @@ typedef union{
 ```
 
 ## A few more tricks
-* When you create a pointer to a structure using the `&` operator you can use the special `->` infix operator to deference it. This is very used for example when working with linked lists in C
+* When you create a pointer to a structure using the `&` operator you can use the special `->` infix operator to deference it. This is used for example when working with linked lists in C
 * The new defined type can be used just as other basic types for almost everything. Try for example to create an array of type `student` and see how it works.
 * Structs can be copied or assigned but you can not compare them!