Practice Questions for Recursion | Set 1

Last Updated : 20 Feb, 2023

Explain the functionality of the following functions.

Question 1

C++

int fun1(int x, int y) 
{ 
    if (x == 0) 
        return y; 
    else
        return fun1(x - 1, x + y); 
}

C

int fun1(int x, int y) 
{ 
    if (x == 0) 
        return y; 
    else
        return fun1(x - 1, x + y); 
}

Java

static int fun1(int x, int y) 
{ 
    if (x == 0) 
        return y; 
    else
        return fun1(x - 1, x + y); 
}

Python3

def fun1(x, y) : 
  
    if (x == 0) : 
        return y 
    else : 
        return fun1(x - 1, x + y) 
  
# This code is contributed by divyesh072019

C#

static int fun1(int x, int y) 
{ 
    if (x == 0) 
        return y; 
    else
        return fun1(x - 1, x + y); 
} 
  
// This code is contributed by divyesh072019

Javascript

<script> 
  
function fun1(x, y) 
{ 
     if (x == 0)  
        return y 
    else 
        return fun1(x - 1, x + y) 
} 
  
// This code is contributed by gottumukkalabobby 
  
</script>

Answer: The function fun1() calculates and returns ((1 + 2 … + x-1 + x) +y), which is x(x+1)/2 + y. For example, if x is 5 and y is 2, then fun should return 15 + 2 = 17.

Question 2

C++

// minimum index finder 
  
int minIndex(int arr[], int s, int e) 
{ 
    int sml = INT32_MAX; 
    int mindex; 
    for (int i = s; i < e; i++) { 
        if (sml > arr[i]) { 
            sml = arr[i]; 
            mindex = i; 
        } 
    } 
    return mindex; 
} 
  
void fun2(int arr[], int start_index, int end_index) 
{ 
    if (start_index >= end_index) 
        return; 
    int min_index; 
    int temp; 
  
    // minIndex() returns index of minimum value in 
    // array arr[start_index...end_index]  
    min_index = minIndex(arr, start_index, end_index); 
  
    // swap the element at start_index and min_index 
    swap(arr[start_index], arr[min_index]); 
  
    fun2(arr, start_index + 1, end_index); 
} 
  
// This code is contributed by nishant_0073

C

// minimum index finder 
  
int minIndex(int arr[], int s, int e) 
{ 
    int sml = INT32_MAX; 
    int mindex; 
    for (int i = s; i < e; i++) { 
        if (sml > arr[i]) { 
            sml = arr[i]; 
            mindex = i; 
        } 
    } 
    return mindex; 
} 
  
void fun2(int arr[], int start_index, int end_index) 
{ 
    if (start_index >= end_index) 
        return; 
    int min_index; 
    int temp; 
  
    // minIndex() returns index of minimum value in 
    // array arr[start_index...end_index]  
    min_index = minIndex(arr, start_index, end_index); 
  
    temp = arr[start_index]; 
    arr[start_index] = arr[min_index]; 
    arr[min_index] = temp; 
  
    fun2(arr, start_index + 1, end_index); 
}

Java

// minimum index finder 
static int minIndex(int arr[], int s, int e) 
{ 
    int sml = Integer.MAX_VALUE; 
    int mindex = ; 
    for (int i = s; i < e; i++) { 
        if (sml > arr[i]) { 
            sml = arr[i]; 
            mindex = i; 
        } 
    } 
    return mindex; 
} 
  
static void fun2(int arr[], int start_index, int end_index) 
{ 
    if (start_index >= end_index) 
        return; 
    int min_index; 
    int temp; 
  
    // minIndex() returns index of minimum value in 
    //   array arr[start_index...end_index] 
    min_index = minIndex(arr, start_index, end_index); 
  
    temp = arr[start_index]; 
    arr[start_index] = arr[min_index]; 
    arr[min_index] = temp; 
  
    fun2(arr, start_index + 1, end_index); 
} 
  
// This code is contributed by nishant_0073

Python3

# Minimum index finder 
def minIndex(arr, s, e): 
      
    sml = sys.maxsize 
    mindex = 0
      
    for i in range(s, e): 
        if (sml > arr[i]): 
            sml = arr[i] 
            mindex = i 
              
    return mindex 
  
def fun2(arr, start_index, end_index): 
      
    if (start_index >= end_index): 
        return
          
    # minIndex() returns index of minimum value in 
    # array arr[start_index...end_index] 
    min_index = minIndex(arr, start_index, end_index) 
    arr[start_index], arr[min_index] = arr[min_index], arr[start_index] 
    fun2(arr, start_index + 1, end_index) 
  
# This code is contributed by rag2127

C#

// minimum index finder 
static int minIndex(int[] arr, int s, int e) 
{ 
    int sml = Int32.MaxValue; 
    int mindex; 
    for(int i = s; i < e; i++) 
    { 
        if(sml > arr[i]) 
        { 
            sml = arr[i]; 
            mindex = i; 
        } 
    } 
    return mindex;    
} 
static void fun2(int[] arr, int start_index, int end_index)     
{ 
    if(start_index >= end_index) 
    { 
        return; 
    } 
    int min_index; 
    int temp; 
    
    // minIndex() returns index of minimum value in 
    //   array arr[start_index...end_index] 
    min_index = minIndex(arr, start_index, end_index); 
    temp = arr[start_index]; 
    arr[start_index] = arr[min_index]; 
    arr[min_index] = temp; 
   
    fun2(arr, start_index + 1, end_index); 
} 
  
// This code is contributed by avanitrachhadiya2155 

Javascript

<script> 
//Javascript Implementation 
// minimum index finder 
   
function minIndex(arr, s, e) 
{ 
    var sml = Number.MAX_SAFE_INTEGER; 
    var mindex; 
    for (int i = s; i < e; i++) { 
        if (sml > arr[i]) { 
            sml = arr[i]; 
            mindex = i; 
        } 
    } 
    return mindex; 
} 
   
function fun2(arr, start_index, end_index) 
{ 
    if (start_index >= end_index) 
        return; 
    var min_index; 
    var temp; 
   
    // minIndex() returns index of minimum value in 
    // array arr[start_index...end_index] 
    min_index = minIndex(arr, start_index, end_index); 
   
    // swap the element at start_index and min_index 
    temp = arr[start_index]; 
    arr[start_index] = arr[min_index]; 
    arr[min_index] = temp; 
   
    fun2(arr, start_index + 1, end_index); 
} 
// This code is contributed by shubhamsingh10 
</script>

Answer: The function fun2() is a recursive implementation of Selection Sort.

Time complexity: O(N²)

Auxiliary Space: O(1)

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