Practice Questions for Recursion | Set 1

Explain the functionality of the following functions. 

Question 1 

C

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

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C++

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

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Java

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

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Answer: The function fun() 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

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// 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);
}

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C++

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// 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

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Java

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// 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

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

Please write comments if you find any of the answers/codes incorrect, or you want to share more information about the topics discussed above.
 

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Improved By : NikSta, nishant_0073

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