using System;

public class Program

{

    // ex1

    public static bool IsPalindrom (char[] ar, int i, int k)

    {

        if (i >= k)

            return true;

        if (ar[i] != ar[k])

            return false;

        return IsPalindrom (ar, i + 1, k - 1);

    }

    // ex2

    // assumption: if the size of the array is smaller than 2 the method returns false

    public static bool IsSumPairSmaller10 (int[] ar)

    {

        return IsSumPairSmaller10(ar,ar.Length-1);

    }

    private static bool IsSumPairSmaller10 (int[] ar, int i)

    {

        if (i<1) return false;     // the size of the array is 1 or 0     

        if (i==1) return (ar[0]+ar[1]<10);      // the size of the array is 2

        return (ar[i]+ar[i-1]<10 && IsSumPairSmaller10(ar,i-1));

    }

    // ex3

    // assumption: the array is not empty

    // אם יש כמה ערכים זהים יוחזר האינדקס הגבוה יותר

    public static int IndexMinItem (int[] ar, int i)

    {

        if (i==ar.Length-1)

            return i;

        int ind = IndexMinItem (ar,i+1);

        if (ar[i]<ar[ind]) return i;

        return ind;

    }

    // ex4

    //assumption: if the size of the array is 1 than the method returns true

    //assumption: the array is not empty

    //runtime: O(n^2)

    public static bool IsItemBiggerThanSumOfRestItemsAfter (int[] ar, int i)

    {

        if (i==ar.Length-1)

            return true;

        return ar[i]>SumR(ar,i+1) && IsItemBiggerThanSumOfRestItemsAfter(ar,i+1);

    }

    private static int SumR (int[] ar, int i)

    {

       if (i == ar.Length) return 0;                       

       return (ar[i] + SumR(ar,i+1));    

    }

    public static void Main()

    {

        Console.WriteLine("Hello World");

        //char[] ar = {'a','x','a'};     // true

        //char[] ar = {'a','x','x','a'};   // true

        //char[] ar = {'a','x','b','a'};  // false

        //Console.WriteLine(IsPalindrom(ar,0,ar.Length-1));

        //int[] ar = {3,5,8,1};   //false

        //int[] ar = {3};   //false

        //int[] ar={} ;   //false

        //int[] ar = {3,5};   //true

        //int[] ar = {3,5,0,1,6};   //true

        //Console.WriteLine(IsSumPairSmaller10(ar));

        //int[] ar = {3,5,8,1,6};   //3

        //int[] ar = {5};   //0

        //int[] ar = {1,5,1,1,6};   // 3

        //Console.WriteLine(IndexMinItem(ar,0));

​

        int[] ar = {20,10,5,2,1};   //true

        //int[] ar = {1};   //true

        //int[] ar = {20,10,3,5};   //false

        Console.WriteLine(IsItemBiggerThanSumOfRestItemsAfter(ar,0));

    }

}

​

​