多项式相加数据结构及实现

设有两个多项式
p1:1+2x+3x^2+5x^5+10x^100
p2:2+3x^2+4x^4+1x^5+6x^6
 其相加的结果应为
p3:3+2x+6x^2+4x^4+6x^5+6x^6+10x^100

应如何设计其数据结构和算法?

方法如下:
定义一个类Polynomial
采用SortedDictionary<int, int> Data 作为数据结构，容纳其级数和系数.

 class Polynomial
    {
      public  SortedDictionary<int, int> Data=new SortedDictionary<int,int>();
        
         public static Polynomial operator+ (Polynomial p1,Polynomial p2)
        {
         return p1.Add(p2);
        }
        public Polynomial Add(Polynomial other)
        {
            Polynomial result = new Polynomial();

            foreach (KeyValuePair<int, int> pair in this.Data)
            {
                result.Data.Add(pair.Key, pair.Value);
            }
            

            foreach (int keyItem in other.Data.Keys)
            {
                if (result.Data.ContainsKey(keyItem))
                {
                    result.Data[keyItem] = result.Data[keyItem] + other.Data[keyItem];
                }
                else
                {
                    result.Data.Add(keyItem, other.Data[keyItem]);
                }
            }

            return result;
        }

        public Polynomial(SortedDictionary<int, int> data)
        {
            this.Data = data;
        }

        public Polynomial()
        {

        }

        public override string ToString()
        {
            StringBuilder strList = new StringBuilder();
          
            foreach (KeyValuePair<int, int> pair in this.Data)
            {
                string temp = pair.Value.ToString(); ;
                if (pair.Key >=1)
                {
                    temp += "x";
                }
                if (pair.Key > 1)
                {
                    temp += "^" + pair.Key;
                }

                temp+="+";

                strList.Append(temp);

            }
            if (strList.Length >= 1)
            {
                strList.Remove(strList.Length - 1, 1);
            }

            return strList.ToString();
        }

    }

单元测试如下：

        /// <summary>
        ///Add 的测试
        ///</summary>
        [TestMethod()]
        public void AddTest()
        {
           

            SortedDictionary<int, int> obj1 = new SortedDictionary<int, int>();
            obj1.Add(0, 1);
            obj1.Add(1, 2);
            obj1.Add(2, 3);
            obj1.Add(5, 5);
            obj1.Add(100, 10);

            SortedDictionary<int, int> obj2 = new SortedDictionary<int, int>();
            obj2.Add(0, 2);
            obj2.Add(2, 3);
            obj2.Add(4, 4);
            obj2.Add(5, 1);
            obj2.Add(6, 6);

            Polynomial p1 = new Polynomial(obj1);
            Polynomial p2 = new Polynomial(obj2);

            Polynomial p3 = p1.Add(p2);

            bool succ = true;
            SortedDictionary<int,int> dic=p3.Data;
            

            if (!(dic[0] == 3))
            {
                succ = false;
            }
            if (!(dic[1] == 2))
            {
                succ = false;
            }
            if (!(dic[2] == 6))
            {
                succ = false;
            }
            if (!(dic[4] == 4))
            {
                succ = false;
            }
            if (!(dic[5] == 6))
            {
                succ = false;
            }
            if (!(dic[6] == 6))
            {
                succ = false;
            }
            if (!(dic[100] == 10))
            {
                succ = false;
            }

            Assert.AreEqual(succ, true);
            Debug.WriteLine(p1.ToString());
            Debug.WriteLine(p2.ToString());
            Debug.WriteLine(p3.ToString());

            string targetStr = "3+2x+6x^2+4x^4+6x^5+6x^6+10x^100";
            string str = p3.ToString();

            Assert.AreEqual(targetStr, str);


        }