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中等
链表
数学
双指针

1634. 求两个多项式链表的和 🔒

English Version

题目描述

多项式链表是一种特殊形式的链表，每个节点表示多项式的一项。

每个节点有三个属性：

  • coefficient：该项的系数。项 9x4 的系数是 9 。
  • power：该项的指数。项 9x4 的指数是 4 。
  • next：指向下一个节点的指针（引用），如果当前节点为链表的最后一个节点则为 null 。

例如，多项式 5x3 + 4x - 7 可以表示成如下图所示的多项式链表：

多项式链表必须是标准形式的，即多项式必须 严格 按指数 power 的递减顺序排列（即降幂排列）。另外，系数 coefficient 为 0 的项需要省略。

给定两个多项式链表的头节点 poly1 和 poly2，返回它们的和的头节点。

PolyNode 格式：

输入/输出格式表示为 n 个节点的列表，其中每个节点表示为 [coefficient, power] 。例如，多项式 5x3 + 4x - 7 表示为： [[5,3],[4,1],[-7,0]] 。

 

示例 1：

输入：poly1 = [[1,1]], poly2 = [[1,0]]
输出：[[1,1],[1,0]]
解释：poly1 = x. poly2 = 1. 和为 x + 1.

示例 2：

输入：poly1 = [[2,2],[4,1],[3,0]], poly2 = [[3,2],[-4,1],[-1,0]]
输出：[[5,2],[2,0]]
解释：poly1 = 2x2 + 4x + 3. poly2 = 3x2 - 4x - 1. 和为 5x2 + 2. 注意，我们省略 "0x" 项。

示例 3：

输入：poly1 = [[1,2]], poly2 = [[-1,2]]
输出：[]
解释：和为 0。我们返回空链表。

 

提示：

  • 0 <= n <= 104
  • -109 <= PolyNode.coefficient <= 109
  • PolyNode.coefficient != 0
  • 0 <= PolyNode.power <= 109
  • PolyNode.power > PolyNode.next.power

解法

方法一：遍历链表

我们可以同时遍历两个链表，根据指数大小关系，将节点添加到结果链表中。

最后，如果链表 $1$ 或链表 $2$ 还有剩余节点，将其添加到结果链表中。

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为两个链表中节点数的较大值。

Python3

# Definition for polynomial singly-linked list.
# class PolyNode:
#     def __init__(self, x=0, y=0, next=None):
#         self.coefficient = x
#         self.power = y
#         self.next = next


class Solution:
    def addPoly(self, poly1: "PolyNode", poly2: "PolyNode") -> "PolyNode":
        dummy = curr = PolyNode()
        while poly1 and poly2:
            if poly1.power > poly2.power:
                curr.next = poly1
                poly1 = poly1.next
                curr = curr.next
            elif poly1.power < poly2.power:
                curr.next = poly2
                poly2 = poly2.next
                curr = curr.next
            else:
                if c := poly1.coefficient + poly2.coefficient:
                    curr.next = PolyNode(c, poly1.power)
                    curr = curr.next
                poly1 = poly1.next
                poly2 = poly2.next
        curr.next = poly1 or poly2
        return dummy.next

Java

/**
 * Definition for polynomial singly-linked list.
 * class PolyNode {
 *     int coefficient, power;
 *     PolyNode next = null;

 *     PolyNode() {}
 *     PolyNode(int x, int y) { this.coefficient = x; this.power = y; }
 *     PolyNode(int x, int y, PolyNode next) { this.coefficient = x; this.power = y; this.next =
 next; }
 * }
 */

class Solution {
    public PolyNode addPoly(PolyNode poly1, PolyNode poly2) {
        PolyNode dummy = new PolyNode();
        PolyNode curr = dummy;
        while (poly1 != null && poly2 != null) {
            if (poly1.power > poly2.power) {
                curr.next = poly1;
                poly1 = poly1.next;
                curr = curr.next;
            } else if (poly1.power < poly2.power) {
                curr.next = poly2;
                poly2 = poly2.next;
                curr = curr.next;
            } else {
                int c = poly1.coefficient + poly2.coefficient;
                if (c != 0) {
                    curr.next = new PolyNode(c, poly1.power);
                    curr = curr.next;
                }
                poly1 = poly1.next;
                poly2 = poly2.next;
            }
        }
        if (poly1 == null) {
            curr.next = poly2;
        }
        if (poly2 == null) {
            curr.next = poly1;
        }
        return dummy.next;
    }
}

C++

/**
 * Definition for polynomial singly-linked list->
 * struct PolyNode {
 *     int coefficient, power;
 *     PolyNode *next;
 *     PolyNode(): coefficient(0), power(0), next(nullptr) {};
 *     PolyNode(int x, int y): coefficient(x), power(y), next(nullptr) {};
 *     PolyNode(int x, int y, PolyNode* next): coefficient(x), power(y), next(next) {};
 * };
 */

class Solution {
public:
    PolyNode* addPoly(PolyNode* poly1, PolyNode* poly2) {
        PolyNode* dummy = new PolyNode();
        PolyNode* curr = dummy;
        while (poly1 && poly2) {
            if (poly1->power > poly2->power) {
                curr->next = poly1;
                poly1 = poly1->next;
                curr = curr->next;
            } else if (poly1->power < poly2->power) {
                curr->next = poly2;
                poly2 = poly2->next;
                curr = curr->next;
            } else {
                int c = poly1->coefficient + poly2->coefficient;
                if (c != 0) {
                    curr->next = new PolyNode(c, poly1->power);
                    curr = curr->next;
                }
                poly1 = poly1->next;
                poly2 = poly2->next;
            }
        }
        if (!poly1) {
            curr->next = poly2;
        }
        if (!poly2) {
            curr->next = poly1;
        }
        return dummy->next;
    }
};

JavaScript

/**
 * Definition for polynomial singly-linked list.
 * function PolyNode(x=0, y=0, next=null) {
 *     this.coefficient = x;
 *     this.power = y;
 *     this.next = next;
 * }
 */

/**
 * @param {PolyNode} poly1
 * @param {PolyNode} poly2
 * @return {PolyNode}
 */
var addPoly = function (poly1, poly2) {
    const dummy = new PolyNode();
    let curr = dummy;
    while (poly1 && poly2) {
        if (poly1.power > poly2.power) {
            curr.next = poly1;
            poly1 = poly1.next;
            curr = curr.next;
        } else if (poly1.power < poly2.power) {
            curr.next = poly2;
            poly2 = poly2.next;
            curr = curr.next;
        } else {
            const c = poly1.coefficient + poly2.coefficient;
            if (c != 0) {
                curr.next = new PolyNode(c, poly1.power);
                curr = curr.next;
            }
            poly1 = poly1.next;
            poly2 = poly2.next;
        }
    }
    curr.next = poly1 || poly2;
    return dummy.next;
};

C#

/**
 * Definition for polynomial singly-linked list.
 * public class PolyNode {
 *     public int coefficient, power;
 *     public PolyNode next;
 *
 *     public PolyNode(int x=0, int y=0, PolyNode next=null) {
 *         this.coefficient = x;
 *         this.power = y;
 *         this.next = next;
 *     }
 * }
 */

public class Solution {
    public PolyNode AddPoly(PolyNode poly1, PolyNode poly2) {
        PolyNode dummy = new PolyNode();
        PolyNode curr = dummy;
        while (poly1 != null && poly2 != null) {
            if (poly1.power > poly2.power) {
                curr.next = poly1;
                poly1 = poly1.next;
                curr = curr.next;
            } else if (poly1.power < poly2.power) {
                curr.next = poly2;
                poly2 = poly2.next;
                curr = curr.next;
            } else {
                int c = poly1.coefficient + poly2.coefficient;
                if (c != 0) {
                    curr.next = new PolyNode(c, poly1.power);
                    curr = curr.next;
                }
                poly1 = poly1.next;
                poly2 = poly2.next;
            }
        }
        if (poly1 == null) {
            curr.next = poly2;
        }
        if (poly2 == null) {
            curr.next = poly1;
        }
        return dummy.next;
    }
}