数据结构中的多项式相加C语言

在C语言中，实现多项式相加可以使用链表数据结构来表示多项式。每个节点表示一个项，包含系数和指数两个属性。

首先，我们需要定义一个节点结构体来表示多项式的每一项：

typedef struct Node {
    int coefficient;  // 系数
    int exponent;     // 指数
    struct Node* next;  // 指向下一个节点的指针
} Node;

然后，我们可以定义一个函数来创建一个多项式的链表：

Node* createNode(int coefficient, int exponent) {
    Node* newNode = (Node*)malloc(sizeof(Node));
    newNode->coefficient = coefficient;
    newNode->exponent = exponent;
    newNode->next = NULL;
    return newNode;
}

Node* createPolynomial() {
    Node* head = NULL;
    int coefficient, exponent;
    int numTerms;

    printf("请输入多项式的项数：");
    scanf("%d", &numTerms);

    for (int i = 0; i < numTerms; i++) {
        printf("请输入第%d项的系数和指数：", i + 1);
        scanf("%d %d", &coefficient, &exponent);

        Node* newNode = createNode(coefficient, exponent);

        if (head == NULL) {
            head = newNode;
        } else {
            Node* current = head;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
    }

    return head;
}

接下来，我们可以定义一个函数来实现多项式相加：

Node* addPolynomials(Node* poly1, Node* poly2) {
    Node* result = NULL;
    Node* current1 = poly1;
    Node* current2 = poly2;

    while (current1 != NULL && current2 != NULL) {
        if (current1->exponent > current2->exponent) {
            Node* newNode = createNode(current1->coefficient, current1->exponent);
            if (result == NULL) {
                result = newNode;
            } else {
                Node* current = result;
                while (current->next != NULL) {
                    current = current->next;
                }
                current->next = newNode;
            }
            current1 = current1->next;
        } else if (current1->exponent < current2->exponent) {
            Node* newNode = createNode(current2->coefficient, current2->exponent);
            if (result == NULL) {
                result = newNode;
            } else {
                Node* current = result;
                while (current->next != NULL) {
                    current = current->next;
                }
                current->next = newNode;
            }
            current2 = current2->next;
        } else {
            int sum = current1->coefficient + current2->coefficient;
            if (sum != 0) {
                Node* newNode = createNode(sum, current1->exponent);
                if (result == NULL) {
                    result = newNode;
                } else {
                    Node* current = result;
                    while (current->next != NULL) {
                        current = current->next;
                    }
                    current->next = newNode;
                }
            }
            current1 = current1->next;
            current2 = current2->next;
        }
    }

    // 将剩余的项添加到结果中
    while (current1 != NULL) {
        Node* newNode = createNode(current1->coefficient, current1->exponent);
        if (result == NULL) {
            result = newNode;
        } else {
            Node* current = result;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
        current1 = current1->next;
    }

    while (current2 != NULL) {
        Node* newNode = createNode(current2->coefficient, current2->exponent);
        if (result == NULL) {
            result = newNode;
        } else {
            Node* current = result;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
        current2 = current2->next;
    }

    return result;
}

最后，我们可以定义一个函数来打印多项式：

void printPolynomial(Node* poly) {
    Node* current = poly;

    while (current != NULL) {
        printf("%dx^%d ", current->coefficient, current->exponent);
        if (current->next != NULL) {
            printf("+ ");
        }
        current = current->next;
    }

    printf("\n");
}

使用上述函数，我们可以实现多项式相加的功能。以下是一个示例程序：

#include <stdio.h>
#include <stdlib.h>

typedef struct Node {
    int coefficient;  // 系数
    int exponent;     // 指数
    struct Node* next;  // 指向下一个节点的指针
} Node;

Node* createNode(int coefficient, int exponent) {
    Node* newNode = (Node*)malloc(sizeof(Node));
    newNode->coefficient = coefficient;
    newNode->exponent = exponent;
    newNode->next = NULL;
    return newNode;
}

Node* createPolynomial() {
    Node* head = NULL;
    int coefficient, exponent;
    int numTerms;

    printf("请输入多项式的项数：");
    scanf("%d", &numTerms);

    for (int i = 0; i < numTerms; i++) {
        printf("请输入第%d项的系数和指数：", i + 1);
        scanf("%d %d", &coefficient, &exponent);

        Node* newNode = createNode(coefficient, exponent);

        if (head == NULL) {
            head = newNode;
        } else {
            Node* current = head;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
    }

    return head;
}

Node* addPolynomials(Node* poly1, Node* poly2) {
    Node* result = NULL;
    Node* current1 = poly1;
    Node* current2 = poly2;

    while (current1 != NULL && current2 != NULL) {
        if (current1->exponent > current2->exponent) {
            Node* newNode = createNode(current1->coefficient, current1->exponent);
            if (result == NULL) {
                result = newNode;
            } else {
                Node* current = result;
                while (current->next != NULL) {
                    current = current->next;
                }
                current->next = newNode;
            }
            current1 = current1->next;
        } else if (current1->exponent < current2->exponent) {
            Node* newNode = createNode(current2->coefficient, current2->exponent);
            if (result == NULL) {
                result = newNode;
            } else {
                Node* current = result;
                while (current->next != NULL) {
                    current = current->next;
                }
                current->next = newNode;
            }
            current2 = current2->next;
        } else {
            int sum = current1->coefficient + current2->coefficient;
            if (sum != 0) {
                Node* newNode = createNode(sum, current1->exponent);
                if (result == NULL) {
                    result = newNode;
                } else {
                    Node* current = result;
                    while (current->next != NULL) {
                        current = current->next;
                    }
                    current->next = newNode;
                }
            }
            current1 = current1->next;
            current2 = current2->next;
        }
    }

    // 将剩余的项添加到结果中
    while (current1 != NULL) {
        Node* newNode = createNode(current1->coefficient, current1->exponent);
        if (result == NULL) {
            result = newNode;
        } else {
            Node* current = result;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
        current1 = current1->next;
    }

    while (current2 != NULL) {
        Node* newNode = createNode(current2->coefficient, current2->exponent);
        if (result == NULL) {
            result = newNode;
        } else {
            Node* current = result;
            while (current->next != NULL) {
                current = current->next;
            }
            current->next = newNode;
        }
        current2 = current2->next;
    }

    return result;
}

void printPolynomial(Node* poly) {
    Node* current = poly;

    while (current != NULL) {
        printf("%dx^%d ", current->coefficient, current->exponent);
        if (current->next != NULL) {
            printf("+ ");
        }
        current = current->next;
    }

    printf("\n");
}

int main() {
    printf("请输入第一个多项式：\n");
    Node* poly1 = createPolynomial();

    printf("请输入第二个多项式：\n");
    Node* poly2 = createPolynomial();

    Node* result = addPolynomials(poly1, poly2);

    printf("相加后的多项式为：");
    printPolynomial(result);

    return 0;
}

希望以上代码能够帮助到你！如果有任何问题，请随时提问。