实例3-1 树的同构

最新推荐文章于 2025-08-25 09:41:13 发布

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本文介绍了一种使用结构数组实现的二叉树存储结构，并通过输入两组二叉树的数据来判断它们是否同构。代码实现了二叉树的创建及同构性的检查，适合用于理解二叉树的基本操作及递归算法。

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

/*
8
A 1 2
B 3 4
C 5 -
D - -
E 6 -
G 7 -
F - -
H - -
8
G - 4
B 7 6
F - -
A 5 1
H - -
C 0 -
D - -
E 2 -
*/

// 二叉树的存储结构：结构数组，也叫静态链表
#define ElementType char
#define MaxSize 10
#define Tree int
#define Null -1
struct TreeNode {
    ElementType Data;
    Tree Left;
    Tree Right;
} Tree1[MaxSize], Tree2[MaxSize];

// 建立二叉树
Tree BuildTree(struct TreeNode T[]) {
    int N, i;
    char cl, cr;
    Tree Root = -1;
    scanf("%d\n", &N);
    int *check = (int*)malloc(N*sizeof(int));

    if (N) {
        for (i = 0; i < N; i++) check[i] = 0;
        for (i = 0; i < N; i++) {
            scanf("\n%c %c %c\n", &T[i].Data, &cl, &cr);
            if (cl != '-') {
                T[i].Left = cl - '0';
                check[T[i].Left] = 1;
            }
            else T[i].Left = Null;

            if (cr != '-') {
                T[i].Right = cr - '0';
                check[T[i].Right] = 1;
            }
            else T[i].Right = Null;
        }
        for (i = 0; i < N; i++) {
            if (!check[i]) break;
        }
        Root = i;
    }
    return Root;
}

int Isomorphic(Tree R1, Tree R2) {
    if ((R1 == Null) && (R2 == Null)) return 1;
    if ((R1 == Null) && (R2 != Null) || ((R1 != Null) && (R2 == Null))) return 0;
    if (Tree1[R1].Data != Tree2[R2].Data) return 0;
    if (Tree1[R1].Left == Null && Tree2[R2].Left == Null)
        Isomorphic(Tree1[R1].Right, Tree2[R2].Right);
    if (Tree1[R1].Right == Null && Tree2[R2].Right == Null)
        Isomorphic(Tree1[R1].Left, Tree2[R2].Left);
    if ((Tree1[R1].Left != Null && Tree2[R2].Left != Null) && (Tree1[Tree1[R1].Left].Data == Tree2[Tree2[R1].Left].Data))
        return Isomorphic(Tree1[R1].Left, Tree2[R2].Left) && Isomorphic(Tree1[R1].Right, Tree2[R2].Right);
    else
        return Isomorphic(Tree1[R1].Left, Tree2[R2].Right) && Isomorphic(Tree1[R1].Left, Tree2[R2].Right);
}

int main() {
    Tree tree1, tree2;
    tree1 = BuildTree(Tree1);
    tree2 = BuildTree(Tree2);
    if (Isomorphic(tree1, tree2))
        printf("YES!\n");
    else
        printf("NO!\n");
    return 0;
}