洛谷 P3884 二叉树问题

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#C语言 #Python #结构体 #二叉树

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本文探讨了如何使用C语言和Python分别实现二叉树的深度优先遍历和广度优先遍历，涉及结构体定义、节点操作和相关数据结构。通过实例展示了计算最大深度和宽度的方法，并在最后给出一个查找两个节点在树中最近公共祖先的算法。

题目：https://www.luogu.com.cn/problem/P3884

C语言代码：

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

struct BinTree
{
    int left, right;
    int deep, fa;
};

struct BinTree bt[105];
int t[105], width[105], fa[105][105];//fa[x,y]:xÔÚµÚy²ãµÄ×æÏÈ
int MaxW = 0, MaxD = 0;

int max(int x, int y)
{
    if (x > y)
        return x;
    else
        return y;
}

void build(int x, int y)
{
    int i;

    if (t[y]==0)
    {
        bt[x].left = y;
        t[x] = 1;
    }
    else
    {
        bt[x].right = y;
    }

    bt[y].deep = bt[x].deep + 1;
    width[bt[y].deep]++;
    MaxW = max(width[bt[y].deep], MaxW);
    MaxD = max(bt[y].deep, MaxD);

    for (i = 1; i <= bt[x].deep; i++)
        fa[y][i] = fa[x][i];
    fa[y][bt[y].deep] = y;

}

int find(int x, int y)
{
    int i;

    i = bt[y].deep;
    while (fa[x][i] != fa[y][i])
    {
        i--;
    }
    return i;
}

int main()
{
    int i, n, x, y, z;

    scanf("%d", &n);

    memset(t, 0, sizeof(t));
    memset(width, 0, sizeof(width));
    bt[1].deep = 1;
    fa[1][1] = 1;
    width[1] = 1;
    for (i = 1; i < n; i++)
    {
        scanf("%d%d", &x, &y);
        build(x, y);
    }

    scanf("%d%d", &x, &y);
    if (bt[x].deep > bt[y].deep)
        z = find(x, y);
    else
        z = find(y, x);

    printf("%d\n%d\n", MaxD, MaxW);
    printf("%d\n", (bt[x].deep - z)*2 + bt[y].deep - z);

    return 0;
}

Python：

数组初始化：

NodeList = [BinTree() for i in range(n+1)]
width = [0 for i in range(n+1)]
fa = [[0 for i in range(n+1)] for j in range(n+1)]

定义结构体：

class BinTree(object):
    def __init__(self):
        self.left = None
        self.right = None
        self.deep = None

None表示没有初始值

定义变量：

x = BinTree()
x.left = ...

代码：

class BinTree(object):
    def __init__(self):
        self.left = None
        self.right = None
        self.deep = None
def build(x, y):
    global MaxD, MaxW

    if NodeList[x].left == None:
        NodeList[x].left = y
    else:
        NodeList[x].right = y
    NodeList[y].deep = NodeList[x].deep + 1
    width[NodeList[y].deep] += 1
    MaxD = max(MaxD, NodeList[y].deep)
    MaxW = max(MaxW, width[NodeList[y].deep])
    for i in range(1, NodeList[x].deep + 1):
        fa[y][i] = fa[x][i]
#        print(y, i, fa[y][i])
    fa[y][NodeList[y].deep] = y
#    print(y, NodeList[y].deep, fa[y][NodeList[y].deep])


def find(x, y):
    i = NodeList[y].deep
    while fa[x][i] != fa[y][i]:
        i -= 1
    return i

n = eval(input())
MaxD = 0
MaxW = 0
NodeList = [BinTree() for i in range(n+1)]
width = [0 for i in range(n+1)]
fa = [[0 for i in range(n+1)] for j in range(n+1)]

NodeList[1].deep = 1
fa[1][1] = 1
width[1] = 1

for i in range(n - 1):
    s = input()
    x = s.split(' ')
    build(eval(x[0]), eval(x[1]))

s = input()
y = s.split(' ')
x1 = eval(y[0])
y1 = eval(y[1])
if NodeList[x1].deep > NodeList[y1].deep:
    z = find(x1, y1)
else:
    z = find(y1, x1)
print(MaxD)
print(MaxW)
print((NodeList[x1].deep - z) * 2 + NodeList[y1].deep - z)