sicily 1034. Forest

Description

In the field of computer science, forest is important and deeply researched , it is a model for many data structures . Now it’s your job here to calculate the depth and width of given forests.

Precisely, a forest here is a directed graph with neither loop nor two edges pointing to the same node. Nodes with no edge pointing to are roots, we define that roots are at level 0 . If there’s an edge points from node A to node B , then node B is called a child of node A , and we define that B is at level (k+1) if and only if A is at level k .

We define the depth of a forest is the maximum level number of all the nodes , the width of a forest is the maximum number of nodes at the same level.

Input

There’re several test cases. For each case, in the first line there are two integer numbers n and m (1≤n≤100, 0≤m≤100, m≤n*n) indicating the number of nodes and edges respectively , then m lines followed , for each line of these m lines there are two integer numbers a and b (1≤a,b≤n)indicating there’s an edge pointing from a to b. Nodes are represented by numbers between 1 and n .n=0 indicates end of input.

Output

For each case output one line of answer , if it’s not a forest , i.e. there’s at least one loop or two edges pointing to the same node, output “INVALID”(without quotation mark), otherwise output the depth and width of the forest, separated by a white space.

Sample Input

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Sample Output

0 1
INVALID
1 2
INVALID

这题主要考虑环的问题吧，还有要注意的就是单个元素自身成环和没有根节点的情况

#include <iostream>
#include <cstring>
#include <stack>
#include <vector>

using namespace std;

struct Node{
    Node(int v = -1, int l = 0):value(v), level(l) { }
    int value;
    int level;
};

int main(int argc, char const *argv[])
{
    int n, m, a, b;
    int level[101];  // 记录每层的个数
    bool visited[101];  // 用于判断是否形成环
    while (cin >> n >> m && n != 0) {
        vector<int> node[101];
        Node parent[101];  // 记录父节点

        memset(level, 0, sizeof(level));
        memset(visited, false, sizeof(visited));
        bool isSucceed = true;

        for (int i = 0; i != m; ++i) {
            cin >> a >> b;
            if (a == b) {  // 元素指向自身
                isSucceed = false;
                continue;
            }

            node[a - 1].push_back(b - 1);  // 元素值是从 1 开始的
            if (parent[b - 1].value == -1)
                parent[b - 1].value = a - 1;
            else
                isSucceed = false;
        }

        bool hasRoot = false;  // 是否有根节点
        if (isSucceed) {
            for (int i = 0; i != n; ++i) {
                if (!isSucceed)
                    break;
                if (parent[i].value == -1) {  // 从根节点遍历每一棵树
                    hasRoot = true;
                    stack<int> s;
                    s.push(i);
                    while (!s.empty()) {
                        if (!isSucceed)
                            break;
                        int current = s.top();
                        visited[current] = true;
                        if (current != i)
                            parent[current].level = parent[parent[current].value].level + 1;  // 子节点level等于父节点+1

                        s.pop();
                        for (int j = 0; j != node[current].size(); ++j) {
                            if (visited[node[current][j]]) {  // 形成了环
                                isSucceed = false;
                                break;
                            }
                            s.push(node[current][j]);
                        }
                    }
                }
            }
        }
        if (isSucceed) {
            for (int i = 0; i != n; ++i) {
                level[parent[i].level]++;
            }
        }
        if (!isSucceed || !hasRoot) {
            cout << "INVALID" << endl;
            continue;
        }

        int levelMax = -1;
        int index = -1;
        for (int i = 0; i != n; ++i) {
            if (level[i] == 0)
                break;
            if (levelMax < level[i]) {
                levelMax = level[i];
            }
            index++;
        }
        cout << index << " " << levelMax << endl;
    }

    return 0;
}