2603.收集树中金币

链接：2603.收集树中金币
难度：Hard
标签：树、图、拓扑排序、数组
简介：你需要收集树中所有的金币，并且回到出发节点，请你返回最少经过的边数。

题解 1 - cpp

• 编辑时间：2023-03-26
• 执行用时：632ms
• 内存消耗：206.8MB
• 编程语言：cpp
• 解法介绍：先删除所有没有金币的叶子节点，再遍历两次，删除有金币的叶子节点，剩下的节点就是所有需要遍历的节点。

class Solution {
public:
    int collectTheCoins(vector<int>& coins, vector<vector<int>>& edges) {
        int n = coins.size();
        vector<vector<int>> list(n);
        vector<int> cnts(n, 0);
        for (auto &edge : edges) {
            list[edge[0]].push_back(edge[1]);
            list[edge[1]].push_back(edge[0]);
            cnts[edge[0]] += 1;
            cnts[edge[1]] += 1;
        }
        int cur_edges = n - 1;
        queue<int> q;
        // 第一次刪除所有的无金币叶子节点
        for (int i = 0; i < n; i++) {
            if (cnts[i] == 1 && coins[i] == 0) q.push(i); 
        }
        while (q.size()) {
            int idx = q.front();
            q.pop();
            cur_edges -= 1;
            for (auto &next : list[idx]) {
                cnts[next] -= 1;
                if (cnts[next] == 1 && coins[next] == 0) q.push(next);
            }
        }
        // 第二次寻找所有的叶子金币节点
        for (int i = 0; i < n; i++) {
            if (cnts[i] == 1 && coins[i] == 1) q.push(i);
        }
        cur_edges -= q.size();
        while (q.size()) {
            int idx = q.front();
            q.pop();
            for (auto &next : list[idx]) {
                cnts[next] -= 1;
                if (cnts[next] == 1) {
                    cnts[next] -= 1;
                    cur_edges -= 1;
                }
            }
        }
        return max(cur_edges * 2, 0);
    }
};

题解 2 - python

• 编辑时间：2023-03-26
• 执行用时：256ms
• 内存消耗：27.6MB
• 编程语言：python
• 解法介绍：同上。

class Solution:
    def collectTheCoins(self, coins: List[int], edges: List[List[int]]) -> int:
        n = len(coins)
        l = [[] for _ in range(n)]
        cnts = [0] * n
        for edge in edges:
            l[edge[0]].append(edge[1])
            l[edge[1]].append(edge[0])
            cnts[edge[0]] += 1
            cnts[edge[1]] += 1
        cur_edges = n - 1
        q = deque()
        for i in range(n):
            if cnts[i] == 1 and coins[i] == 0:
                q.append(i)
        while len(q):
            idx = q.popleft()
            cur_edges -= 1
            for ne in l[idx]:
                cnts[ne] -= 1
                if cnts[ne] == 1 and coins[ne] == 0:
                    q.append(ne)
        for i in range(n):
            if cnts[i] == 1 and coins[i] == 1:
                q.append(i)
        cur_edges -= len(q)
        while len(q):
            idx = q.popleft()
            for ne in l[idx]:
                cnts[ne] -= 1
                if cnts[ne] == 1:
                    cnts[ne] -= 1
                    cur_edges -= 1
        return max(cur_edges * 2, 0)

题解 3 - rust

• 编辑时间：2023-03-26
• 执行用时：52ms
• 内存消耗：5.2MB
• 编程语言：rust
• 解法介绍：同上。

impl Solution {
    pub fn collect_the_coins(coins: Vec<i32>, edges: Vec<Vec<i32>>) -> i32 {
        let n = coins.len();
        let mut list = vec![vec![]; n];
        let mut cnts = vec![0; n];
        for edge in edges {
            list[edge[0] as usize].push(edge[1]);
            list[edge[1] as usize].push(edge[0]);
            cnts[edge[0] as usize] += 1;
            cnts[edge[1] as usize] += 1;
        }
        let mut cur_edges = n - 1;
        let mut q = std::collections::VecDeque::<usize>::new();
        for i in 0..n {
            if cnts[i] == 1 && coins[i] == 0 {
                q.push_back(i);
            }
        }
        while !q.is_empty() {
            let idx = q.pop_front().unwrap();
            cur_edges -= 1;
            for next in list[idx].iter() {
                let next = *next as usize;
                cnts[next] -= 1;
                if cnts[next] == 1 && coins[next] == 0 {
                    q.push_back(next)
                }
            }
        }
        for i in 0..n {
            if cnts[i] == 1 && coins[i] == 1 {
                q.push_back(i);
            }
        }
        cur_edges -= q.len();
        while !q.is_empty() {
            let idx = q.pop_front().unwrap();
            for next in list[idx].iter() {
                let next = *next as usize;
                cnts[next] -= 1;
                if cnts[next] == 1 {
                    cnts[next] -= 1;
                    cur_edges -= 1;
                }
            }
        }
        0.max(2 * cur_edges as i32)
    }
}

题解 4 - python

• 编辑时间：2023-09-21
• 执行用时：3812ms
• 内存消耗：28.9MB
• 编程语言：python
• 解法介绍：同上。

class Solution:
    def collectTheCoins(self, coins: List[int], edges: List[List[int]]) -> int:
        n = len(edges) + 1
        nodes: List[List[int]] = [[] for _ in range(n)]
        for [n1, n2] in edges:
            nodes[n1].append(n2)
            nodes[n2].append(n1)
        egde_sum = n - 1
        # 把叶子没金币的删掉
        q = deque(i for i in range(n) if len(nodes[i]) == 1 and coins[i] == 0)
        while q:
            cur = q.pop()
            for idx in nodes[cur]:
                egde_sum -= 1
                nodes[idx].remove(cur)
                if len(nodes[idx]) == 1 and coins[idx] == 0:
                    q.append(idx)
        # 遍历所有叶子有金币的
        q = deque(i for i in range(n) if len(nodes[i]) == 1 and coins[i] == 1)
        while q:
            cur = q.pop()
            egde_sum -= 1
            for idx in nodes[cur]:
                nodes[idx].remove(cur)
                # 如果他只剩一条边，那就也可以不遍历他
                if len(nodes[idx]) == 1:
                    egde_sum -= 1
        return max(egde_sum * 2, 0)