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Jul 6, 2025
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[pull] master from youngyangyang04:master #3

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3 changes: 1 addition & 2 deletions problems/0042.接雨水.md
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Expand Up @@ -14,8 +14,7 @@

示例 1：

![](https://code-thinking-1253855093.cos.ap-guangzhou.myqcloud.com/pics/20210713205038.png)

![image](https://file1.kamacoder.com/i/algo/2025-07-04_12-06-59.jpg)
* 输入：height = [0,1,0,2,1,0,1,3,2,1,2,1]
* 输出：6
* 解释：上面是由数组 [0,1,0,2,1,0,1,3,2,1,2,1] 表示的高度图，在这种情况下，可以接 6 个单位的雨水（蓝色部分表示雨水）。
Expand Down
1 change: 0 additions & 1 deletion problems/kamacoder/0044.开发商购买土地.md
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Expand Up @@ -613,4 +613,3 @@ func main() {
}
```

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0047.参会dijkstra堆.md
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Expand Up @@ -927,4 +927,3 @@ func main() {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0047.参会dijkstra朴素.md
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### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0053.寻宝-Kruskal.md
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Expand Up @@ -760,4 +760,3 @@ int main()
}

```
<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0053.寻宝-prim.md
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### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0054.替换数字.md
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Expand Up @@ -432,4 +432,3 @@ echo $s;

### Rust:

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0055.右旋字符串.md
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### Rust:

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0058.区间和.md
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Expand Up @@ -408,4 +408,3 @@ func main() {
}
```

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0094.城市间货物运输I-SPFA.md
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Expand Up @@ -536,4 +536,3 @@ main()



<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0094.城市间货物运输I.md
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Expand Up @@ -538,4 +538,3 @@ main()

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
101 changes: 97 additions & 4 deletions problems/kamacoder/0095.城市间货物运输II.md
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Expand Up @@ -183,7 +183,6 @@ struct Edge { //邻接表
Edge(int t, int w): to(t), val(w) {} // 构造函数
};


int main() {
int n, m, p1, p2, val;
cin >> n >> m;
Expand Down Expand Up @@ -229,16 +228,111 @@ int main() {
}
}
}

if (flag) cout << "circle" << endl;
else if (minDist[end] == INT_MAX) {
cout << "unconnected" << endl;
} else {
cout << minDist[end] << endl;
}

}
```

以上代码看上去没问题，但提交之后会发现报错了，为什么呢？

例如这组数据：

```
4 6
1 4 3
1 2 1
1 3 1
3 2 -2
2 4 1
3 4 0
```

如图：

![](https://file1.kamacoder.com/i/algo/2025-06-03_16-12-41.jpg)

上面代码在执行的过程中，节点4 已经出队列了，但 计算入度会反复计算 节点4的入度，导致 误判 该图有环。

我们需要记录哪些节点已经出队列了，哪些节点在队列里面，对于已经出队列的节点不用统计入度，以下为优化后的代码：

```CPP
#include <iostream>
#include <vector>
#include <queue>
#include <list>
#include <climits>
using namespace std;

struct Edge { //邻接表
int to; // 链接的节点
int val; // 边的权重

Edge(int t, int w): to(t), val(w) {} // 构造函数
};


int main() {
int n, m, p1, p2, val;
cin >> n >> m;

vector<list<Edge>> grid(n + 1); // 邻接表

// 将所有边保存起来
for(int i = 0; i < m; i++){
cin >> p1 >> p2 >> val;
// p1 指向 p2，权值为 val
grid[p1].push_back(Edge(p2, val));
}
int start = 1; // 起点
int end = n; // 终点

vector<int> minDist(n + 1 , INT_MAX);
minDist[start] = 0;

queue<int> que;
que.push(start); // 队列里放入起点

vector<int> count(n+1, 0); // 记录节点加入队列几次
count[start]++;
vector<bool> inQueue(n+1, false); // 记录节点是否在队列中

bool flag = false;
while (!que.empty()) {

int node = que.front(); que.pop();
inQueue[node] = false; // 节点出队

for (Edge edge : grid[node]) {
int from = node;
int to = edge.to;
int value = edge.val;
if (minDist[to] > minDist[from] + value) { // 开始松弛
minDist[to] = minDist[from] + value;
if (!inQueue[to]) { // 避免重复入队
que.push(to);
inQueue[to] = true;
count[to]++;
if (count[to] == n) {// 如果加入队列次数超过 n-1次 就说明该图与负权回路
flag = true;
while (!que.empty()) que.pop();
break;
}
}
}
}
}

if (flag) cout << "circle" << endl;
else if (minDist[end] == INT_MAX) {
cout << "unconnected" << endl;
} else {
cout << minDist[end] << endl;
}
}
```

## 其他语言版本
Expand Down Expand Up @@ -456,4 +550,3 @@ if __name__ == "__main__":

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0096.城市间货物运输III.md
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Expand Up @@ -922,4 +922,3 @@ if __name__ == "__main__":

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0097.小明逛公园.md
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Expand Up @@ -574,4 +574,3 @@ if __name__ == '__main__':

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
2 changes: 1 addition & 1 deletion problems/kamacoder/0098.所有可达路径.md
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Expand Up @@ -72,6 +72,7 @@
* 1 <= N <= 100
* 1 <= M <= 500

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[所有可达路径](https://www.bilibili.com/video/BV1VePeepEpP),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

## 插曲

Expand Down Expand Up @@ -887,4 +888,3 @@ async function dfs(graph, x, n) {



<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0099.岛屿的数量广搜.md
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## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：广搜有陷阱啊！！ | 广度优先搜索 | 卡码网：99.岛屿数量](https://www.bilibili.com/video/BV18PRGYcEiB/),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

注意题目中每座岛屿只能由**水平方向和/或竖直方向上**相邻的陆地连接形成。

也就是说斜角度链接是不算了， 例如示例二，是三个岛屿，如图：
Expand Down Expand Up @@ -557,4 +559,3 @@ object Solution {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0099.岛屿的数量深搜.md
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## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：来用深搜解决一道题目，两种深搜写法，你掉坑了吗？ | 卡码网：99.岛屿数量](https://www.bilibili.com/video/BV18PRGYcEiB/),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

注意题目中每座岛屿只能由**水平方向和/或竖直方向上**相邻的陆地连接形成。

也就是说斜角度链接是不算了， 例如示例二，是三个岛屿，如图：
Expand Down Expand Up @@ -459,4 +461,3 @@ object Solution {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0100.岛屿的最大面积.md
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Expand Up @@ -44,6 +44,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：深搜也有陷阱啊！！ | 深搜优先搜索 | 卡码网：100.岛屿的最大面积](https://www.bilibili.com/video/BV1FzoyY5EXH),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

注意题目中每座岛屿只能由**水平方向和/或竖直方向上**相邻的陆地连接形成。

也就是说斜角度链接是不算了， 例如示例二，是三个岛屿，如图：
Expand Down Expand Up @@ -890,4 +892,3 @@ main();

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0101.孤岛的总面积.md
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Expand Up @@ -48,6 +48,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：岛屿问题再出新花样 | 深搜优先搜索 | 卡码网：101.孤岛总面积](https://www.bilibili.com/video/BV1mmZJYRESc),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

本题使用dfs，bfs，并查集都是可以的。

本题要求找到不靠边的陆地面积，那么我们只要从周边找到陆地然后 通过 dfs或者bfs 将周边靠陆地且相邻的陆地都变成海洋，然后再去重新遍历地图 统计此时还剩下的陆地就可以了。
Expand Down Expand Up @@ -700,4 +702,3 @@ const bfs = (graph, x, y) => {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0102.沉没孤岛.md
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Expand Up @@ -55,6 +55,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：岛屿问题也需要逆向思考 | 深搜优先搜索DFS | 卡码网：102.沉没孤岛](https://www.bilibili.com/video/BV1fjdWYyEGu),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

这道题目和[0101.孤岛的总面积](https://kamacoder.com/problempage.php?pid=1173)正好反过来了，[0101.孤岛的总面积](https://kamacoder.com/problempage.php?pid=1173)是求 地图中间的空格数，而本题是要把地图中间的 1 都改成 0 。

那么两题在思路上也是差不多的。
Expand Down Expand Up @@ -503,4 +505,3 @@ const bfs = (graph, x, y) => {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0103.水流问题.md
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Expand Up @@ -59,6 +59,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：水流向何方？ | 深搜优先搜索DFS| 广度优先搜索BFS | 卡码网：103.水流问题](https://www.bilibili.com/video/BV1WNoEYrEio),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

一个比较直白的想法，其实就是 遍历每个点，然后看这个点 能不能同时到达第一组边界和第二组边界。

至于遍历方式，可以用dfs，也可以用bfs，以下用dfs来举例。
Expand Down Expand Up @@ -854,4 +856,3 @@ const isResult = (x, y) => {



<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0104.建造最大岛屿.md
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Expand Up @@ -50,6 +50,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：岛屿问题上难度了！ |深搜优先搜索DFS | 广度优先搜索BFS | 卡码网：104.建造最大岛屿](https://www.bilibili.com/video/BV1Dn5CzZEw1/),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

本题的一个暴力想法，应该是遍历地图尝试 将每一个 0 改成1，然后去搜索地图中的最大的岛屿面积。

计算地图的最大面积：遍历地图 + 深搜岛屿，时间复杂度为 n * n。
Expand Down Expand Up @@ -663,4 +665,3 @@ const dfs = (graph, visited, x, y, mark) => {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
5 changes: 3 additions & 2 deletions problems/kamacoder/0105.有向图的完全可达性.md
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@@ -1,7 +1,7 @@

<p align="center"><strong><a href="./qita/join.md">参与本项目</a>，贡献其他语言版本的代码，拥抱开源，让更多学习算法的小伙伴们受益！</strong></p>

# 105.有向图的完全可达性
# 105.有向图的完全联通

[卡码网题目链接（ACM模式）](https://kamacoder.com/problempage.php?pid=1177)

Expand Down Expand Up @@ -44,6 +44,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：这次我们能到达有向图的所有节点吗？| 深度优先搜索 | 卡码网：105. 有向图的完全联通](https://www.bilibili.com/video/BV1QRJ6ziEvJ),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

本题给我们是一个有向图， 意识到这是有向图很重要！

接下来我们再画一个图，从图里可以直观看出来，节点6 是 不能到达节点1 的
Expand Down Expand Up @@ -553,4 +555,3 @@ rl.on('close',()=>{

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
3 changes: 2 additions & 1 deletion problems/kamacoder/0106.岛屿的周长.md
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Expand Up @@ -47,6 +47,8 @@

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：这次的岛屿问题有点简单了。。 卡码网：106.岛屿的周长](https://www.bilibili.com/video/BV13fjczSEyV),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

岛屿问题最容易让人想到BFS或者DFS，但本题确实还用不上。

为了避免大家惯性思维，所以给大家安排了这道题目。
Expand Down Expand Up @@ -359,4 +361,3 @@ func parseLine(line string, count int) []int {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
1 change: 0 additions & 1 deletion problems/kamacoder/0107.寻找存在的路径.md
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Expand Up @@ -422,4 +422,3 @@ const isSame = (u, v) => {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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Expand Up @@ -596,4 +596,3 @@ const getRemoveEdge = (edges) => {

### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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Expand Up @@ -63,6 +63,8 @@ yhn

## 思路

**[《代码随想录》算法视频公开课](https://programmercarl.com/other/gongkaike.html)：[图论：朴实无华的广搜这么难？ | 广度优先搜索 | 卡码网：110.字符串接龙](https://www.bilibili.com/video/BV1QEEizDEC4),相信结合视频再看本篇题解，更有助于大家对本题的理解**。

以示例1为例，从这个图中可以看出 abc 到 def的路线 不止一条，但最短的一条路径上是4个节点。

![](https://file1.kamacoder.com/i/algo/20250317105155.png)
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### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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### C

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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Expand Up @@ -684,4 +684,3 @@ int main() {



<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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Expand Up @@ -91,4 +91,3 @@ cout << result[result.size() - 1];
等大家将图论刷完，就会感受到我的良苦用心。加油


<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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Expand Up @@ -454,4 +454,3 @@ void join(int u, int v) {

敬请期待 并查集题目精讲系列。

<div align="center"><a href="https://www.nowcoder.com/link/wx_sqlcarl199" target="_blank"><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20220416223343.png" width="1000"/></a></div>
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