1.自然数的拆分问题
思路：
使用深度优先算法，用递归拆分n即可
代码：
#include <bits/stdc++.h>
using namespace std;
vector<int> a;
void f(int remain,int start,int n)
{int j=0;if(remain==0){for(j=0;j<a.size();j++){if(j!=a.size()-1){cout<<a[j]<<"+";}else{cout<<a[j];}}cout<<endl;return;}for(int i=start;i<=remain&&i<n;i++){a.push_back(i);f(remain-i,i,n);a.pop_back();}
}
int main()
{int n,i;cin>>n;f(n,1,n);return 0;
}
2.填涂颜色
思路：
使用深度优先搜索，从边界上的0开始搜索直到遇到1，将这些0打上标记，搜索完成后剩余的0即为所求
代码：
#include <bits/stdc++.h>
using namespace std;
int arry[32][32];
void dfs(int x,int y,int n)
{if(x>=n||x<0||y>=n||y<0||arry[x][y]!=0){return;}arry[x][y]=-1;dfs(x+1,y,n);dfs(x-1,y,n);dfs(x,y+1,n);dfs(x,y-1,n);
}
int main()
{int n,i,j;cin>>n;for(i=0;i<n;i++){for(j=0;j<n;j++){cin>>arry[i][j];}}for(i=0;i<n;i++){if(arry[i][0]==0){dfs(i,0,n);}}for(i=0;i<n;i++){if(arry[i][n-1]==0){dfs(i,n-1,n);}}for(j=0;j<n;j++){if(arry[0][j]==0){dfs(0,j,n);}}for(j=0;j<n;j++){if(arry[n-1][j]==0){dfs(n-1,j,n);}}for(i=0;i<n;i++){for(j=0;j<n;j++){if(arry[i][j]==0){arry[i][j]=2;}if(arry[i][j]==-1){arry[i][j]=0;}cout<<arry[i][j]<<" ";}cout<<endl;}return 0;
}
3.显示图像
思路：
利用广度优先算法，先将白色的点的距离记为0，其余记为可能的最大值m+n，白点加入队列，取出一个扩展，如果扩展完的点距离大于1，更新距离
代码：
#include <bits/stdc++.h>
using namespace std;
int dx[4] = {-1, 1, 0, 0};
int dy[4] = {0, 0, -1, 1};
void bfs(vector<vector<int>>& screen,vector<vector<int>>& distance,int N,int M)
{queue<pair<int, int>> q;for(int i=0;i<N;i++){for(int j=0;j<M;j++) {if(screen[i][j]==1) {distance[i][j] = 0;q.push({i, j});}}}while (!q.empty()) {pair<int,int> p=q.front();q.pop();for(int k=0;k<4;k++){int nx=p.first+dx[k];int ny=p.second+dy[k];if (nx>=0&&nx<N&&ny>=0&&ny<M) {if (distance[nx][ny] > distance[p.first][p.second] + 1) {distance[nx][ny]=distance[p.first][p.second]+1;q.push({nx, ny});}}}}
}int main()
{int N,M;cin>>N>>M; vector<vector<int>> screen(N, vector<int>(M));vector<vector<int>> distance(N, vector<int>(M, N + M));char ch;ch=getchar();for(int i=0;i<N;i++) {for(int j=0;j<M;j++) {ch=getchar();if(ch=='1'){screen[i][j]=1;}if(ch=='0'){screen[i][j]=0;}}ch=getchar();}bfs(screen,distance,N,M);for(int i=0;i<N;i++) {for(int j=0;j<M;j++) {cout<<distance[i][j]<<" ";}cout<<endl;}return 0;
}
4.健康的荷斯坦奶牛 Healthy Holsteins
思路：
使用深度优先算法，得到最优解
代码：
#include <bits/stdc++.h>
using namespace std;
int v, g;
vector<int> vitamin_needs;
vector<vector<int>> feeds;
vector<int> selected;
vector<int> best_feeds;
int min_feeds = 16;
void dfs(int index, vector<int> vitamin)
{if (all_of(vitamin.begin(), vitamin.end(), [](int x) { return x <= 0; })) {if (selected.size() < min_feeds) {min_feeds = selected.size();best_feeds = selected;} else if (selected.size() == min_feeds) {if (selected < best_feeds) {best_feeds = selected;}}return;}if (index == g || selected.size() >= min_feeds) {return;}dfs(index + 1, vitamin);for (int i = 0; i < v; ++i) {vitamin[i] -= feeds[index][i];}selected.push_back(index + 1);dfs(index + 1, vitamin);selected.pop_back();
}int main()
{cin >> v;vitamin_needs.resize(v);for (int i = 0; i < v; ++i){cin >> vitamin_needs[i];}cin >> g;feeds.resize(g, vector<int>(v));for (int i = 0; i < g; ++i) {for (int j = 0; j < v; ++j) {cin >> feeds[i][j];}}dfs(0, vitamin_needs);cout << min_feeds << " ";for (int i = 0; i < best_feeds.size(); ++i) {cout << best_feeds[i] << (i == best_feeds.size() - 1 ? "\n" : " ");}return 0;
}学习总结：
通过这次的学习，我学习了深度优先搜索和广度优先搜索的相关知识，通过这两种算法可以高效的搜索图或者树中的内容
