diff --git a/20240919/CSP常考算法模板/BFS.cpp b/20240919/CSP常考算法模板/BFS.cpp
new file mode 100644
index 0000000..83620aa
--- /dev/null
+++ b/20240919/CSP常考算法模板/BFS.cpp
@@ -0,0 +1,73 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+struct node {
+    int x, y, s;
+};
+
+queue<node> q;
+int a[51][51];
+int dir[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};  // �������� 
+bool flag = false, book[51][51];
+int n, m, sx, sy, ex, ey;
+
+void bfs(int sx,int sy)
+{
+	q.push({sx, sy, 0}); // ����֮��, ������ԭ
+    book[sx][sy] = true;
+
+    while(!q.empty() && !flag) {
+        node temp = q.front();
+        q.pop();
+        for(int i=0; i<4;i++) {
+        	//����µ�λ������ 
+            int nx =  temp.x + dir[i][0];
+            int ny =  temp.y + dir[i][1];
+            //�ж��µ�λ���Ƿ�Խ�� 
+            if(nx<1 || nx > n || ny < 1 || ny > m)
+                continue;
+            // ����µ�λ����ƽ�� ���� û���߹� 
+            if(a[nx][ny]==0 && !book[nx][ny]) {
+                q.push({nx, ny, temp.s+1});
+				book[nx][ny] = true;
+				// �µ�λ���Ƿ�Ϊ�յ� 
+	            if(nx==ex && ny==ey) {
+	                flag = true;
+	                cout<<temp.s+1;
+	                break;
+	            }
+            }
+        }
+    }
+}
+
+int main() {
+
+    cin>>n>>m;
+    for(int i=1; i<=n; i++) {
+        for(int j=1; j<=m; j++) {
+            cin>>a[i][j];
+        }
+    }
+
+    cin>>sx>>sy>>ex>>ey;
+	
+	bfs(sx,sy);
+    
+	if(!flag)
+		cout<<"no"; 
+    return 0;
+}
+
+/*
+5 4
+0 0 1 0
+0 0 0 0
+0 0 1 0
+0 1 0 0
+0 0 0 1
+1 1 4 3
+
+���
+7
+*/ 
diff --git a/20240919/CSP常考算法模板/DFS.cpp b/20240919/CSP常考算法模板/DFS.cpp
new file mode 100644
index 0000000..f106c85
--- /dev/null
+++ b/20240919/CSP常考算法模板/DFS.cpp
@@ -0,0 +1,61 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int n,m,p,q,minn=INT_MAX;
+int a[51][51];
+bool book[51][51];
+// �������� 
+int dir[4][2]={ {0,1} ,  //������ 
+                {1,0} ,   //������ 
+				{0,-1},   //������ 
+				{-1,0}  } ;//������ 
+				
+void dfs(int x,int y,int step){
+	// �ж��Ƿ��յ� 
+	if(x==p && y==q){
+		minn = min(minn, step);
+		return;
+	}
+	
+	// ��֦ 
+	if(step>=minn) // ���δ���յ㲽�����Ѿ��ﵽ�򳬹���Сֵ���ͷ��ء� 
+		return;
+	
+	// ö��ÿһ������ 
+	for(int i=0; i<=3; i++){
+		//������һ��������� 
+		int nx=x+dir[i][0];
+		int ny=y+dir[i][1];
+
+        // �ж��Ƿ�Խ�� 
+		if(nx<1 || nx>n || ny<1 || ny>m) 
+		   continue;
+		
+		if(a[nx][ny]==0 && !book[nx][ny]){
+			book[nx][ny]=true;
+			dfs(nx,ny,step+1);
+			book[nx][ny]=false; // ����
+		}
+	}
+
+}
+
+int main(){
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+	
+	int i ,j,startx,starty;
+	cin>>n>>m; 
+	//�����Թ�
+	for(i=1;i<=n;i++)
+	    for(j=1;j<=m;j++)
+	        cin>>a[i][j];
+	
+	cin>>startx>>starty>>p>>q;
+
+	book[startx][starty]=true;
+	dfs(startx,starty,0);
+	
+	cout<<minn<<endl;
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/LCA_倍增.cpp b/20240919/CSP常考算法模板/LCA_倍增.cpp
new file mode 100644
index 0000000..fd88b36
--- /dev/null
+++ b/20240919/CSP常考算法模板/LCA_倍增.cpp
@@ -0,0 +1,84 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 500001;
+
+struct Edge {
+    int to; 
+    int nxt;
+} e[2*N];
+
+int n,m,s;
+int depth[N], Log[N];
+int dbl[N][20]; //�������� 
+int head[N], tot;
+
+void addEdge(int x,int y) {
+    e[++tot].to=y;
+    e[tot].nxt=head[x];
+    head[x]=tot;
+}
+
+void dfs(int cur, int fa) {
+    depth[cur]=depth[fa]+1;
+    dbl[cur][0]=fa;
+    for(int i=1; (1<<i) < depth[cur]; i++) {
+    	int mid = dbl[cur][i-1];
+    	dbl[cur][i]=dbl[mid][i-1];  // ���㱶������
+	}
+
+    for(int i=head[cur]; i>0; i=e[i].nxt) {
+        if(e[i].to != fa)  // �����ӽڵ� 
+            dfs(e[i].to, cur);
+    }
+}
+
+int lca(int x,int y) {
+	// ������������ͬһ�߶ȣ���һ����
+    if(depth[x]<depth[y]) { // �涨x���� 
+        swap(x,y);
+    }
+
+    while(depth[x]>depth[y]) {
+        x=dbl[x][Log[depth[x]-depth[y]]];
+    }
+
+    if(x==y)
+        return x;
+
+    // ������ͬʱ������������LCA����һ��Ϊֹ
+    for(int i=Log[depth[x]]; i>=0; i--)
+        if(dbl[x][i] != dbl[y][i]) {
+            x=dbl[x][i];
+            y=dbl[y][i];
+        }
+
+    return dbl[x][0];
+}
+
+/*
+�����㷨ʱ�临�Ӷ���O(nlogn)
+*/
+int main() {
+    scanf("%d%d%d",&n,&m,&s);
+    for(int i=1; i<=n-1; i++) {
+        int x,y;
+        scanf("%d%d",&x,&y);
+        addEdge(x,y);
+        addEdge(y,x);
+    }
+    dfs(s,0); // ����
+
+    // Ԥ�����������Ż�
+    for(int i=2; i<=n; i++) {
+        Log[i]=Log[i>>1] + 1;
+    }
+
+    for(int i=1; i<=m; i++) {
+        int x, y;
+        scanf("%d%d", &x, &y);
+        printf("%d\n", lca(x, y));
+    }
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表.cpp b/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表.cpp
new file mode 100644
index 0000000..049d98a
--- /dev/null
+++ b/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表.cpp	
@@ -0,0 +1,87 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 500001;
+
+int n,m,s;
+int depth[N], Log[N];
+int dbl[N][20];  //��������
+int tot;
+vector<int> graph[N];
+
+void dfs(int cur, int fa) {
+    //todo
+    depth[cur]=depth[fa]+1;
+    dbl[cur][0]=fa;
+    for(int i=1;(1<<i)<depth[cur];i++)
+    {
+    	int mid=dbl[cur][i-1];
+    	dbl[cur][i]=dbl[mid][i-1];
+	}
+	for(int v:graph[cur])
+	{
+		if(v!=fa)
+		{
+			dfs(v,cur);
+		}
+	}
+}
+
+int lca(int x,int y) {
+	// ������������ͬһ�߶ȣ���һ����
+    // TODO 
+	if(depth[x]<depth[y])
+	{
+		swap(x,y);
+	}
+	while(depth[x]>depth[y])
+	{
+		int h=Log[depth[x]-depth[y]];
+		x=dbl[x][h];
+	}
+	
+    if(x==y)
+        return x;
+
+    // ������ͬʱ������������LCA����һ��Ϊֹ
+    // TODO
+    int h=Log[depth[x]];
+    for(int i=h;i>=0;i--)
+    {
+    	if(dbl[x][i]!=dbl[y][i])
+    	{
+    		x=dbl[x][i];
+    		y=dbl[y][i];
+		}
+	}
+    return dbl[x][0];
+}
+
+/*
+�����㷨ʱ�临�Ӷ���O(nlogn)
+*/
+int main() {
+    scanf("%d%d%d",&n,&m,&s);
+    for(int i=1; i<=n-1; i++) {
+        int x,y;
+        scanf("%d%d",&x,&y);
+        //todo
+        graph[x].push_back(y);
+        graph[y].push_back(x);
+    }
+    dfs(s,0); // ����
+
+    // Ԥ�����������Ż�
+    for(int i=2; i<=n; i++) {
+        //todo 
+        Log[i]=Log[i/2]+1;
+    }
+
+    for(int i=1; i<=m; i++) {
+        int x,y;
+        scanf("%d%d",&x,&y);
+        printf("%d\n",lca(x,y));
+    }
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表_todo.cpp b/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表_todo.cpp
new file mode 100644
index 0000000..3bb9c75
--- /dev/null
+++ b/20240919/CSP常考算法模板/P3379【模板】LCA_倍增 -邻接表_todo.cpp	
@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 500001;
+
+int n,m,s;
+int depth[N], Log[N];
+int dbl[N][20];  //��������
+int tot;
+vector<int> graph[N];
+
+void dfs(int cur, int fa) {
+    //todo
+}
+
+int lca(int x,int y) {
+	// ������������ͬһ�߶ȣ���һ����
+    // TODO 
+
+    if(x==y)
+        return x;
+
+    // ������ͬʱ������������LCA����һ��Ϊֹ
+    // TODO
+
+    return dbl[x][0];
+}
+
+/*
+�����㷨ʱ�临�Ӷ���O(nlogn)
+*/
+int main() {
+    scanf("%d%d%d",&n,&m,&s);
+    for(int i=1; i<=n-1; i++) {
+        int x,y;
+        scanf("%d%d",&x,&y);
+        //todo
+    }
+    dfs(s,0); // ����
+
+    // Ԥ�����������Ż�
+    for(int i=2; i<=n; i++) {
+        //todo 
+    }
+
+    for(int i=1; i<=m; i++) {
+        int x,y;
+        scanf("%d%d",&x,&y);
+        printf("%d\n",lca(x,y));
+    }
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/RMQ.cpp b/20240919/CSP常考算法模板/RMQ.cpp
new file mode 100644
index 0000000..28baf7c
--- /dev/null
+++ b/20240919/CSP常考算法模板/RMQ.cpp
@@ -0,0 +1,39 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 1e6 + 5;
+const int LOGN = 20;
+
+int Log[N] = {-1}, f[N][LOGN + 1], a[N]; // f[i][j]  �洢[i, i+2^j-1]֮�����ֵ
+int n, m;
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(0), cout.tie(0);
+
+    cin>>n>>m;
+    for(int i=1; i<=n; ++i) {
+        cin>>a[i];
+    }
+
+    for(int i=1; i<=n; ++i) {
+        f[i][0]=a[i];
+        Log[i]=Log[i>>1] + 1;   // Ԥ����������Ϊ1~n��logֵ
+    }
+
+    for(int j=1; j<=LOGN; j++) {  // ע����j
+        for(int i=1; i+(1<<j)-1<=n; i++) {  // ע��Ҫ������(1<<j)
+            f[i][j]=max(f[i][j-1], f[i+(1<<(j-1))][j-1]);
+        }
+    }
+
+    for (int i = 1; i <= m; i++) {
+        int x, y;
+        cin>>x>>y;//3 8
+        int s=Log[y-x+1];
+        cout<<max(f[x][s], f[y-(1<<s)+1][s])<<endl;
+    }
+
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/二分查找_加速查询.cpp b/20240919/CSP常考算法模板/二分查找_加速查询.cpp
new file mode 100644
index 0000000..0b9d079
--- /dev/null
+++ b/20240919/CSP常考算法模板/二分查找_加速查询.cpp
@@ -0,0 +1,38 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int a[11]={5, 13, 19, 21, 37, 56, 64, 75, 80, 88, 92};
+
+int main()
+{
+	int x;
+	cin>>x;
+	int l=0,r=10;
+	int ans;
+	while(l<=r)
+	{
+		int mid=(l+r)/2;
+		if(x==a[mid])
+		{
+			cout<<mid;
+			return 0;
+		}
+		if(x<a[mid])
+		{
+			r=mid-1;
+		}
+		else
+		{
+			ans=mid;
+			l=mid+1;
+		}
+	}
+	cout<<"Not found!";
+	
+	return 0;	
+}
+
+//5
+//1 -2 3 1 -4
+
+
diff --git a/20240919/CSP常考算法模板/二分查找_满足条件的最值问题.cpp b/20240919/CSP常考算法模板/二分查找_满足条件的最值问题.cpp
new file mode 100644
index 0000000..5130ab8
--- /dev/null
+++ b/20240919/CSP常考算法模板/二分查找_满足条件的最值问题.cpp
@@ -0,0 +1,47 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int n, tmax;
+int t[10001];
+
+bool check(int k) {
+    priority_queue<int, vector<int>, greater<int> > pq;
+    for(int i=0; i<k; i++) {
+        pq.push(t[i]);
+    }
+    for(int i=k; i<n; i++) {
+        int a = pq.top();
+        pq.pop();
+        pq.push(a + t[i]);
+    }
+    while(pq.size() > 1) {
+        pq.pop();
+    }
+    return tmax >= pq.top(); 
+}
+
+int main() {
+//	freopen("cowdance.in","r",stdin);
+//	freopen("cowdance.out","w",stdout);
+//	
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+	
+	cin>>n>>tmax;
+	for(int i=0; i<n; i++) {
+		cin>>t[i];
+	}
+	int left = 1, right = n, ans = n;
+	while(left<=right) {
+		int mid = (left+right)/2;
+		if(check(mid)) {
+			ans = mid;
+			right = mid - 1;
+		} else {
+			left = mid + 1;
+		}
+	}
+	cout<<ans<<endl;
+
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/二维前缀和.cpp b/20240919/CSP常考算法模板/二维前缀和.cpp
new file mode 100644
index 0000000..a877ad6
--- /dev/null
+++ b/20240919/CSP常考算法模板/二维前缀和.cpp
@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+using namespace std;
+int x[4][5] = {{},{0,3,2,1,5},{0,7,1,2,8},{0,1,3,4,6}};
+int prefix[4][5];
+int sum[4][5];
+int main()
+{
+
+	for(int i=1;i<=3;i++)
+	{
+		for(int j=1;j<=4;j++)
+		{
+			//todo
+			prefix[i][j]=prfix[i-1][j]+prefix[i][j-1]-prefix[i-1][j-1]+x[i][j];
+		}
+	}
+	for(int i=1;i<=3;i++)
+	{
+		for(int j=1;j<=4;j++)
+		{
+			cout<<prefix[i][j]<<" ";
+		}
+		cout<<endl;
+	}
+	int a=1,b=1,A=3,B=4;
+	int ans=prefix[A][B]-prefix[A][b-1]-prefix[a-1][B]+prefix[a-1][b-1];
+	cout<<ans;
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/全排列.cpp b/20240919/CSP常考算法模板/全排列.cpp
new file mode 100644
index 0000000..4c7ced9
--- /dev/null
+++ b/20240919/CSP常考算法模板/全排列.cpp
@@ -0,0 +1,39 @@
+#include<bits/stdc++.h>
+using namespace std;
+bool book[10];  //false��ʾû�ù� 
+int a[10]; 
+
+void print()
+{
+	for(int i=1;i<=4;i++)
+	{
+		cout<<a[i]<<" ";
+	}
+	cout<<endl;
+}
+
+void dfs(int step)
+{
+	if(step==5)
+	{
+		print();
+		return ;
+	}
+	for(int i=1;i<=4;i++)
+	{
+		if(!book[i])
+		{
+			book[i]=true;
+			a[step]=i;
+			dfs(step+1);
+			book[i]=false;
+		}	
+	}	
+ } 
+
+int main()
+{
+	dfs(1);
+	
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/前缀和.cpp b/20240919/CSP常考算法模板/前缀和.cpp
new file mode 100644
index 0000000..4e15911
--- /dev/null
+++ b/20240919/CSP常考算法模板/前缀和.cpp
@@ -0,0 +1,37 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int n, a[1001], prefix[1001];
+
+int main()
+{
+	freopen("bcount.in","r",stdin);
+	freopen("bcount.out","w",stdout);
+	cin>>n;
+
+	for(int i=1; i<=n; i++)
+	{
+		cin>>a[i];
+		//todo
+		prefix[i]=prefix[i-1]+a[i];
+	}
+		
+	int ans = INT_MIN;
+	for(int i=1;i<=n;i++) //begin location
+	{
+		for(int j=i;j<=n;j++)  //end location
+		{
+			ans=max(ans,prefix[j]-prefix[i-1]);
+		}
+	}
+	
+
+	cout<<ans<<endl;
+	
+	return 0;	
+}
+
+//5
+//1 -2 3 1 -4
+
+
diff --git a/20240919/CSP常考算法模板/区间dp/区间dp_合并石子.cpp b/20240919/CSP常考算法模板/区间dp/区间dp_合并石子.cpp
new file mode 100644
index 0000000..ebc6bbf
--- /dev/null
+++ b/20240919/CSP常考算法模板/区间dp/区间dp_合并石子.cpp
@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int a[101];
+int sum[101]; // prefix sum
+int f[101][101];
+/*
+���䶯̬�滮���ⲽ�裺
+1.���������Ʋ�dp[i][j]�ĺ���
+�����ǣ��ѵ�1�ѵ���n��ʯ�Ӻϳ�һ�ѣ���С�ĵ÷�
+dp[i][j]�ĺ��壺�ѵ�i�ѵ���j��ʯ�Ӻϳ�һ�ѣ���С�ĵ÷�
+2.���ݹ����Ƴ�dp[i][j]��״̬ת�ƹ�ʽ
+��i-j֮��ѡһ���м�ֵk�� 
+dp[i][j]=dp[i][k]+dp[k+1][j]+(sum[j]-s[i-1]);
+3.�߽����⣨�����趨dp[0][0],dp[0][j],dp[i][0],dp[i][j],dp[i][i]��ʼֵ��
+
+*/
+
+/*
+input
+7
+13
+7
+8
+16
+21
+4
+18
+
+output
+239
+*/ 
+int main() {
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+	int n;
+	cin>>n;
+	
+	for(int i=1; i<=n; i++) {
+		cin>>a[i];
+		sum[i] = sum[i-1] + a[i];
+	}
+		
+	for(int i=n-1; i>=1; i--) {		//һ��Ҫ���� 
+		for(int j=i+1; j<=n; j++) {
+			f[i][j] = INT_MAX;
+			for(int k=i; k<=j-1; k++) {
+				f[i][j] = min(f[i][j], f[i][k]+f[k+1][j] + sum[j]-sum[i-1]);
+			}
+		} 
+	}
+	
+	cout<<f[1][n]<<endl;
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/图的存储_vector.cpp b/20240919/CSP常考算法模板/图的存储_vector.cpp
new file mode 100644
index 0000000..b60eaf5
--- /dev/null
+++ b/20240919/CSP常考算法模板/图的存储_vector.cpp
@@ -0,0 +1,38 @@
+#include <bits/stdc++.h>
+using namespace std;
+vector<int> graph[101];
+
+int main()
+{
+	int n,m,x,y;
+	cin>>n>>m;
+	for(int i=1;i<=m;i++)
+	{
+		cin>>x>>y;
+		//todo
+		graph[x].push_back(y);
+		graph[y].push_back(x);
+	}
+	for(int i=1;i<=n;i++)
+	{
+		//todo
+//		for(int j=0;j<graph[i].size();j++)
+//		{
+//			cout<<graph[i][j]<<" ";
+//		}
+		for(int j:graph[i])
+		{
+			cout<<j<<" ";
+		}
+		cout<<endl;
+	}
+    return 0;
+}
+/*
+5 5
+1 2
+2 3
+3 4
+4 5
+5 1
+*/
diff --git a/20240919/CSP常考算法模板/并查集.cpp b/20240919/CSP常考算法模板/并查集.cpp
new file mode 100644
index 0000000..548d358
--- /dev/null
+++ b/20240919/CSP常考算法模板/并查集.cpp
@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+using namespace std;
+int n,m,p;
+int f[5001];
+
+int find(int x)
+{
+	if(x==f[x])
+	{
+		return x;
+	}
+	return f[x]=find(f[x]);
+}
+
+void merge(int u, int v)
+{
+	int fu=find(u);
+	int fv=find(v);
+	if(fu!=fv)
+	{
+		f[fu]=fv;
+	}
+}
+
+int main() 
+{
+    cin>>n>>m>>p;
+    for(int i=1;i<=n;i++)
+    {
+		f[i]=i; 
+	}
+	for(int i=1;i<=m;i++)
+    {
+    	int a,b;
+		cin>>a>>b;
+		merge(a,b);
+	}
+    
+    for(int i=1;i<=p;i++)
+    {
+    	int a,b;
+    	cin>>a>>b;
+    	if(find(a)==find(b))
+    	{
+    		cout<<"Yes"<<endl;
+		}
+		else
+		{
+			cout<<"No"<<endl;
+		}
+	}
+  
+
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/并查集样例程序.cpp b/20240919/CSP常考算法模板/并查集样例程序.cpp
new file mode 100644
index 0000000..f11ce9a
--- /dev/null
+++ b/20240919/CSP常考算法模板/并查集样例程序.cpp
@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+using namespace std;
+int n,m,p;
+int f[5001];
+
+int find(int x)
+{
+	if(x==f[x])
+	{
+		return x;
+	}
+	return find(f[x]);
+}
+
+void merge(int u, int v)
+{
+	int fu=find(u);
+	int fv=find(v);
+	if(fu!=fv)
+	{
+		f[fu]=fv;
+	}
+}
+
+int main() 
+{
+    cin>>n>>m>>p;
+    for(int i=1;i<=n;i++)
+    {
+		f[i]=i; 
+	}
+	for(int i=1;i<=m;i++)
+    {
+    	int a,b;
+		cin>>a>>b;
+		merge(a,b);
+	}
+    
+    for(int i=1;i<=p;i++)
+    {
+    	int a,b;
+    	cin>>a>>b;
+    	if(find(a)==find(b))
+    	{
+    		cout<<"Yes"<<endl;
+		}
+		else
+		{
+			cout<<"No"<<endl;
+		}
+	}
+  
+
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/快速幂.cpp b/20240919/CSP常考算法模板/快速幂.cpp
new file mode 100644
index 0000000..a929796
--- /dev/null
+++ b/20240919/CSP常考算法模板/快速幂.cpp
@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int b, p, k;
+
+/*
+ԭ����a*b%k=(a%k)*(b%k)%k
+�����κ�һ����Ȼ����p=2*(p/2)+p%2
+*/
+int f(int p) {
+    if(p==0)           // b^0%k
+        return 1%k;
+    int t=f(p/2)%k;
+    t=(t*t)%k;   // b^p%k=(b^(p/2))^2%k
+    if(p%2==1)
+        t=(t*b)%k;  // ���p��������b^p%k=((b^(p/2))^2)*b%k
+    return t;
+}
+
+int main(){
+    cin>>b>>p>>k;
+    int tmpb=b;
+    b%=k;
+    printf("%d^%d mod %d=%d", tmpb, p, k, f(p));
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/拓扑排序.cpp b/20240919/CSP常考算法模板/拓扑排序.cpp
new file mode 100644
index 0000000..35ec145
--- /dev/null
+++ b/20240919/CSP常考算法模板/拓扑排序.cpp
@@ -0,0 +1,36 @@
+#include<bits/stdc++.h>
+using namespace std;
+const int MAX_A=100005;
+int to[MAX_A];
+int inDegree[MAX_A];
+
+int main() {
+    int n;
+    cin>>n;
+    for (int i=1; i<=n; i++) {
+        cin>>to[i];
+        inDegree[to[i]]++;
+    }
+    queue<int> q;
+    int cnt = 0;
+    for (int i=1; i<=n; i++) {
+        if (inDegree[i]==0) {
+            q.push(i);
+            cnt++;
+        }
+    }
+    while (q.size()>0) {
+        int t=q.front();
+        q.pop();
+        int v = to[t];
+        inDegree[v]--;
+        if (inDegree[v]==0) {
+            q.push(v);
+            cnt++;
+        }
+    }
+    cout<<n-cnt<<endl;
+
+
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/最小生成树/最小生成树_Prim(稠密图)..cpp b/20240919/CSP常考算法模板/最小生成树/最小生成树_Prim(稠密图)..cpp
new file mode 100644
index 0000000..80f6335
--- /dev/null
+++ b/20240919/CSP常考算法模板/最小生成树/最小生成树_Prim(稠密图)..cpp
@@ -0,0 +1,62 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+struct edge {
+    int to, w;
+} a[10001];
+
+int dis[101];
+int ans, cnt;
+vector<edge> graph[101];
+bool visit[101];
+struct cmp  //�º���
+{
+    bool operator()(const edge &a, const edge &b) { 
+		return a.w > b.w;
+	}
+};
+priority_queue<edge, vector<edge>, cmp> pq;
+int main() {
+    int n,m,k;
+    cin>>n>>m;
+   
+     for (int j = 1; j <= m; j++) {
+       	int a,b,c;
+       	cin>>a>>b>>c;
+       	graph[a].push_back({b,c});
+       	graph[b].push_back({a,c});
+    }
+	for (int i = 1; i <= n; i++) {	
+		dis[i]=INT_MAX/2;
+	}
+	visit[1]=true;
+	for(int i=0;i<graph[1].size();i++)
+	{
+		edge e=graph[1][i];
+		dis[e.to]=e.w;
+	}
+
+    pq.push({1, 0});
+
+    while (!pq.empty()) {
+      	//todo
+    }
+    cout << ans << endl;
+    return 0;
+}
+
+/*
+6 9
+2 4 11
+3 5 13
+4 6 3
+5 6 4
+2 3 6
+4 5 7
+1 2 1
+3 4 9
+1 3 2
+*/
+
+
+
diff --git a/20240919/CSP常考算法模板/最小生成树/最小生成树_kruskal(稀疏图).cpp b/20240919/CSP常考算法模板/最小生成树/最小生成树_kruskal(稀疏图).cpp
new file mode 100644
index 0000000..bc4adfb
--- /dev/null
+++ b/20240919/CSP常考算法模板/最小生成树/最小生成树_kruskal(稀疏图).cpp
@@ -0,0 +1,82 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+struct edge {
+    int x, y, w;
+} a[10001];
+
+int f[101];
+int ans, cnt;
+
+bool cmp(edge x, edge y) { 
+	return x.w < y.w; 
+}
+
+//int getDistance(int x1, int y1, int x2, int y2) {
+//    return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);  // ���Ҫ������ƽ��
+//}
+
+int n, m;
+int find(int x) {
+    if (x == f[x]) 
+		return x;
+    return f[x]=find(f[x]);
+}
+
+void merge(int x, int y) {
+    int fx = find(x);
+    int fy = find(y);
+    if (fx != fy) {
+        //�������һ������
+        f[fy] = fx;
+    }
+}
+void kruskal()
+{
+	for (int i = 1; i <= n; i++) {
+        f[i] = i;
+    }
+    for (int i = 1; i <= m; i++) {
+        int u=a[i].x;
+        int v=a[i].y;
+        if(find(u)!=find(v))
+        {
+        	cnt++;
+        	ans+=a[i].w;
+        	merge(u,v);
+		}
+        if(cnt==n-1)
+        {
+        	break;
+		}
+    }
+}
+
+int main() {
+    
+    cin>>n>>m;
+    
+    for (int j = 1; j <= m; j++) {
+       		cin>>a[j].x>>a[j].y>>a[j].w;
+    }
+	sort(a + 1, a + m + 1, cmp);  //����
+	kruskal();
+    cout << ans << endl;
+    return 0;
+}
+
+/*
+6 9
+2 4 11
+3 5 13
+4 6 3
+5 6 4
+2 3 6
+4 5 7
+1 2 1
+3 4 9
+1 3 2
+*/
+
+
+
diff --git a/20240919/CSP常考算法模板/最短路径/单源最短路径Dijkstra.cpp b/20240919/CSP常考算法模板/最短路径/单源最短路径Dijkstra.cpp
new file mode 100644
index 0000000..c4ee647
--- /dev/null
+++ b/20240919/CSP常考算法模板/最短路径/单源最短路径Dijkstra.cpp
@@ -0,0 +1,65 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 2501;
+const int M = 15001;
+
+struct point {
+    int id;
+    int len;
+};
+
+vector<point> g[N];
+int t, c, ts, te;
+int rs, re, ci;
+int dis[N];
+bool vis[N];
+
+struct cmp  //�º���
+{
+    bool operator()(point a, point b) { 
+		return a.len > b.len;  //priority_queue�����������sort�Ĺ����෴ 
+	}
+};
+
+priority_queue<point, vector<point>, cmp> pq;
+
+void Dijkstra()
+{
+	memset(dis, 0x3f, sizeof(dis));
+    dis[ts] = 0;  // ע���� ʼ����ts������
+    pq.push({ts, 0});
+
+    while (pq.size()>0) {
+        int id = pq.top().id;  // ȡ����ǰ����Դ������ĵ�
+        pq.pop();
+
+        if (vis[id]) continue;
+        vis[id] = 1;
+
+        for (point e:g[id]) {
+        	
+            if (dis[e.id] > dis[id] + e.len) {
+                dis[e.id] = dis[id] + e.len;
+                pq.push({e.id, dis[e.id]});
+            }
+        }
+    }
+} 
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(0);
+
+    cin >> t >> c >> ts >> te;
+    for (int i = 0; i < c; i++) {
+        cin >> rs >> re >> ci;
+        g[rs].push_back({re,ci});
+        g[re].push_back({rs,ci});
+    }
+
+    Dijkstra();
+
+    cout << dis[te] << endl;
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/最短路径/单源最短路径SPFA(有负边）.cpp b/20240919/CSP常考算法模板/最短路径/单源最短路径SPFA(有负边）.cpp
new file mode 100644
index 0000000..776a56f
--- /dev/null
+++ b/20240919/CSP常考算法模板/最短路径/单源最短路径SPFA(有负边）.cpp
@@ -0,0 +1,61 @@
+#include <bits/stdc++.h>
+using namespace std;
+int dis[2501];
+bool exist[2501];//���ÿ�����Ƿ���queue�� 
+struct point
+{
+	int to;
+	int w;
+};
+int n,m,s,t;
+vector<point> graph[2501];
+
+void SPFA()
+{
+	memset(dis, 0x3f, sizeof(dis));
+    dis[s] = 0;  // ע���� ʼ����s������
+    queue<int> q;
+    q.push(s);
+    exist[s]=1;
+	 
+   	while(q.size()>0)
+   	{
+   		int from=q.front();
+		q.pop();
+		exist[from]=0;
+		for(int i=0;i<graph[from].size();i++)
+		{
+//			for(int temp:graph[from])
+				
+			int to=graph[from][i].to;
+			int w=graph[from][i].w;
+			if(dis[from]+w<dis[to])
+			{
+				dis[to]=dis[from]+w;
+				if(exist[to]==0)
+				{
+					q.push(to);
+    				exist[to]=1;
+				}	
+			}
+		}	
+	}
+} 
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(0);
+	
+    cin >> n >> m >> s >> t;
+    for (int i = 1; i <=m ; i++) {
+    	int a,b,c;
+        cin >> a >> b >> c;
+        graph[a].push_back({b,c});
+        graph[b].push_back({a,c});
+    }
+
+    SPFA(); 
+
+    cout << dis[t] << endl;
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/最短路径/多源最短路径Floyed.cpp b/20240919/CSP常考算法模板/最短路径/多源最短路径Floyed.cpp
new file mode 100644
index 0000000..605fcae
--- /dev/null
+++ b/20240919/CSP常考算法模板/最短路径/多源最短路径Floyed.cpp
@@ -0,0 +1,58 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int a[101][3];
+double f[101][101];
+int n,i,j,k,x,y,m,s,e;
+int main()
+{
+//    freopen("short.in","r",stdin);
+//    freopen("short.out","w",stdout);
+    cin >> n;
+    for (i = 1; i <= n; i++)
+        cin >> a[i][1] >> a[i][2];
+    cin >> m;
+    memset(f,0x7f,sizeof(f));        //��ʼ��f����Ϊ���ֵ
+    
+	//Ԥ������x��y�����
+//    for (i = 1; i <= m; i++)                           
+//    {
+//      	cin >> x >> y;
+//      	f[y][x] = f[x][y] = sqrt(pow(a[x][1]-a[y][1],2)+pow(a[x][2]-a[y][2],2));
+//                     //pow(x,y)��ʾx^y������x,y����Ϊdouble���ͣ�Ҫ��cmath��
+//    }
+
+    for (i = 1; i <= n; i++)
+    	f[i][i]=0;
+    cin >> s >> e;
+    for (k = 1; k <= n; k++)  //k��ʾ��ת��                   //floyed ���·�㷨
+    {
+	   for (i = 1; i <= n; i++)
+        {
+		    for (j = 1; j <= n; j++)
+            {
+            	if (f[i][k]+f[k][j] < f[i][j])
+                 f[i][j] = f[i][k] + f[k][j]; 
+			}
+        }
+	}
+    printf("%.2lf\n",f[s][e]);
+    return 0;
+}
+/*
+5 
+0 0 
+2 0 
+2 2 
+0 2 
+3 1 
+5 
+1 2 
+1 3 
+1 4 
+2 5 
+3 5 
+1 5 
+*/
+
+
diff --git a/20240919/CSP常考算法模板/树上问题_dfs.cpp b/20240919/CSP常考算法模板/树上问题_dfs.cpp
new file mode 100644
index 0000000..5a916c1
--- /dev/null
+++ b/20240919/CSP常考算法模板/树上问题_dfs.cpp
@@ -0,0 +1,54 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int MAXN = 1e5 + 5;
+
+//dep[u]����u�����
+//leaf[u]������uΪ���������У������dz���Ǹ�Ҷ�ӽڵ����ȡ�
+int n , m , rt , leaf[MAXN] , dep[MAXN];
+
+vector<int> graph[MAXN];
+
+// ���dep[u]��leaf[u]
+int dfs(int u, int fa) {  // ���ؾ���u�������Ҷ�ӽڵ����
+    dep[u] = dep[fa] + 1;
+    // u��Ҷ�ӽڵ�
+    if(graph[u].size()==1) {
+		leaf[u] = dep[u];
+        return leaf[u];
+    }
+    for(int v : graph[u]) {
+		if(v == fa) continue;
+
+        leaf[u] = min(dfs(v , u) , leaf[u]);
+    }
+    return leaf[u];
+}
+
+// �ڵ�u�ܹ������������farmer����
+int dfs2(int u, int fa) {
+    if(dep[u] - 1 >= leaf[u] - dep[u]) return 1;
+    int cnt = 0;
+    for (int v : graph[u]) {
+        if (v == fa) continue;
+        cnt += dfs2(v, u);
+    }
+    return cnt;
+}
+
+int main() {
+	// freopen("atlarge.in", "r", stdin);
+    // freopen("atlarge.out", "w", stdout);
+
+    memset(leaf , 0x3f , sizeof(leaf));
+    scanf("%d%d" , &n, &rt);
+    for(int i = 0; i < n - 1 ; i++) {
+    	int u, v;
+        scanf("%d%d" , &u , &v);
+        graph[u].push_back(v);
+		graph[v].push_back(u);
+    }
+    dfs(rt , 0);
+    printf("%d\n" , dfs2(rt, 0));
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/树状数组/树状数组( 单点修改 区间查询).cpp b/20240919/CSP常考算法模板/树状数组/树状数组( 单点修改 区间查询).cpp
new file mode 100644
index 0000000..e4d072c
--- /dev/null
+++ b/20240919/CSP常考算法模板/树状数组/树状数组( 单点修改 区间查询).cpp	
@@ -0,0 +1,46 @@
+#include <bits/stdc++.h>
+#define ll long long
+using namespace std;
+
+const int MAXN = 1e6 + 10;
+ll c[MAXN];
+int n, q, k, a, b;
+
+int lowbit(int x) {
+	return x&(-x);
+}
+
+void update(int x, int v) {
+	for(int i=x;i<=n;i+=lowbit(i))
+        c[i]+=v;
+}
+
+ll getSum(int x) {
+	ll ans=0;
+	for(int i=x; i>0; i-=lowbit(i))
+		ans+=c[i];
+	return ans;
+}
+
+int main() {
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+
+	int v;
+	cin>>n>>q;
+	for(int i=1; i<=n; i++) {
+		cin>>v;
+		update(i, v);
+	}
+
+	for(int i=1; i<=q; i++) {
+		cin>>k>>a>>b;
+		if(k==1) {
+			update(a, b);
+		} else {
+			cout<<getSum(b)-getSum(a-1)<<endl;
+		}
+	}
+
+	return 0;
+}
diff --git a/20240919/CSP常考算法模板/树状数组/树状数组.pdf b/20240919/CSP常考算法模板/树状数组/树状数组.pdf
new file mode 100644
index 0000000..7bb84f7
Binary files /dev/null and b/20240919/CSP常考算法模板/树状数组/树状数组.pdf differ
diff --git a/20240919/CSP常考算法模板/树的先序排列.cpp b/20240919/CSP常考算法模板/树的先序排列.cpp
new file mode 100644
index 0000000..2d78927
--- /dev/null
+++ b/20240919/CSP常考算法模板/树的先序排列.cpp
@@ -0,0 +1,39 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+void preOrder(string in,string post){
+	if(in.length() == 0) {
+		return;
+	}
+	char root=post[post.size()-1];
+	cout<<root; //������ڵ�
+	int k=in.find(root);
+
+	//�ݹ���������
+	preOrder(in.substr(0, k), post.substr(0, k));
+	preOrder(in.substr(k+1), post.substr(k, in.size()-k-1)); 
+}
+
+void postOrder(string pre, string in)
+{
+	if (pre.length() == 0) {
+		return;
+	}
+	char root = pre[0];
+	int k = in.find(root);
+	//�ݹ���������
+	postOrder(pre.substr(1, k), in.substr(0, k));
+	postOrder(pre.substr(k+1), in.substr(k+1));
+	putchar(root); //������ڵ�
+}
+
+int main(){
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+	
+    string inOrder, postOrder;
+    cin>>inOrder>>postOrder;
+    preOrder(inOrder, postOrder);
+    cout<<endl;
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/树的存储和搜索.cpp b/20240919/CSP常考算法模板/树的存储和搜索.cpp
new file mode 100644
index 0000000..3223528
--- /dev/null
+++ b/20240919/CSP常考算法模板/树的存储和搜索.cpp
@@ -0,0 +1,87 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+vector<int> g[200010];
+
+long long hay[200010];
+struct node
+{
+	int to;
+	long long w;
+};
+vector<node> m[200010];
+long long avg = 0;
+int ans = 0;
+int indegree[200010];
+
+void dfs(int u, int f) {
+    for (int v : g[u]) {
+        if (v != f) 
+		{
+			dfs(v, u);
+		}
+    }
+    if(hay[u]==avg)
+    	return;
+
+    ans++;
+    if (hay[u] > avg) {
+    	m[u].push_back({f, hay[u] - avg});
+        hay[f] += hay[u] - avg;
+        indegree[f]++;
+    } else {
+        hay[f] -= avg-hay[u];
+        m[f].push_back({u, avg-hay[u]});
+        indegree[u]++;
+    }
+}
+
+
+/*
+����dfs�ҵ�ÿ���߰���٣�Ȼ���и�ϸ�������ֱ�������ܳ��ָ�����
+����Ҫ����һ��bfs���ȴ�û����ȵĵ㿪ʼ�ߣ������������
+*/
+int main() {
+    int n;
+    cin >> n;
+    for (int i = 1; i <= n; i++) {
+        scanf("%lld", &hay[i]);
+        avg += hay[i];
+    }
+
+    avg /= n;
+    for (int i = 1; i < n; i++) {
+        int a, b;
+        cin>>a>>b;
+        g[a].push_back(b);
+        g[b].push_back(a);
+    }
+
+    dfs(1, 0);
+    cout << ans << endl;
+    queue<int> q;
+
+    for (int i = 1; i <= n; i++)
+    {
+		if (indegree[i] == 0) 
+		{
+			q.push(i);
+		}
+	} 
+	while(q.size()>0)
+	{
+		int cur=q.front();
+		q.pop();
+		for(node i:m[cur])
+		{
+			cout<<cur<<" "<<i.to<<" "<<i.w<<endl;
+			indegree[i.to]--;
+			if(indegree[i.to]==0)
+			{
+				q.push(i.to);
+			}
+		}
+	} 
+
+   
+}
diff --git a/20240919/CSP常考算法模板/混合背包.cpp b/20240919/CSP常考算法模板/混合背包.cpp
new file mode 100644
index 0000000..a50b2fa
--- /dev/null
+++ b/20240919/CSP常考算法模板/混合背包.cpp
@@ -0,0 +1,32 @@
+#include <bits/stdc++.h>
+using namespace std;
+int m, n;
+int w[31], c[31], p[31];
+int f[201];
+
+/*
+10 3
+2  1  0
+3  3  1
+4  5  4
+*/
+
+int main(){
+    scanf("%d%d",&m,&n);
+    for (int i = 1; i <= n; i++)
+        scanf("%d%d%d",&w[i],&c[i],&p[i]);
+    for (int i = 1; i <= n; i++)
+        if (p[i] == 0)  {                                   //��ȫ����
+            for (int j = w[i]; j <= m; j++)
+                f[j] = max(f[j], f[j-w[i]]+c[i]);
+        }
+        else {
+            for (int j = 1; j <= p[i]; j++)           //01�����Ͷ��ر���
+                for (int k = m; k >= w[i]; k--)
+                    f[k] = max(f[k],f[k-w[i]]+c[i]);
+        }
+        
+    printf("%d",f[m]); 
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/线性dp_求最长不下降序列_逆推.cpp b/20240919/CSP常考算法模板/线性dp_求最长不下降序列_逆推.cpp
new file mode 100644
index 0000000..b03762a
--- /dev/null
+++ b/20240919/CSP常考算法模板/线性dp_求最长不下降序列_逆推.cpp
@@ -0,0 +1,62 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int a[100], dp[100], trace[100];
+
+/*
+14
+13 7 9 16 38 24 37 18 44 19 21 22 63 15
+
+���
+max=8
+7 9 16 18 19 21 22 63 
+*/
+int main()
+{
+	int n;
+	cin>>n;
+	for(int i=1; i<=n; i++)
+	{
+		cin>>a[i]; // ԭʼ����
+		dp[i]=1;   // LIS 
+		trace[i]=0; // ��һ������λ��
+	}
+
+	// ��LIS
+	for(int i=n-1; i>=1; i--)
+	{
+		int maxlis=0;
+		int maxindex=0;
+		for(int j=i+1; j<=n; j++)
+		{
+			if(a[j]>a[i] && dp[j]>maxlis)
+			{
+				maxlis=dp[j];
+				maxindex=j;
+			}
+		}
+		
+		if(maxlis>0)
+		{
+			dp[i]=maxlis+1;
+			trace[i]=maxindex;
+		}
+	}
+
+	int pos=1;
+	for(int i=2; i<=n; i++)
+	{
+		if(dp[i]>dp[pos])
+			pos=i;
+	} 
+	cout<<"max="<<dp[pos]<<endl;
+	
+	// �������½�����
+	while(pos!=0)
+	{
+		cout<<a[pos]<<" ";
+		pos=trace[pos];
+	}
+	
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/线段树(区间修改，区间查询).cpp b/20240919/CSP常考算法模板/线段树(区间修改，区间查询).cpp
new file mode 100644
index 0000000..7915467
--- /dev/null
+++ b/20240919/CSP常考算法模板/线段树(区间修改，区间查询).cpp
@@ -0,0 +1,71 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define LL long long
+
+const int SIZE = 1e6;
+
+struct node{
+	int l, r;
+	LL w; // ����� 
+};
+
+node tree[4*SIZE + 1]; // ��4����С
+
+inline void build(int k, int l, int r) { // k������ǰ�ڵ���
+	tree[k].l = l;
+	tree[k].r = r;
+    if (l == r) { // Ҷ�ӽڵ� 
+        scanf("%lld", &tree[k].w);
+        return;
+    }
+    int mid = l + r >> 1;  // �൱�� (l + r) >> 1 k
+    int lc = k << 1, rc = lc | 1;
+    build(lc, l, mid); // ������
+    build(rc, mid + 1, r); // ������
+    tree[k].w = tree[lc].w + tree[rc].w;
+}
+
+// �����޸�
+inline void changePoint(int k, int x, int c) {
+    if (tree[k].l == tree[k].r) { // �ҵ�Ҷ�ӽڵ�
+        tree[k].w += c;
+        return;
+    }
+    int mid = tree[k].l + tree[k].r >> 1;
+    int lc = k << 1, rc = lc | 1;
+    if (x <= mid)
+        changePoint(lc, x, c);
+    else
+        changePoint(rc, x, c);
+    tree[k].w = tree[lc].w + tree[rc].w;
+}
+
+// �����ѯ
+inline LL queryInterval(int k, int L, int R) {
+    if (tree[k].l >= L && tree[k].r <= R)
+        return tree[k].w;
+
+    int mid = tree[k].l + tree[k].r >> 1;
+    int lc = k<<1, rc = lc | 1;
+    LL ans = 0;
+    if (L <= mid)
+        ans += queryInterval(lc, L, R);
+    if (R > mid)
+        ans += queryInterval(rc, L, R);
+    return ans;
+}
+
+int main() {
+    int n, q;
+	scanf("%d%d", &n, &q);
+    build(1, 1, n);
+    for (int i = 1; i <= q; i++) {
+        int opt, x, y;
+        scanf("%d%d%d", &opt, &x, &y);
+        if (opt == 1)
+            changePoint(1, x, y);
+        if (opt == 2)
+            printf("%lld\n", queryInterval(1, x, y));
+    }
+    return 0;
+}
diff --git a/20240919/CSP常考算法模板/背包问题_01.cpp b/20240919/CSP常考算法模板/背包问题_01.cpp
new file mode 100644
index 0000000..466d5d7
--- /dev/null
+++ b/20240919/CSP常考算法模板/背包问题_01.cpp
@@ -0,0 +1,32 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int maxm = 201, maxn = 31;
+int m, n;
+int w[maxn], c[maxn];
+int f[maxn][maxm]; 
+
+/*
+10 4
+2  1
+3  3
+4  5
+7  9
+*/
+int main(){
+	ios::sync_with_stdio(false);
+	cin.tie(0);
+	
+    cin>>m>>n;           //��������m����Ʒ����n
+    for (int i = 1; i <= n; i++)    //�ڳ�ʼ��ѭ���������֣�����һ����������ʼ��
+        cin>>w[i]>>c[i];    //ÿ����Ʒ�������ͼ�ֵ
+    for (int i = 1; i <= n; i++)    // f[i][v]��ʾǰi����Ʒ��������������v�����ż�ֵ
+        for (int v = m; v > 0; v--)
+            if (w[i] <= v)  
+				f[i][v] = max(f[i-1][v],f[i-1][v-w[i]]+c[i]);
+            else  
+				f[i][v] = f[i-1][v];
+    cout<<f[n][m]<<endl;           // f[n][m]Ϊ���Ž�
+    return 0;
+}
+
diff --git a/20240919/CSP常考算法模板/背包问题_多重.cpp b/20240919/CSP常考算法模板/背包问题_多重.cpp
new file mode 100644
index 0000000..01312d2
--- /dev/null
+++ b/20240919/CSP常考算法模板/背包问题_多重.cpp
@@ -0,0 +1,46 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int v[10001],w[10001];
+int f[6001];
+int n,m,n1;
+
+/*
+������������
+5 1000
+80 20 4
+40 50 9
+30 50 7
+40 30 6
+20 20 1
+�����������
+1040
+
+*/
+int main() {
+    scanf("%d%d",&n,&m);
+    for(int i=1;i<=n;i++){
+        int x,y,s,t=1;
+        scanf("%d%d%d",&x,&y,&s);
+        while (s>=t) {
+            v[++n1]=x*t;          //�൱��n1++;  v[n1]=x*t;
+            w[n1]=y*t;
+            s-=t;
+            t*=2;
+        }
+        //��s��2��ָ���ֶѣ�1��2��4������2^(k-1)��s-2^k+1,
+        if(s>0) {
+            v[++n1]=x*s;
+            w[n1]=y*s; 
+		}
+   	}
+   	
+   	for(int i=1;i<=n1;i++)
+        for(int j=m;j>=v[i];j--)
+           f[j]=max(f[j],f[j-v[i]]+w[i]); 
+    printf("%d\n",f[m]);
+    
+    return 0;
+}
+
+
diff --git a/20240919/CSP常考算法模板/背包问题_完全.cpp b/20240919/CSP常考算法模板/背包问题_完全.cpp
new file mode 100644
index 0000000..ea62b7b
--- /dev/null
+++ b/20240919/CSP常考算法模板/背包问题_完全.cpp
@@ -0,0 +1,20 @@
+#include <bits/stdc++.h>
+using namespace std;
+const int maxm=2001,maxn=31;
+int n,m,v,i;
+int c[maxn],w[maxn];
+int f[maxm];
+
+int main()
+{
+    scanf("%d%d",&m,&n);            //��������m����Ʒ����n
+    for(i=1;i<=n;i++) 
+        scanf("%d%d",&w[i],&c[i]);
+    for(i=1;i<=n;i++)
+        for(v=w[i];v<=m;v++)            //�� f[v]��ʾ����������v���������ֵ
+            if(f[v-w[i]]+c[i]>f[v])  
+				f[v]=f[v-w[i]]+c[i];
+    printf("max=%d\n",f[m]);         // f[m]Ϊ���Ž�
+    return 0;
+}
+