update learn RMQ st

.gitignore

@@ -52,3 +52,4 @@ day5/hard/hard
 day5/perfect/perfect
 day5/good/good
 day5/fair/fair
+day5/RMQ/st

README.md

@@ -71,6 +71,7 @@ ll ksm(ll a,ll b,ll M){
 
 # [RMQ 区间最值问题](./day5/RMQ_by_chat.md)
 >点击跳转
+[自己手动实践](./day5/RMQ/st.cpp)
 
 # 排序
 ## 稳定性

day5/RMQ/chat.cpp

@@ -0,0 +1,49 @@
+#include <iostream>
+#include <vector>
+#include <cmath>
+using namespace std;
+
+class SparseTable {
+private:
+    vector<vector<int>> st;
+    vector<int> log;
+    int n;
+
+public:
+    SparseTable(const vector<int>& arr) {
+        n = arr.size();
+        int K = log2(n) + 1;
+        st.assign(n, vector<int>(K));
+        log.assign(n + 1, 0);//为什么要n+1
+
+        // 初始化 log 数组
+        log[1] = 0;
+        for (int i = 2; i <= n; ++i) {
+            log[i] = log[i / 2] + 1;
+        }
+
+        // 初始化 st 数组
+        for (int i = 0; i < n; ++i) {
+            st[i][0] = arr[i];
+        }
+
+        // 动态规划填充 st 数组
+        for (int j = 1; j <= K; ++j) {
+            for (int i = 0; (i + (1 << j)) <= n; ++i) {
+                st[i][j] = min(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);//为什么是j-1?
+            }
+        }
+    }
+
+    int query(int L, int R) {
+        int j = log[R - L + 1];
+        return min(st[L][j], st[R - (1 << j) + 1][j]);
+    }
+};
+
+int main() {
+    vector<int> arr = {1, 3, 5, 7, 9, 11};
+    SparseTable sparseTable(arr);
+    cout << "Min value in range [1, 4]: " << sparseTable.query(1, 4) << endl;
+    return 0;
+}

day5/RMQ/st.cpp

@@ -0,0 +1,45 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+#define PRINT_VALUE(v){cout<<#v<<" :"<<v<<endl;}
+
+struct SparseTable{
+private:
+    vector<vector<int>> st;
+    vector<int> log;
+    int n;
+public:
+    SparseTable(const vector<int> &arr){
+        n=arr.size();
+        int K=log2(n)+1;
+        st.assign(n,vector<int>(K));
+        log.assign(n+1,0);
+
+        log[1]=0;
+        for(int i=2;i<=n;i++){
+            log[i]=log[i/2]+1;
+        }
+        for(int i=0;i<n;i++){
+            st[i][0]=arr[i];
+        }
+        for(int j=1;j<=K;j++){
+            for(int i=0;(i+(1<<j))<=n;i++){
+                st[i][j]=min(st[i][j-1],st[i+(1<<(j-1))][j-1]);
+            }
+        }
+    }
+    int query(int l,int r){
+        int j=this->log[r-l+1];
+        return min(this->st[l][j],this->st[r-(1<<j)+1][j]);
+                    //因为log[i]向下取整，所以此时r>=(1<<j)求右边的区间就是st[]
+    }
+};
+
+int main(){
+    vector<int> v={1, 3, 5, 7, 9, 11};
+    SparseTable st_min(v);
+    // PRINT_VALUE(st_min.query(1,2));
+    PRINT_VALUE(st_min.query(1, 4));
+
+}   
+

day5/RMQ/st_raw.cpp

@@ -0,0 +1,7 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+
+int main(){
+    
+}