From a4edd067a0b01aa430f543ddcd7ace66d0cc1b18 Mon Sep 17 00:00:00 2001
From: 33Arsenic75 <122697564+33Arsenic75@users.noreply.github.com>
Date: Thu, 13 Jun 2024 22:03:11 +0530
Subject: [PATCH] .

---
 problem-of-the-day/day15/Counting Tilings.cpp |  35 +++
 problem-of-the-day/day15/Removal Game.cpp     |  29 +++
 .../day15/maximal_rectangle.cpp               |  41 ++++
 .../day15/palindromic_partitioning.cpp        |  42 ++++
 problem-of-the-day/day15/rod_cutting.cpp      |  41 ++++
 .../day16/Dynamic_Range_Minimum_Queries.cpp   | 202 ++++++++++++++++++
 .../day16/Dynamic_Range_Sum_Queries.cpp       | 202 ++++++++++++++++++
 problem-of-the-day/day16/Forest_Queries.cpp   | 145 +++++++++++++
 .../day16/Range_Xor_Queries.cpp               |  40 ++++
 .../day16/Static_Range_Minimum_Queries.cpp    | 193 +++++++++++++++++
 .../day16/Static_Range_Sum_Queries.cpp        |  41 ++++
 11 files changed, 1011 insertions(+)
 create mode 100644 problem-of-the-day/day15/Counting Tilings.cpp
 create mode 100644 problem-of-the-day/day15/Removal Game.cpp
 create mode 100644 problem-of-the-day/day15/maximal_rectangle.cpp
 create mode 100644 problem-of-the-day/day15/palindromic_partitioning.cpp
 create mode 100644 problem-of-the-day/day15/rod_cutting.cpp
 create mode 100644 problem-of-the-day/day16/Dynamic_Range_Minimum_Queries.cpp
 create mode 100644 problem-of-the-day/day16/Dynamic_Range_Sum_Queries.cpp
 create mode 100644 problem-of-the-day/day16/Forest_Queries.cpp
 create mode 100644 problem-of-the-day/day16/Range_Xor_Queries.cpp
 create mode 100644 problem-of-the-day/day16/Static_Range_Minimum_Queries.cpp
 create mode 100644 problem-of-the-day/day16/Static_Range_Sum_Queries.cpp

diff --git a/problem-of-the-day/day15/Counting Tilings.cpp b/problem-of-the-day/day15/Counting Tilings.cpp
new file mode 100644
index 0000000..dd294b9
--- /dev/null
+++ b/problem-of-the-day/day15/Counting Tilings.cpp	
@@ -0,0 +1,35 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+typedef long long ll;
+const int maxN = 11;
+const int maxM = 1001;
+const ll MOD = 1e9+7;
+
+int N, M;
+ll dp[maxN][maxM][1<<maxN];
+
+int main(){
+    scanf("%d %d", &N, &M);
+    dp[N][0][0] = 1;
+    for(int i = 1; i <= M; i++){
+        for(int j = 0; j < (1<<N); j++)
+            dp[0][i][j<<1] = dp[N][i-1][j];
+
+        for(int j = 1; j <= N; j++){
+            int x = 1<<(j-1);
+            int y = 1<<j;
+            for(int mask = 0; mask < (1<<(N+1)); mask++){
+                dp[j-1][i][mask] %= MOD;
+                if((mask&x) && (mask&y))    continue;
+                if(mask&x)                  dp[j][i][mask^x] += dp[j-1][i][mask];
+                else if(mask&y)             dp[j][i][mask^y] += dp[j-1][i][mask];
+                else {
+                    dp[j][i][mask^x] += dp[j-1][i][mask];
+                    dp[j][i][mask^y] += dp[j-1][i][mask];
+                }
+            }
+        }
+    }
+    printf("%lld\n", dp[N][M][0] % MOD);
+}
diff --git a/problem-of-the-day/day15/Removal Game.cpp b/problem-of-the-day/day15/Removal Game.cpp
new file mode 100644
index 0000000..a537f8e
--- /dev/null
+++ b/problem-of-the-day/day15/Removal Game.cpp	
@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+typedef long long ll;
+const int maxN = 5000;
+
+int N, x[maxN+1];
+ll p[maxN+1], dp[maxN+1][maxN+1];
+bool found[maxN+1][maxN+1];
+
+ll sum(int l, int r){
+	return p[r] - p[l-1];
+}
+
+ll solve(int l, int r){
+	if(found[l][r])	return dp[l][r];
+	if(l == r)		return x[l];
+	found[l][r]=true;
+	return dp[l][r] = max(x[l]+sum(l+1, r)-solve(l+1, r), x[r]+sum(l,r-1)-solve(l,r-1));
+}
+
+int main(){
+	scanf("%d", &N);
+	for(int i = 1; i <= N; i++){
+		scanf("%d", &x[i]);
+		p[i] = p[i-1] + x[i];
+	}
+	printf("%lld\n", solve(1, N));
+}
diff --git a/problem-of-the-day/day15/maximal_rectangle.cpp b/problem-of-the-day/day15/maximal_rectangle.cpp
new file mode 100644
index 0000000..b362225
--- /dev/null
+++ b/problem-of-the-day/day15/maximal_rectangle.cpp
@@ -0,0 +1,41 @@
+#include <vector>
+#include <stack>
+#include <algorithm>
+
+using namespace std;
+
+class Solution {
+public:
+    int largestRectangleArea(vector<int>& heights) {
+        int ans = 0;
+        stack<int> stk;
+        
+        for (int i = 0; i <= heights.size(); ++i) {
+            while (!stk.empty() && (i == heights.size() || heights[stk.top()] > heights[i])) {
+                int h = heights[stk.top()];
+                stk.pop();
+                int w = stk.empty() ? i : i - stk.top() - 1;
+                ans = max(ans, h * w);
+            }
+            stk.push(i);
+        }
+        
+        return ans;
+    }
+    
+    int maximalRectangle(vector<vector<char>>& matrix) {
+        if (matrix.empty())
+            return 0;
+        
+        int ans = 0;
+        vector<int> hist(matrix[0].size(), 0);
+        
+        for (auto& row : matrix) {
+            for (int i = 0; i < row.size(); ++i)
+                hist[i] = row[i] == '0' ? 0 : hist[i] + 1;
+            ans = max(ans, largestRectangleArea(hist));
+        }
+        
+        return ans;
+    }
+};
\ No newline at end of file
diff --git a/problem-of-the-day/day15/palindromic_partitioning.cpp b/problem-of-the-day/day15/palindromic_partitioning.cpp
new file mode 100644
index 0000000..f0e7bf2
--- /dev/null
+++ b/problem-of-the-day/day15/palindromic_partitioning.cpp
@@ -0,0 +1,42 @@
+class Solution {
+public:
+    bool isPalindrome(int i, int j, string& s)
+    {
+        while (i < j) {
+            if (s[i] != s[j])
+                return false;
+            i++;
+            j--;
+        }
+        return true;
+    }
+
+    int solve(int i, int n, string& str, vector<int>& dp)
+    {
+
+        if (i == n)
+            return 0;
+
+        if (dp[i] != -1)
+            return dp[i];
+
+        int minCost = INT_MAX;
+        
+        for (int j = i; j < n; j++) {
+            if (isPalindrome(i, j, str)) {
+                
+                int cost = 1 + solve(j + 1, n, str, dp);
+                minCost = min(minCost, cost);
+            }
+        }
+        return dp[i] = minCost;
+    }
+
+    int palindromicPartition(string str)
+    {
+        int n = str.size();
+        vector<int> dp(n, -1);
+
+        return solve(0, n, str, dp) - 1;
+    }
+};
diff --git a/problem-of-the-day/day15/rod_cutting.cpp b/problem-of-the-day/day15/rod_cutting.cpp
new file mode 100644
index 0000000..c266348
--- /dev/null
+++ b/problem-of-the-day/day15/rod_cutting.cpp
@@ -0,0 +1,41 @@
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// Function to solve the unbounded knapsack problem
+int unboundedKnapsack(int n, int W, vector<int>& val, vector<int>& wt) {
+    vector<int> cur(W + 1, 0); // Create a vector to store the current DP state
+
+    // Base Condition
+    for (int i = wt[0]; i <= W; i++) {
+        cur[i] = (i / wt[0]) * val[0]; // Calculate the maximum value for the first item
+    }
+
+    for (int ind = 1; ind < n; ind++) {
+        for (int cap = 0; cap <= W; cap++) {
+            int notTaken = cur[cap]; // Maximum value without taking the current item
+
+            int taken = INT_MIN;
+            if (wt[ind] <= cap)
+                taken = val[ind] + cur[cap - wt[ind]]; // Maximum value by taking the current item
+
+            cur[cap] = max(notTaken, taken); // Store the maximum value in the current DP state
+        }
+    }
+
+    return cur[W]; // Return the maximum value considering all items and the knapsack capacity
+}
+
+int main() {
+    vector<int> wt = {2, 4, 6}; // Weight of items
+    vector<int> val = {5, 11, 13}; // Value of items
+    int W = 10; // Weight capacity of the knapsack
+    int n = wt.size(); // Number of items
+
+    // Call the function to calculate and output the maximum value the thief can steal
+    cout << "The Maximum value of items the thief can steal is " << unboundedKnapsack(n, W, val, wt) << endl;
+
+    return 0; // Return 0 to indicate successful program execution
+}
+
+// Refer to this link for detailed explanation - https://www.youtube.com/watch?v=mO8XpGoJwuo
\ No newline at end of file
diff --git a/problem-of-the-day/day16/Dynamic_Range_Minimum_Queries.cpp b/problem-of-the-day/day16/Dynamic_Range_Minimum_Queries.cpp
new file mode 100644
index 0000000..b1a0c6e
--- /dev/null
+++ b/problem-of-the-day/day16/Dynamic_Range_Minimum_Queries.cpp
@@ -0,0 +1,202 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+#define f first
+#define mk make_pair
+#define in insert
+#define py cout << "YES" << endl
+#define pn cout << "NO" << endl
+template <int MOD=998244353>
+struct Modular {
+  int value;
+  static const int MOD_value = MOD;
+
+  Modular(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
+  Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}
+
+  Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
+  Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
+  Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}
+
+  friend Modular mexp(Modular a, long long e) {
+    Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
+    return res;
+  }
+  friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }
+
+  Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
+  friend Modular operator+(Modular a, Modular const b) { return a += b; }
+  friend Modular operator-(Modular a, Modular const b) { return a -= b; }
+  friend Modular operator-(Modular const a) { return 0 - a; }
+  friend Modular operator*(Modular a, Modular const b) { return a *= b; }
+  friend Modular operator/(Modular a, Modular const b) { return a /= b; }
+  friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
+  friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
+  friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}
+};
+template <typename T> void chkmin(T &x, T y) {
+  if (x > y)
+    x = y;
+}
+template <typename T> void chkmax(T &x, T y) {
+  if (x < y)
+    x = y;
+}
+
+void sigsev(int n, vector<int> &prime) {
+    prime.push_back(2);
+    vector<bool>ispm(n + 1, true);
+
+    for(int j = 3; j <= n; j += 2) {
+      if(!ispm[j])continue;
+      else{
+        prime.push_back(j);
+        for(int i = j*j; i <= n; i += j) {
+          ispm[i] = false;
+        }
+      }
+    }
+}
+
+class UF {
+public:
+  int *id, cnt, *sz;
+  // Create an empty union find data structure with N isolated sets.
+  UF(int N) {
+    cnt = N; id = new int[N]; sz = new int[N];
+    for (int i = 0; i<N; i++)  id[i] = i, sz[i] = 1; }
+  ~UF() { delete[] id; delete[] sz; }
+  // Return the id of component corresponding to object p.
+  int find(int p) {
+    int root = p;
+    while (root != id[root])    root = id[root];
+    while (p != root) { int newp = id[p]; id[p] = root; p = newp; }
+    return root;
+  }
+  // Replace sets containing x and y with their union.
+  void merge(int x, int y) {
+    int i = find(x); int j = find(y); if (i == j) return;
+    // make smaller root point to larger one
+    if (sz[i] < sz[j]) { id[i] = j, sz[j] += sz[i]; }
+    else { id[j] = i, sz[i] += sz[j]; }
+    cnt--;
+  }
+  // Are objects x and y in the same set?
+  bool connected(int x, int y) { return find(x) == find(y); }
+  // Return the number of disjoint sets.
+    int count() { return cnt; }
+};
+
+class SG {
+public:
+    vector<int>data;
+    int n;
+    vector<int>tree;
+    function<int(int, int)> operation;
+    int default_val;
+    SG(vector<int>&data , int default_val , function<int(int, int)> op):operation(op) {
+        this->data = data;
+        n = data.size();
+        this->default_val = default_val;
+        tree.resize(4*n);
+        build(0, n-1, 1);
+    }
+    void build(int l, int r, int node) {
+        if(l == r) {
+            tree[node] = data[l];
+            // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+            return;
+        }
+        int mid = (l+r)/2;
+        build(l, mid, 2*node);
+        build(mid+1, r, 2*node+1);
+        tree[node] = operation(tree[2*node], tree[2*node+1]);
+        // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+    }
+    int query(int v, int tl, int tr, int l , int r){
+        if (l > r) return default_val;
+        else if (l == tl && r == tr) {
+            return tree[v];
+        }
+        int tm = (tl + tr) / 2;
+        return operation(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
+    }
+    int query(int ql, int qr) {
+        return query(1, 0, n-1, ql, qr);
+    }
+    void buildup(int v){
+        if(v==0)return;
+        tree[v] = operation(tree[v*2], tree[v*2+1]);
+        buildup(v/2);
+    }
+    void update(int v, int tl, int tr, int l, int r, int new_val) {
+        if (l > r)
+            return;
+        if (l == tl && r == tr) {
+            tree[v] = new_val;
+        } else {
+            int tm = (tl + tr) / 2;
+            update(v*2, tl, tm, l, min(r, tm), new_val);
+            update(v*2+1, tm+1, tr, max(l, tm+1), r, new_val);
+            buildup(v);
+        }
+    }
+    void update(int l, int r, int new_val){
+        update(1, 0, n-1, l, r, new_val);
+    }
+};
+
+#ifndef ONLINE_JUDGE
+#define debug(x) cout << #x << " = " << x << endl
+#define show1(v)                                                               \
+  for (auto i : v)                                                             \
+  cout << i << ' '
+#define show(v)                                                                \
+  show1(v);                                                                    \
+  cout << '\n'
+#define gcd __algo_gcd
+#else
+#define debug(x)
+#endif
+
+
+// ------------------------------------------***--------------------------------------------------
+
+
+int32_t main() {
+    int n,q; cin>>n>>q;
+    vector<int>a(n);
+    rep(i,0,n)cin>>a[i];
+    int qq,l,r,k,u;
+    SG s = SG(a, INT32_MAX, [](int a, int b) { return min(a,b); });
+    while(q--){
+        cin>>qq;
+        if(qq==1){
+            cin>>k>>u;  
+            s.update(k-1, k-1, u);
+        }
+        else if(qq==2){
+            cin>>l>>r;
+            cout<<s.query(l-1,r-1)<<'\n';
+        }
+    }
+
+  return 0;
+}
diff --git a/problem-of-the-day/day16/Dynamic_Range_Sum_Queries.cpp b/problem-of-the-day/day16/Dynamic_Range_Sum_Queries.cpp
new file mode 100644
index 0000000..dd5765f
--- /dev/null
+++ b/problem-of-the-day/day16/Dynamic_Range_Sum_Queries.cpp
@@ -0,0 +1,202 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+#define f first
+#define mk make_pair
+#define in insert
+#define py cout << "YES" << endl
+#define pn cout << "NO" << endl
+template <int MOD=998244353>
+struct Modular {
+  int value;
+  static const int MOD_value = MOD;
+
+  Modular(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
+  Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}
+
+  Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
+  Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
+  Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}
+
+  friend Modular mexp(Modular a, long long e) {
+    Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
+    return res;
+  }
+  friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }
+
+  Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
+  friend Modular operator+(Modular a, Modular const b) { return a += b; }
+  friend Modular operator-(Modular a, Modular const b) { return a -= b; }
+  friend Modular operator-(Modular const a) { return 0 - a; }
+  friend Modular operator*(Modular a, Modular const b) { return a *= b; }
+  friend Modular operator/(Modular a, Modular const b) { return a /= b; }
+  friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
+  friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
+  friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}
+};
+template <typename T> void chkmin(T &x, T y) {
+  if (x > y)
+    x = y;
+}
+template <typename T> void chkmax(T &x, T y) {
+  if (x < y)
+    x = y;
+}
+
+void sigsev(int n, vector<int> &prime) {
+    prime.push_back(2);
+    vector<bool>ispm(n + 1, true);
+
+    for(int j = 3; j <= n; j += 2) {
+      if(!ispm[j])continue;
+      else{
+        prime.push_back(j);
+        for(int i = j*j; i <= n; i += j) {
+          ispm[i] = false;
+        }
+      }
+    }
+}
+
+class UF {
+public:
+  int *id, cnt, *sz;
+  // Create an empty union find data structure with N isolated sets.
+  UF(int N) {
+    cnt = N; id = new int[N]; sz = new int[N];
+    for (int i = 0; i<N; i++)  id[i] = i, sz[i] = 1; }
+  ~UF() { delete[] id; delete[] sz; }
+  // Return the id of component corresponding to object p.
+  int find(int p) {
+    int root = p;
+    while (root != id[root])    root = id[root];
+    while (p != root) { int newp = id[p]; id[p] = root; p = newp; }
+    return root;
+  }
+  // Replace sets containing x and y with their union.
+  void merge(int x, int y) {
+    int i = find(x); int j = find(y); if (i == j) return;
+    // make smaller root point to larger one
+    if (sz[i] < sz[j]) { id[i] = j, sz[j] += sz[i]; }
+    else { id[j] = i, sz[i] += sz[j]; }
+    cnt--;
+  }
+  // Are objects x and y in the same set?
+  bool connected(int x, int y) { return find(x) == find(y); }
+  // Return the number of disjoint sets.
+    int count() { return cnt; }
+};
+
+class SG {
+public:
+    vector<int>data;
+    int n;
+    vector<int>tree;
+    function<int(int, int)> operation;
+    int default_val;
+    SG(vector<int>&data , int default_val , function<int(int, int)> op):operation(op) {
+        this->data = data;
+        n = data.size();
+        this->default_val = default_val;
+        tree.resize(4*n);
+        build(0, n-1, 1);
+    }
+    void build(int l, int r, int node) {
+        if(l == r) {
+            tree[node] = data[l];
+            // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+            return;
+        }
+        int mid = (l+r)/2;
+        build(l, mid, 2*node);
+        build(mid+1, r, 2*node+1);
+        tree[node] = operation(tree[2*node], tree[2*node+1]);
+        // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+    }
+    int query(int v, int tl, int tr, int l , int r){
+        if (l > r) return default_val;
+        else if (l == tl && r == tr) {
+            return tree[v];
+        }
+        int tm = (tl + tr) / 2;
+        return operation(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
+    }
+    int query(int ql, int qr) {
+        return query(1, 0, n-1, ql, qr);
+    }
+    void buildup(int v){
+        if(v==0)return;
+        tree[v] = operation(tree[v*2], tree[v*2+1]);
+        buildup(v/2);
+    }
+    void update(int v, int tl, int tr, int l, int r, int new_val) {
+        if (l > r)
+            return;
+        if (l == tl && r == tr) {
+            tree[v] = new_val;
+        } else {
+            int tm = (tl + tr) / 2;
+            update(v*2, tl, tm, l, min(r, tm), new_val);
+            update(v*2+1, tm+1, tr, max(l, tm+1), r, new_val);
+            buildup(v);
+        }
+    }
+    void update(int l, int r, int new_val){
+        update(1, 0, n-1, l, r, new_val);
+    }
+};
+
+#ifndef ONLINE_JUDGE
+#define debug(x) cout << #x << " = " << x << endl
+#define show1(v)                                                               \
+  for (auto i : v)                                                             \
+  cout << i << ' '
+#define show(v)                                                                \
+  show1(v);                                                                    \
+  cout << '\n'
+#define gcd __algo_gcd
+#else
+#define debug(x)
+#endif
+
+
+// ------------------------------------------***--------------------------------------------------
+
+
+int32_t main() {
+    int n,q; cin>>n>>q;
+    vector<int>a(n);
+    rep(i,0,n)cin>>a[i];
+    int qq,l,r,k,u;
+    SG s = SG(a, 0, [](int a, int b) { return a+b; });
+    while(q--){
+        cin>>qq;
+        if(qq==1){
+            cin>>k>>u;  
+            s.update(k-1, k-1, u);
+        }
+        else if(qq==2){
+            cin>>l>>r;
+            cout<<s.query(l-1,r-1)<<'\n';
+        }
+    }
+
+  return 0;
+}
diff --git a/problem-of-the-day/day16/Forest_Queries.cpp b/problem-of-the-day/day16/Forest_Queries.cpp
new file mode 100644
index 0000000..4279e8c
--- /dev/null
+++ b/problem-of-the-day/day16/Forest_Queries.cpp
@@ -0,0 +1,145 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+#define f first
+#define mk make_pair
+#define in insert
+#define py cout << "YES" << endl
+#define pn cout << "NO" << endl
+template <int MOD=998244353>
+struct Modular {
+  int value;
+  static const int MOD_value = MOD;
+
+  Modular(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
+  Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}
+
+  Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
+  Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
+  Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}
+
+  friend Modular mexp(Modular a, long long e) {
+    Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
+    return res;
+  }
+  friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }
+
+  Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
+  friend Modular operator+(Modular a, Modular const b) { return a += b; }
+  friend Modular operator-(Modular a, Modular const b) { return a -= b; }
+  friend Modular operator-(Modular const a) { return 0 - a; }
+  friend Modular operator*(Modular a, Modular const b) { return a *= b; }
+  friend Modular operator/(Modular a, Modular const b) { return a /= b; }
+  friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
+  friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
+  friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}
+};
+template <typename T> void chkmin(T &x, T y) {
+  if (x > y)
+    x = y;
+}
+template <typename T> void chkmax(T &x, T y) {
+  if (x < y)
+    x = y;
+}
+
+void sigsev(int n, vector<int> &prime) {
+    prime.push_back(2);
+    vector<bool>ispm(n + 1, true);
+
+    for(int j = 3; j <= n; j += 2) {
+      if(!ispm[j])continue;
+      else{
+        prime.push_back(j);
+        for(int i = j*j; i <= n; i += j) {
+          ispm[i] = false;
+        }
+      }
+    }
+}
+
+class UF {
+public:
+  int *id, cnt, *sz;
+  // Create an empty union find data structure with N isolated sets.
+  UF(int N) {
+    cnt = N; id = new int[N]; sz = new int[N];
+    for (int i = 0; i<N; i++)  id[i] = i, sz[i] = 1; }
+  ~UF() { delete[] id; delete[] sz; }
+  // Return the id of component corresponding to object p.
+  int find(int p) {
+    int root = p;
+    while (root != id[root])    root = id[root];
+    while (p != root) { int newp = id[p]; id[p] = root; p = newp; }
+    return root;
+  }
+  // Replace sets containing x and y with their union.
+  void merge(int x, int y) {
+    int i = find(x); int j = find(y); if (i == j) return;
+    // make smaller root point to larger one
+    if (sz[i] < sz[j]) { id[i] = j, sz[j] += sz[i]; }
+    else { id[j] = i, sz[i] += sz[j]; }
+    cnt--;
+  }
+  // Are objects x and y in the same set?
+  bool connected(int x, int y) { return find(x) == find(y); }
+  // Return the number of disjoint sets.
+    int count() { return cnt; }
+};
+
+#ifndef ONLINE_JUDGE
+#define debug(x) cout << #x << " = " << x << endl
+#define show1(v)                                                               \
+  for (auto i : v)                                                             \
+  cout << i << ' '
+#define show(v)                                                                \
+  show1(v);                                                                    \
+  cout << '\n'
+#define gcd __algo_gcd
+#else
+#define debug(x)
+#endif
+
+
+// ------------------------------------------***--------------------------------------------------
+
+
+
+
+int32_t main() {
+    int n,q;cin>>n>>q;
+    vector<vector<int>>a(n+1,vector<int>(n+1,0));
+    char c;
+    rep(i,1,n+1){
+        rep(j,1,n+1){
+            cin>>c;
+            a[i][j] = a[i-1][j] + a[i][j-1] - a[i-1][j-1] + (c == '*');
+        }
+    }
+    int y1,x1,y2,x2;
+    int ans;
+    while(q--){
+        cin>>y1>>x1>>y2>>x2;
+        ans = a[y2][x2] - a[y1-1][x2] - a[y2][x1-1] + a[y1-1][x1-1];
+        cout<<ans<<'\n';
+    }
+
+  return 0;
+}
diff --git a/problem-of-the-day/day16/Range_Xor_Queries.cpp b/problem-of-the-day/day16/Range_Xor_Queries.cpp
new file mode 100644
index 0000000..b99b9b6
--- /dev/null
+++ b/problem-of-the-day/day16/Range_Xor_Queries.cpp
@@ -0,0 +1,40 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+#define f first
+
+// ------------------------------------------***--------------------------------------------------
+
+
+
+
+int32_t main() {
+    int n,q;cin>>n>>q;
+    vector<int>a(n+1,0);
+    rep(i,1,n+1)cin>>a[i];
+    rep(i,1,n+1)a[i]^=a[i-1];
+    int l,r;
+    while(q--){
+        cin >> l >> r; 
+        cout << (a[r] ^ a[l - 1]) << '\n'; 
+    }
+
+  return 0;
+}
diff --git a/problem-of-the-day/day16/Static_Range_Minimum_Queries.cpp b/problem-of-the-day/day16/Static_Range_Minimum_Queries.cpp
new file mode 100644
index 0000000..db19b21
--- /dev/null
+++ b/problem-of-the-day/day16/Static_Range_Minimum_Queries.cpp
@@ -0,0 +1,193 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+#define f first
+#define mk make_pair
+#define in insert
+#define py cout << "YES" << endl
+#define pn cout << "NO" << endl
+template <int MOD=998244353>
+struct Modular {
+  int value;
+  static const int MOD_value = MOD;
+
+  Modular(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
+  Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}
+
+  Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
+  Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
+  Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}
+
+  friend Modular mexp(Modular a, long long e) {
+    Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
+    return res;
+  }
+  friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }
+
+  Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
+  friend Modular operator+(Modular a, Modular const b) { return a += b; }
+  friend Modular operator-(Modular a, Modular const b) { return a -= b; }
+  friend Modular operator-(Modular const a) { return 0 - a; }
+  friend Modular operator*(Modular a, Modular const b) { return a *= b; }
+  friend Modular operator/(Modular a, Modular const b) { return a /= b; }
+  friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
+  friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
+  friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}
+};
+template <typename T> void chkmin(T &x, T y) {
+  if (x > y)
+    x = y;
+}
+template <typename T> void chkmax(T &x, T y) {
+  if (x < y)
+    x = y;
+}
+
+void sigsev(int n, vector<int> &prime) {
+    prime.push_back(2);
+    vector<bool>ispm(n + 1, true);
+
+    for(int j = 3; j <= n; j += 2) {
+      if(!ispm[j])continue;
+      else{
+        prime.push_back(j);
+        for(int i = j*j; i <= n; i += j) {
+          ispm[i] = false;
+        }
+      }
+    }
+}
+
+class UF {
+public:
+  int *id, cnt, *sz;
+  // Create an empty union find data structure with N isolated sets.
+  UF(int N) {
+    cnt = N; id = new int[N]; sz = new int[N];
+    for (int i = 0; i<N; i++)  id[i] = i, sz[i] = 1; }
+  ~UF() { delete[] id; delete[] sz; }
+  // Return the id of component corresponding to object p.
+  int find(int p) {
+    int root = p;
+    while (root != id[root])    root = id[root];
+    while (p != root) { int newp = id[p]; id[p] = root; p = newp; }
+    return root;
+  }
+  // Replace sets containing x and y with their union.
+  void merge(int x, int y) {
+    int i = find(x); int j = find(y); if (i == j) return;
+    // make smaller root point to larger one
+    if (sz[i] < sz[j]) { id[i] = j, sz[j] += sz[i]; }
+    else { id[j] = i, sz[i] += sz[j]; }
+    cnt--;
+  }
+  // Are objects x and y in the same set?
+  bool connected(int x, int y) { return find(x) == find(y); }
+  // Return the number of disjoint sets.
+    int count() { return cnt; }
+};
+
+class SG {
+public:
+    vector<int>data;
+    int n;
+    vector<int>tree;
+    function<int(int, int)> operation;
+    int default_val;
+    SG(vector<int>&data , int default_val , function<int(int, int)> op):operation(op) {
+        this->data = data;
+        n = data.size();
+        this->default_val = default_val;
+        tree.resize(4*n);
+        build(0, n-1, 1);
+    }
+    void build(int l, int r, int node) {
+        if(l == r) {
+            tree[node] = data[l];
+            // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+            return;
+        }
+        int mid = (l+r)/2;
+        build(l, mid, 2*node);
+        build(mid+1, r, 2*node+1);
+        tree[node] = operation(tree[2*node], tree[2*node+1]);
+        // cout<<l<<" "<<r<<" "<<tree[node]<<endl;
+    }
+    int query(int v, int tl, int tr, int l , int r){
+        if (l > r) return default_val;
+        else if (l == tl && r == tr) {
+            return tree[v];
+        }
+        int tm = (tl + tr) / 2;
+        return operation(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
+    }
+    int query(int ql, int qr) {
+        return query(1, 0, n-1, ql, qr);
+    }
+    void update(int v, int tl, int tr, int l, int r, int new_val) {
+        if (l > r)
+            return;
+        if (l == tl && r == tr) {
+            tree[v] = new_val;
+        } else {
+            int tm = (tl + tr) / 2;
+            update(v*2, tl, tm, l, min(r, tm), new_val);
+            update(v*2+1, tm+1, tr, max(l, tm+1), r, new_val);
+        }
+    }
+    void update(int l, int r, int new_val){
+        update(1, 0, n-1, l, r, new_val);
+    }
+};
+
+
+#ifndef ONLINE_JUDGE
+#define debug(x) cout << #x << " = " << x << endl
+#define show1(v)                                                               \
+  for (auto i : v)                                                             \
+  cout << i << ' '
+#define show(v)                                                                \
+  show1(v);                                                                    \
+  cout << '\n'
+#define gcd __algo_gcd
+#else
+#define debug(x)
+#endif
+
+
+// ------------------------------------------***--------------------------------------------------
+
+
+
+
+
+int32_t main() {
+    int n,q;
+    cin>>n>>q;
+    vector<int>data(n,0);
+    rep(i,0,n)cin>>data[i];
+    SG s(data, INT32_MAX ,[](int a, int b) { return min(a,b); }); // Using lambda function
+    int l,r;
+    while(q--){
+        cin>>l>>r;
+        cout<<s.query(l-1,r-1)<<endl;
+    }   
+  return 0;
+}
diff --git a/problem-of-the-day/day16/Static_Range_Sum_Queries.cpp b/problem-of-the-day/day16/Static_Range_Sum_Queries.cpp
new file mode 100644
index 0000000..9fa74e6
--- /dev/null
+++ b/problem-of-the-day/day16/Static_Range_Sum_Queries.cpp
@@ -0,0 +1,41 @@
+#include <algorithm>
+#include <bitset>
+#include <deque>
+#include <iostream>
+#include <queue>
+#include <set>
+#include <stack>
+#include <stdlib.h>
+#include <unordered_set>
+#include <vector>
+/// ordered sets support upperbound lowerbound too
+#include <map>
+#include <unordered_map>
+#define len(v) (int)v.size()
+#define all(v) v.begin(), v.end()
+#define rall(v) v.rbegin(), v.rend()
+using namespace std;
+#define int long long
+#define pb push_back
+#define rep(i, a, b) for (int i = a; i < b; i++)
+// ------------------------------------------***--------------------------------------------------
+
+
+
+
+
+int32_t main() {
+    int n,q;cin>>n>>q;
+    vector<int>a(n+1,0);
+    int x;
+    rep(i,1,n+1){
+        cin>>x;
+        a[i]=a[i-1]+x;
+    }
+    int l,r;
+    while(q--){
+        cin>>l>>r;
+        cout<<a[r]-a[l-1]<<'\n';
+    }
+  return 0;
+}