added coin grid, school excursion, sorting methods

Author: mrsac7

README.md

@@ -203,15 +203,15 @@
 * [1086 - Writing Numbers](src/1086%20-%20Writing%20Numbers.cpp)
 * 1113 - String Transform
 * [1147 - Maximum Building I](src/1147%20-%20Maximum%20Building%20I.cpp)
-* 1162 - Sorting Methods
+* [1162 - Sorting Methods](src/1162%20-%20Sorting%20Methods.cpp)
 * 1191 - Cyclic Array
 * 1189 - Food Division
 * [1654 - Bit Problem](src/1654%20-%20Bit%20Problem.cpp)
 * 1698 - Swap Round Sorting
 * [1700 - Tree Isomorphism I](src/1700%20-%20Tree%20Isomorphism%20I.cpp)
 * 1703 - Critical Cities
-* 1706 - School Excursion
-* 1709 - Coin Grid
+* [1706 - School Excursion](src/1706%20-%20School%20Excursion.cpp)
+* [1709 - Coin Grid](src/1709%20-%20Coin%20Grid.cpp)
 * 1742 - Robot Path
 * 1757 - Course Schedule II
 * 1080 - Empty String

src/1162 - Sorting Methods.cpp

@@ -0,0 +1,68 @@
+/*
+Problem Name: Sorting Methods
+Problem Link: https://cses.fi/problemset/task/1162
+Author: Sachin Srivastava (mrsac7)
+*/
+#include<bits/stdc++.h>
+using namespace std;
+
+#define int long long
+#define endl '\n'
+
+const int mxN = 2e5+5;
+int bit[mxN];
+void upd(int k) {
+    for (; k < mxN; k += k&-k)
+        bit[k]++;
+}
+int qry(int k) {
+    int ans = 0;
+    for (; k > 0; k -= k&-k)
+        ans += bit[k];
+    return ans;
+}
+vector<int> adj[mxN];
+int c = 0;
+bool vis[mxN];
+void dfs(int s){
+    if (vis[s]) return;
+    vis[s]=1; c++;
+    for (auto i: adj[s]) dfs(i);
+}
+int ind[mxN];
+signed main(){
+    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
+    #ifdef LOCAL
+    freopen("input.txt", "r" , stdin);
+    freopen("output.txt", "w", stdout);
+    #endif
+    
+    int n; cin>>n;
+    int a[n];
+    int ans1 = 0, ans2 = 0, ans3 = n, ans4 = n;
+    int mx = 0;
+    for (int i = 0; i < n; i++) {
+        cin>>a[i];
+        ans1 += qry(mxN) - qry(a[i]);
+        upd(a[i]);
+        if (i+1 != a[i]) {
+            adj[i+1].push_back(a[i]),
+            adj[a[i]].push_back(i+1);
+        }
+        int it = upper_bound(ind, ind+mx+1, a[i]) - ind;
+        mx = max(mx, it);
+        ind[it] = a[i];
+    }
+    ans3 = n-mx;
+    for (int i = 1; i <= n; i++) {
+        if (!vis[i]) {
+            c = 0; dfs(i);
+            ans2 += c-1;
+        }
+    }
+    for (int i = n-1; i >= 0; i--) {
+        if (a[i] == ans4)
+            ans4--;
+    }
+    cout<<ans1<<' '<<ans2<<' '<<ans3<<' '<<ans4;
+}

src/1706 - School Excursion.cpp

@@ -0,0 +1,66 @@
+/*
+Problem Name: School Excursion
+Problem Link: https://cses.fi/problemset/task/1706
+Author: Sachin Srivastava (mrsac7)
+*/
+#include<bits/stdc++.h>
+using namespace std;
+
+#define int long long
+#define endl '\n'
+
+const int mxN = 1e5+5;
+int c = 0;
+vector<int> adj[mxN];
+bool vis[mxN];
+void dfs(int s){
+    if (vis[s]) return;
+    vis[s]=1; c++;
+    for (auto i: adj[s]) dfs(i);
+}
+int dp[mxN];
+map<int,int> mp;
+signed main(){
+    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
+    #ifdef LOCAL
+    freopen("input.txt", "r" , stdin);
+    freopen("output.txt", "w", stdout);
+    #endif
+    
+    int n, m; cin>>n>>m;
+    for (int i = 0; i < m; i++) {
+        int x,y; cin>>x>>y;
+        adj[x].push_back(y);
+        adj[y].push_back(x);
+    }
+    
+    for (int i = 0; i < n; i++) {
+        if (!vis[i+1]) {
+            c = 0;
+            dfs(i+1);
+            mp[c]++;
+        }
+    }
+    vector<int> v;
+    for (auto [i, c]: mp) {
+        int x = 0;
+        while(1<<x < c) {
+            v.push_back((1<<x)*i);
+            c -= 1<<x;
+            x++;
+        }
+        if (c)
+            v.push_back(c*i);
+    }
+    m = v.size();
+    dp[0] = 1;
+    for (int i = 0; i < m; i++) {
+        for (int j = n; j >= 1; j--) {
+            if (j >= v[i]) {
+                dp[j] = max(dp[j-v[i]], dp[j]);
+            }
+        }
+    }
+    for (int i = 1; i <= n; i++)
+        cout<<dp[i];
+}

src/1709 - Coin Grid.cpp

@@ -0,0 +1,100 @@
+/*
+Problem Name: Coin Grid
+Problem Link: https://cses.fi/problemset/task/1709
+Author: Sachin Srivastava (mrsac7)
+*/
+#include<bits/stdc++.h>
+using namespace std;
+
+#define int long long
+#define endl '\n'
+
+const int mxN = 205;
+const int INF = 1LL<<60;
+vector<tuple<int,int,int>> adj[mxN];
+bool vis[mxN];
+int dfs(int s, int f) {
+    if (s == 201) 
+        return f;
+    vis[s] = 1;
+    for (auto &[i, w, j]: adj[s]) {
+        if (w >= 1 && !vis[i]) {
+            int b = dfs(i, 1);
+            if (b > 0) {
+                w -= b;
+                get<1>(adj[i][j])+=b;
+                return b;
+            }
+        }
+    }
+    return 0;
+}
+set<int> adj2[mxN];
+void dfs(int s){
+    if (vis[s]) return;
+    vis[s] = 1;
+    for (auto i: adj2[s]) dfs(i);
+}
+signed main(){
+    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
+    #ifdef LOCAL
+    freopen("input.txt", "r" , stdin);
+    freopen("output.txt", "w", stdout);
+    #endif
+    
+    int n; cin>>n;
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <=n; j++) {
+            char x; cin>>x;
+            if (x != '.') {
+                int j1 = adj[100+j].size();
+                int j2 = adj[i].size();
+                adj[i].push_back({100+j, 1, j1});
+                adj[100+j].push_back({i, 0, j2});
+                adj2[i].insert(100+j);
+            }
+        }
+    }
+    for (int i = 1; i <= 100; i++) {
+        int j1 = adj[i].size();
+        int j2 = adj[0].size();
+        adj[0].push_back({i, 1, j1});
+        adj[i].push_back({0, 0, j2});
+        j1 = adj[201].size();
+        j2 = adj[100+i].size();
+        adj[100+i].push_back({201, 1, j1});
+        adj[201].push_back({100+i, 0, j2});
+    }
+    int ans = 0;
+    while(1) {
+        memset(vis, 0, sizeof vis);
+        int f = dfs(0, INF);
+        ans += f;
+        if (!f) 
+            break;
+    }
+    cout<<ans<<endl;
+    int k = 0;
+    set<int> st;
+    for (int i = 1; i <= 100; i++) {
+        st.insert(i);
+        for (auto [s, w, j]: adj[i]) {
+            if (w == 0 && s>100) {
+                adj2[i].erase(s);
+                adj2[s].insert(i);
+                st.erase(i);
+            }
+        }
+    }
+    memset(vis, 0, sizeof vis);
+    for (auto i: st) {
+        if (!vis[i])
+            dfs(i);
+    }
+    for (int i = 1; i <= n; i++) {
+        if (!vis[i])
+            cout<<1<<' '<<i<<endl;
+        if (vis[100+i])
+            cout<<2<<' '<<i<<endl;
+    }
+}