s2024 archive

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diff --git a/archive/2024s/advanced.pdf b/archive/2024s/advanced.pdf
diff --git a/archive/2024s/advanced_editorial.pdf b/archive/2024s/advanced_editorial.pdf
diff --git a/archive/2024s/index.html b/archive/2024s/index.html
@@ -0,0 +1,102 @@
+<!doctype html>
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+			mBIT will be hosting the Spring 2024 In-Person and Virtual Round on June 8th! <a href="https://docs.google.com/forms/d/1xuxpRnFR-uMXdiX2p-1oTutfz6PXqIBbLNzJyI6tfqY/edit">Registration is now open!</a>
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+								<strong>Register</strong>
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+		<main class="wrapper">
+
+<section class="hero has-background-primary">
+	<div class="hero-body">
+		<div class="container">
+			<h1 class="title is-1"><span class="has-text-white">Spring 2024</span></h1>
+	</div>
+</section>
+<section class="section">
+	<div class="container">
+		<div class="content"><p>The Spring 2024 round took place on June 8th, 2024. The contest was held both in-person and virtually with 25 teams and 80 competitors coming in-person and another 72 teams with 136 competitors competing online.</p></div>
+		<h2 class="subtitle is-4">Problems</h2>
+		<div class="content">
+			<p>Test solutions on our Codeforces Gyms: <a target="_blank" href="https://codeforces.com/group/stXErQM0NN/members">Problems</a>, <a target="_blank" href="https://docs.google.com/document/d/1084MSbNk0d6hDq9yxOLC4oQ-k5_b4G01_RbIcblRW_E/edit">Editorials</a>
+		</div>
+		<h2 class="subtitle is-4">In person</h2>
+		<h2 class="subtitle is-5">Advanced Division</h2>
+		<div class="content">
+			<p>1. <em>Obesity Epidemic</em> - Gabriel Xu, Avnith Vijayram, Max Wang, Samarth Bhargav (Thomas Jefferson High School for Science and Technology)
+		</div>
+		<h2 class="subtitle is-5">Standard Division</h2>
+		<div class="content">
+			<p class="mb-0"><strong>High School Winners</strong></p>
+			<p>1. <em>mont</em> - David Wang, Bill Qian, Daniel Li, Sam Easaw (Montgomery Blair High School)</p>
+			<p>2. <em>rhhsprogclub</em> - Nathan Zhong, Gavin Zhaom, Jonathan Cai, Alex Zhu (River Hill High School)</p>
+			<p>3. <em>The DP Demons</em> - Taha Rawjani, Matthew Li, Arush Bodla, Rohit Rajakumar (Academies of Loudoun)</p>
+			<p class="mb-0"><strong>Middle School Winners</strong></p>
+			<p>1. <em>cookies</em> - Liam Bryce, Ethan Qin, Ari Bernstein, Asher Bleimund (Takoma Park Middle School)</p>
+			<p>2. <em>Pi Game</em> - Gabriel Phillips, Fox Martone (Takoma Park Middle School)</p>
+			<p>3. <em>Vitruvian Lung</em> - Alex Wang (Takoma Park Middle School), Ruixi Zhang (Takoma Park Middle School), Daniel Hollis (Takoma Park Middle School), Angela Cheng (Robert Frost Middle School)</p>
+			<p class="mb-0"><strong>High School Winners</strong></p>
+			<p>1. <em>mont</em> - David Wang, Bill Qian, Daniel Li, Sam Easaw (Montgomery Blair High School)</p>
+			<p>2. <em>rhhsprogclub</em> - Nathan Zhong, Gavin Zhaom, Jonathan Cai, Alex Zhu (River Hill High School)</p>
+			<p>3. <em>The DP Demons</em> - Taha Rawjani, Matthew Li, Arush Bodla, Rohit Rajakumar (Academies of Loudoun)</p>
+		</div>
+		<h2 class="subtitle is-4">Online</h2>
+		<h2 class="subtitle is-5">Advanced Division</h2>
+		<div class="content">
+			<p>1. <em>ᴉoᴉ uᴉʍ llᴉʍ ǝxuq</em> - Bing-Dong Liu (Irvington High School), Thomas Liu (The Harker School), Brian Xue (Lynbrook High School), Alex Chen (Monta Vista High School)</p>
+			<p>2. <em>Heavy Light Decomposition</em> - Ryan Bai (Canyon Crest Academy), Bálint Rózsa (Bloor C.I.), Daniel Ye (William Lyon Mackenzie C.I.), Maxwell He (Shanghai High School International Division)</p>
+			<p>3. <em>Baby Bottom and Cooked Shrimp</em> - Rain Jiang (Homeschool), Kai Jiang (Homeschool)</p>
+			<p>4. <em>2027 EGOI Team</em> - Julian Wu (Westview High School), Jonathan He (Adlai E. Stevenson High School), Weiming Zhou (Massachussetts Institute of Technology), Tina Wang (Massachussetts Institute of Technology)</p>
+			<p>5. <em>liympanda</em> - Yiming Li (Google)</p>
+		</div>
+	</div>
+</section>
+
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+		<footer class="footer">
+			<div class="content has-text-centered">
+				<p>Organized by students at <a href="https://mbhs.edu">Montgomery Blair High School</a>.</p>
+			</div>
+		</footer>
+		<script src="/ui.js"></script>
+	</body>
+</html>
diff --git a/archive/2024s/solutions/BehindTheScenes.cpp b/archive/2024s/solutions/BehindTheScenes.cpp
@@ -0,0 +1,69 @@
+// int max = 2 147 483 647 (2^31-1)
+// ll max = 9 223 372 036 854 775 807 (2^63-1)
+#include <bits/stdc++.h>
+using namespace std;
+
+#define forn(i, n) for (int i = 0; i < n; i++)
+#define mp make_pair
+#define f first
+#define s second
+#define pb push_back
+#define MOD 1000000007
+
+typedef long long ll;
+typedef long double ld;
+typedef vector<int> vi;
+typedef vector<ll> vl;
+typedef pair<int, int> pi;
+
+// Fast input and output
+void fast_io() {
+    ios_base::sync_with_stdio(0);
+    cin.tie(NULL);
+    cout.tie(NULL);
+}
+
+// Printing pairs and vectors
+template <typename A, typename B>
+ostream &operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
+template <typename A>
+ostream &operator<<(ostream &cout, vector<A> const &v) {
+    cout << "[";
+    forn(i, (int)v.size()) {
+        if (i) cout << ", ";
+        cout << v[i];
+    }
+    return cout << "]";
+}
+
+mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
+// use uniform_int_distribution<int>(a, b)(rng) if you want [a, b].
+
+int main() {
+    fast_io();
+    int n;
+    cin >> n;
+    vector<pi> s(n);
+    forn(i, n) cin >> s[i].f;
+    forn(i, n) s[i].s = i;
+    sort(s.begin(), s.end());
+    string pans;
+    vector<string> ans(n);
+    forn(i, n) {
+        if (i == 0 or s[i].f != s[i - 1].f) {
+            pans = "";
+            forn(j, s[i].f) pans.pb('a');
+        } else {
+            for (int j = s[i].f - 1; j >= 0; j--) {
+                if (pans.at(j) != 'z') {
+                    pans.at(j)++;
+                    break;
+                }
+                pans.at(j) = 'a';
+            }
+        }
+        ans[s[i].s] = pans;
+    }
+    forn(i, n) cout << ans[i] << "\n";
+}
+// code by DanTheMan
diff --git a/archive/2024s/solutions/BehindTheScenes.py b/archive/2024s/solutions/BehindTheScenes.py
@@ -0,0 +1,22 @@
+# faster io
+from sys import stdin, stdout
+
+n = int(stdin.readline())
+l = stdin.readline().split()
+# nextbest[i] represents the lexicographic least unused string of length i
+# must use nested lists because strings are immutable
+nextbest = [[]] * 5001
+for i in range(1, 5001):
+    nextbest[i] = ["a"] * i  # they all start as all a's
+for i in range(n):
+    length = int(l[i])
+    for i in range(length):  # output string represented by nextbest[length]
+        stdout.write(nextbest[length][i])
+    stdout.write(" ")
+    # update nextbest[length] to the next lexicographic string
+    for j in range(length - 1, -1, -1):
+        if nextbest[length][j] == "z":  # set all trailing 'z's to be 'a'
+            nextbest[length][j] = "a"
+        else:  # increment the first non-z letter from back
+            nextbest[length][j] = chr(ord(nextbest[length][j]) + 1)
+            break
diff --git a/archive/2024s/solutions/Boardwalk.cpp b/archive/2024s/solutions/Boardwalk.cpp
@@ -0,0 +1,131 @@
+/*
+Equalize Array
+difference array on circular array
+mcmf
+*/
+
+#include "bits/stdc++.h"
+using namespace std;
+
+#define rep(i, a, b) for (int i = a; i <= b; i++)
+#define all(x) begin(x), end(x)
+#define sz(x) (int)x.size()
+#define f first
+#define s second
+#define nl "\n"
+#define pb push_back
+typedef long long ll;
+typedef vector<int> vi;
+typedef pair<int, int> pii;
+const int MOD = 1e9 + 7;
+
+// copied from ?
+// works for negative edges
+template <class C, class F>
+struct MCMF {
+    static constexpr F eps = (F)1e-9;
+    struct Edge {
+        int v, inv;
+        F cap, flow;
+        C cost;
+        Edge(int v, C cost, F cap, int inv) : v(v), cost(cost), cap(cap), flow(0), inv(inv) {}
+    };
+
+    int s, t, n, m = 0;
+    vector<vector<Edge> > g;
+    vector<C> cost;
+    vi state, path, from;
+
+    MCMF(int n, int ss = -1, int tt = -1) : n(n), g(n + 5), cost(n + 5), state(n + 5), path(n + 5), from(n + 5) {
+        s = ss == -1 ? n + 1 : ss;
+        t = tt == -1 ? n + 2 : tt;
+    }
+
+    void add(int u, int v, F cap, C cost) {
+        g[u].pb(Edge(v, cost, cap, sz(g[v])));
+        g[v].pb(Edge(u, -cost, 0, sz(g[u]) - 1));
+        m += 2;
+    }
+
+    bool bfs() {
+        fill(all(state), 2);
+        fill(all(cost), numeric_limits<C>::max());
+        deque<int> qu;
+        qu.push_back(s);
+        state[s] = 1, cost[s] = 0;
+        while (sz(qu)) {
+            int u = qu.front();
+            qu.pop_front();
+            state[u] = 0;
+            for (Edge &e : g[u])
+                if (e.cap - e.flow > eps)
+                    if (cost[u] + e.cost < cost[e.v]) {
+                        cost[e.v] = cost[u] + e.cost;
+                        path[e.v] = u;
+                        from[e.v] = g[e.v][e.inv].inv;
+                        if (state[e.v] == 0 || (sz(qu) && cost[qu.front()] > cost[e.v]))
+                            qu.push_front(e.v);
+                        else if (state[e.v] == 2)
+                            qu.push_back(e.v);
+                        state[e.v] = 1;
+                    }
+        }
+        return cost[t] != numeric_limits<C>::max();
+    }
+
+    pair<C, F> minCostFlow() {
+        C cost = 0;
+        F flow = 0;
+        while (bfs()) {
+            F nflow = numeric_limits<F>::max();
+            for (int u, v = t; v != s; v = u) {
+                u = path[v];
+                Edge &e = g[u][from[v]];
+                nflow = min(nflow, e.cap - e.flow);
+            }
+            for (int u, v = t; v != s; v = u) {
+                u = path[v];
+                g[u][from[v]].flow += nflow;
+                g[v][g[u][from[v]].inv].flow -= nflow;
+                cost += g[u][from[v]].cost * nflow;
+            }
+            flow += nflow;
+        }
+        return make_pair(cost, flow);
+    }
+};
+
+const int N = 201;
+int n, k;
+int a[N], d[N];
+
+int main() {
+    cin.tie(0)->sync_with_stdio(0);
+
+    cin >> n >> k;
+    MCMF<ll, ll> mf(n + 2, 0, n + 1);
+    rep(i, 1, n) cin >> a[i];
+    a[0] = a[n];
+    ll sumd = 0;
+    rep(i, 1, n) {
+        d[i] = a[i] - a[i - 1];
+    }
+    int maxC = 0;
+    rep(i, 1, k) {
+        int l, r, c;
+        cin >> l >> r >> c;
+        maxC = max(maxC, c);
+        mf.add(l, (r == n ? 1 : r + 1), 1e18, c);
+    }
+    ll need = 0;
+    rep(i, 1, n) {
+        if (d[i] < 0) mf.add(0, i, -d[i], 0);
+        if (d[i] > 0) mf.add(i, n + 1, d[i], 0), need += d[i], sumd += d[i];
+    }
+    auto p = mf.minCostFlow();
+    assert(p.f <= sumd * n * maxC);
+    if (p.s != need)
+        cout << -1;
+    else
+        cout << p.f;
+}