Week5

Code/fenwick_segment_test.cpp

+#include <bits/stdc++.h>
+using namespace std;
+
+#define Mod(x,y) (((x)%(y)+(y))%(y))
+#define rep(i, a, b) for(int (i) = (a); (i) < (b); ++(i))
+#define all(x) begin(x), end(x)
+#define pb push_back
+#define gcd __gcd 
+#define sz(x) (ll)(x.size())
+
+typedef long long ll;
+typedef unsigned long long ull;
+typedef pair<int, int> pii;
+typedef vector<int> vi;
+typedef vector<pii> vii;
+
+const bool debug = false;
+
+const int numberOfServers = 1e6+1;
+int queries = 1e6;
+
+ll servers[numberOfServers];
+ll fenwick[numberOfServers];
+ll segment[4*numberOfServers];
+
+// NAIVE
+
+void updateServers(int a, ll x) {
+    servers[a] += x;
+}
+ll rangeSumServers(int a, int b) {
+    ll sum = 0;
+    rep(i, a, min(b+1, numberOfServers)) sum += servers[i];
+    return sum;
+}
+
+// FENWICK
+
+void updateFenwick(int a, ll x) {
+    while(a < numberOfServers) fenwick[a] += x, a += (a & (-a));
+}
+ll rangeSumFenwick(int a) {
+    ll sum = 0;
+    while(a) sum += fenwick[a], a -= (a & (-a));
+    return sum;
+}
+
+ll rangeSumFenwick(int a, int b) {
+    return rangeSumFenwick(b) - rangeSumFenwick(a-1);
+}
+
+// SEGMENT
+
+void updateSegment(int v, int l, int r, int a, ll x) {
+    if (l == r) { segment[v] += x; return; } 
+    int mid = (l + r) / 2;
+    if (a <= mid) updateSegment(v*2, l, mid, a, x);
+    else updateSegment(v*2+1, mid+1, r, a, x);
+    segment[v] = segment[v*2] + segment[v*2+1];
+}
+void updateSegment(int a, ll x) { updateSegment(1, 0, numberOfServers, a, x); }
+
+ll rangeSumSegment(int v, int l, int r, int a, int b) {
+    if (a > b) return 0;
+    if (a == l && b == r) return segment[v];
+    
+    int mid = (l + r) / 2;
+    return rangeSumSegment(v*2, l, mid, a, min(b, mid))
+         + rangeSumSegment(v*2+1, mid+1, r, max(a, mid+1), b);
+}
+ll rangeSumSegment(int a, int b) { return rangeSumSegment(1, 0, numberOfServers, a, b); }
+
+void solve() {
+    bool compareWithFenwick = true;
+    bool compareWithSegment = true;
+    bool compareWithNaive   = false;
+    if (compareWithFenwick) cout << "Using Fenwick\n";
+    if (compareWithSegment) cout << "Using Segment\n";
+    if (compareWithNaive)   cout << "Using Naive\n";
+    cout << "With number Servers = " << numberOfServers-1 << " and number of queries = " << queries << '\n';
+    
+    // initialize servers
+    srand(time(NULL));
+    rep(a, 1, numberOfServers) {
+        ll x = rand() % 1000;
+        if (compareWithNaive)   updateServers(a, x);
+        if (compareWithFenwick) updateFenwick(a, x);
+        if (compareWithSegment) updateSegment(a, x);
+    }
+
+    // handling the queries
+    while(queries--) {
+        int type = rand() % 2;
+        if (type) {
+            // updating servers
+            int a = rand() % (numberOfServers-1) + 1;
+            ll x = rand() % 1000;
+            if (compareWithNaive)   updateServers(a, x);
+            if (compareWithFenwick) updateFenwick(a, x);
+            if (compareWithSegment) updateSegment(a, x);
+        } else {
+            // range queries
+            int a = rand() % (numberOfServers-1) + 1;
+            int b = rand() % (numberOfServers-1) + 1;
+            if (b < a) swap(a, b);
+
+            ll sumFenwick = (compareWithFenwick ? rangeSumFenwick(a, b) : -1);
+            ll sumSegment = (compareWithSegment ? rangeSumSegment(a, b) : -1);
+            ll sumNaive = (compareWithNaive ? rangeSumServers(a, b) : -1);
+
+            if (compareWithFenwick && compareWithNaive)   assert(sumFenwick == sumNaive);
+            if (compareWithFenwick && compareWithSegment) assert(sumSegment == sumFenwick);
+        }
+    }
+
+    cout << "EVERYTHING OK!\n";
+} 
+
+
+int main() {
+    ios::sync_with_stdio(0);cin.tie(0);
+    cout << setprecision(30) << fixed;
+
+    int test = 1;
+    // cin >> test;
+    while(test--) solve();
+}
\ No newline at end of file

README.md

@@ -12,7 +12,7 @@ You can find the Kattis course page here https://lth.kattis.com/courses
 | 2023-10-26 | Week 2   | Data Structures and Complexity | Prime Factorization and Union-Find
 | 2023-11-09 | Week 3   | Graphs |
 | 2023-11-16 | Week 4   | Dynamic Programming |
-| 2023-11-23 | Week 5   | Fenwick and Segment Trees | Implement an easy to use Fenwick Tree
+| 2023-11-23 | Week 5   | Fenwick and Segment Trees | Implement an easy to use 2-d segment tree
 | 2023-11-30 | Week 6   | Geometry, Number Theory, and Probability |
 | 2023-12-07 | Week 7   | Tries, Suffix Arrays, and Strings |
 | 2023-12-14 | Week 8   | Dynamic Programming Revisited |