Added 6 Xor Gauss problems from Codechef, Codeforces and Spoj

leonardoAnjos16 · leonardoAnjos16 · commit 7f1f55c9b007 · 2023-05-10T10:10:16.000-03:00
diff --git a/Codechef/bitsetbaba_and_power_grid.cpp b/Codechef/bitsetbaba_and_power_grid.cpp
@@ -0,0 +1,34 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int T; cin >> T;
+    while (T--) {
+        int K, M;
+        cin >> K >> M;
+
+        int sz = 0;
+        vector<int> basis(K, 0);
+
+        for (int i = 0; i < M; i++) {
+            int x; cin >> x;
+
+            bool done = false;
+            for (int j = 0; j < K && !done; j++) {
+                if (!(x & (1 << j))) continue;
+
+                if (basis[j]) x ^= basis[j];
+                else basis[j] = x, sz++, done = true;
+            }
+        }
+
+        int ans = 1 << (K - sz);
+        cout << ans << "\n";
+    }
+}
diff --git a/Codeforces/mahmoud_and_ehab_and_yet_another_xor_task.cpp b/Codeforces/mahmoud_and_ehab_and_yet_another_xor_task.cpp
@@ -0,0 +1,70 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+const int MAX = 20;
+const int MOD = 1e9 + 7;
+
+int exp(int a, int n) {
+    if (!n) return 1;
+
+    int ans = exp(a, n >> 1);
+    ans = (1LL * ans * ans) % MOD;
+
+    if (!(n & 1)) return ans;
+    return (1LL * ans * a) % MOD;
+}
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int n, q;
+    cin >> n >> q;
+
+    vector<int> a(n);
+    for (int i = 0; i < n; i++)
+        cin >> a[i];
+
+    vector<tuple<int, int, int>> queries(q);
+    for (int i = 0; i < q; i++) {
+        int l, x;
+        cin >> l >> x;
+        queries[i] = make_tuple(l, x, i);
+    }
+
+    sort(queries.begin(), queries.end());
+
+    vector<int> ans(q, 0);
+    int basis[MAX] = {0}, sz = 0, processed = 0;
+
+    for (auto [l, x, idx]: queries) {
+        while (processed < l) {
+            bool done = false;
+            for (int i = 0; i < MAX && !done; i++) {
+                if (!(a[processed] & (1 << i))) continue;
+
+                if (basis[i]) a[processed] ^= basis[i];
+                else basis[i] = a[processed], sz++, done = true;
+            }
+
+            processed++;
+        }
+
+        bool independent = false;
+        for (int i = 0; i < MAX && !independent; i++) {
+            if (!(x & (1 << i))) continue;
+
+            if (basis[i]) x ^= basis[i];
+            else independent = true;
+        }
+
+        if (!independent)
+            ans[idx] = exp(2, l - sz);
+    }
+
+    for (int i = 0; i < q; i++)
+        cout << ans[i] << "\n";
+}
diff --git a/Codeforces/zero_xor_subset_less.cpp b/Codeforces/zero_xor_subset_less.cpp
@@ -0,0 +1,36 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+const int MAX = 30;
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int n; cin >> n;
+
+    vector<int> a(n);
+    for (int i = 0; i < n; i++)
+        cin >> a[i];
+
+    int x = 0, sz = 0, basis[MAX] = {0};
+    for (int i = 0; i < n; i++) {
+        x ^= a[i];
+
+        int v = x;
+        bool done = false;
+
+        for (int j = 0; j < MAX && !done; j++) {
+            if (!(v & (1 << j))) continue;
+
+            if (basis[j]) v ^= basis[j];
+            else basis[j] = v, sz++, done = true;
+        }
+    }
+
+    if (!x) cout << "-1\n";
+    else cout << sz << "\n";
+}
diff --git a/Other/godzilla_and_pretty_xor.cpp b/Other/godzilla_and_pretty_xor.cpp
@@ -0,0 +1,46 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+const int MAX = 31;
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int n; cin >> n;
+
+    int basis[MAX] = {0}, sz = 0;
+    while (n--) {
+        int t, k;
+        cin >> t >> k;
+
+        if (t == 1) {
+            bool done = false;
+            for (int i = MAX - 1; i >= 0 && !done; i--) {
+                if (!(k & (1 << i))) continue;
+
+                if (basis[i]) k ^= basis[i];
+                else basis[i] = k, sz++, done = true;
+            }
+        } else {
+            int ans = 0, seen = 0;
+            for (int i = MAX - 1; i >= 0; i--) {
+                if (!basis[i]) continue;
+
+                int rem = 1 << (sz - ++seen);
+                if (k > rem) {
+                    k -= rem;
+                    if (!(ans & (1 << i)))
+                        ans ^= basis[i];
+                } else if (ans & (1 << i)) {
+                    ans ^= basis[i];
+                }
+            }
+
+            cout << ans << "\n";
+        }
+    }
+}
diff --git a/Other/two_faced_hobz.cpp b/Other/two_faced_hobz.cpp
@@ -0,0 +1,62 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+const int MAX = 30;
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    freopen("salkan.in", "r", stdin);
+
+    int T; cin >> T;
+    while (T--) {
+        int N, K;
+        cin >> N >> K;
+
+        int XA = 0;
+        vector<int> A(N);
+
+        for (int i = 0; i < N; i++) {
+            cin >> A[i];
+            XA ^= A[i];
+        }
+
+        int basis[MAX] = {0};
+        for (int i = 0; i < N; i++) {
+            int B; cin >> B;
+
+            int v = A[i] ^ B;
+            bool done = false;
+
+            for (int j = MAX - 1; j >= 0 && !done; j--) {
+                if (!(v & (1 << j))) continue;
+
+                if (basis[j]) v ^= basis[j];
+                else basis[j] = v, done = true;
+            }
+        }
+
+        int ans = XA;
+        for (int i = MAX - 1; i >= 0; i--) {
+            if (!basis[i]) continue;
+
+            int aux = (ans & (1 << i)) ? ans : ans ^ basis[i];
+            for (int j = i - 1; j >= 0; j--) {
+                if (!basis[j]) continue;
+
+                if (aux & (1 << j))
+                    aux ^= basis[j];
+            }
+
+            if (aux > K && (ans & (1 << i))) ans ^= basis[i];
+            else if (aux <= K && !(ans & (1 << i))) ans ^= basis[i];
+        }
+
+        if (ans > K) ans = 0;
+        cout << ans << "\n";
+    }
+}
diff --git a/Spoj/xor_maximization.cpp b/Spoj/xor_maximization.cpp
@@ -0,0 +1,37 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define llong long long int
+
+const int MAX = 62;
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int N; cin >> N;
+
+    llong basis[MAX] = {0LL};
+    for (int i = 0; i < N; i++) {
+        llong a; cin >> a;
+
+        bool done = false;
+        for (int j = MAX - 1; j >= 0 && !done; j--) {
+            if (!(a & (1LL << j))) continue;
+
+            if (basis[j]) a ^= basis[j];
+            else {
+                done = true;
+                basis[j] = a;
+            }
+        }
+    }
+
+    llong ans = 0LL;
+    for (int i = MAX - 1; i >= 0; i--)
+        if (basis[i] && !(ans & (1LL << i)))
+            ans ^= basis[i];
+
+    cout << ans << "\n";
+}
