河南萌新联赛2024第（四）场：河南理工大学

A

思路：

B

思路：有一种贪心的写法，将整个数组排序以后比较两个相邻数的同或值，取$max$，不会证明

int th(int x, int y, int z) {int res = 0;for (int i = z - 1; i >= 0; i --) {int dx = (x >> i & 1);int dy = (y >> i & 1);if (dx == dy) res = res * 2 + 1;else res = res * 2;}return res;
}void solve() {int n, m; cin >> n >> m;vector<int> a(n);for (int i = 0; i < n; i ++) {cin >> a[i];}sort(a.rbegin(), a.rend());int ans = 0;for (int i = 1; i < n; i ++) {ans = max(ans, th(a[i], a[i - 1], m));}cout << ans << '\n';
}

思路：字典树的写法，和最大异或对的差不多

int tr[N][2], vis[N][2];
int n, m, idx;void insert(int x) {int p = 0;for (int i = m - 1; i >= 0; i --) {int u = (x >> i & 1);if (!tr[p][u]) tr[p][u] = ++idx;p = tr[p][u];}
}int queyr(int x) {int p = 0, res = 0;for (int i = m - 1; i >= 0; i --) {int u = (x >> i & 1);if (tr[p][u]) res = res * 2 + 1, p = tr[p][u];else res = res * 2, p = tr[p][u ^ 1];}return res;
}void solve() {cin >> n >> m;int ans = 0;for (int i = 0, x; i < n; i ++) {cin >> x;ans = max(ans, queyr(x));insert(x);}cout << ans << '\n';
}

C

思路：

D

思路：直接根号判断素数即可

void solve() {int x; cin >> x;if (!judge(x)) cout << "No\n";else cout << "Yes\n";
}

E

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F

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G

思路：模拟模拟

void solve() {string s; cin >> s;vector<int> a;int sum = 0, res = 0;for (int i = 0; i < s.size(); i ++) {if (s[i] >= '0' && s[i] <= '9') {res = res * 10 + (s[i] - '0');} else {a.push_back(res);res = 0;}}if (res) a.push_back(res);sort(a.rbegin(), a.rend());cout << a[0];sum += a[0];for (int i = 1; i < a.size(); i ++) {cout << '+' << a[i];sum += a[i];}cout << '\n';cout << sum << '\n';
}

H

思路：我肯定要拿最多，要尽量让一半的人拿$1$，奇数偶数讨论一下

void solve() {int n, x; cin >> x >> n;int t;if (n & 1) t = n / 2;else t = n / 2 - 1;cout << x - t << '\n';
}

I

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J

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K

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L

思路：