20180810 提高 练习赛
题目目录，题意什么的先鸽着
第一题 题解
傻逼排序题，将点按 $x$ 轴排序，然后取前六个点即可。
代码：
#include <bits/stdc++.h>
using namespace std;
inline int rd(){int ch,ret,nag=0;while(!isdigit(ch=getchar()))nag=ch=='-';ret=ch-'0';while(isdigit(ch=getchar()))ret=ret*10+ch-'0';return nag?-ret:ret;}
struct Point {
int x, y, id;
inline bool operator< (const Point & res) const {
return x == res.x ? y < res.y : x < res.x;
}
inline void rd(int i) {
x = ::rd(); y = ::rd(); id = i;
}
} a[100005];
int main() {
int n = rd();
for (int i = 0; i < n; i++) a[i].rd(i);
sort(a, a+n);
for (int i = 0; i < 6; i++) printf(i == 5 ? "%d" : "%d ", a[i].id+1);
puts("");
return 0;
}
第二题 题解
记忆化搜索点 $(x,y)$ 能到的最远路径
如果遇到相同的值直接设成 inf
然后询问判断 $l$ 是不是小于等于最远路径
代码
#include <bits/stdc++.h>
using namespace std;
int n, m, q, a[1005][1005], dp[1005][1005];
bool vis[1005][1005];
const int INF = 0x3f3f3f3f;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
int dfs(int x, int y) {
if (vis[x][y]) return dp[x][y];
int ans = 0;
for (int i=0; i<4; i++) {
int nx = dx[i] + x, ny = dy[i] + y;
if (nx < 1 || ny < 1 || nx > n || ny > m) continue;
if (a[nx][ny] < a[x][y]) continue;
if (a[nx][ny] == a[x][y]) { ans = INF; break; }
ans = max(ans, dfs(nx, ny) + 1);
}
return dp[x][y] = ans;
}
int main() {
// freopen("nagame.in", "r",stdin);
// freopen("nagame.out", "w",stdout);
scanf("%d%d", &n,&m);
for (int i=1; i<=n; i++) for (int j=1; j<=m; j++) scanf("%d", &a[i][j]);
for (int i=1; i<=n; i++) for (int j=1; j<=m; j++) if (!vis[i][j]) dfs(i, j);
scanf("%d", &q);
while(q--) {
int x, y, z; scanf("%d%d%d", &x, &y, &z);
printf("%s\n", dp[x][y]>=z ? "= =" : "> <");
}
return 0;
}
第三题 题解
首先考虑一颗树怎么做。当然是树形dp。
然后我们考虑加了一些附件边后怎么做。先求一颗生成树，然后对于剩下的几条边，暴力枚举它两个点的情况：
- 一白一白
- 一白一黑
- 一黑一白
发现如果第一个点是白点，那第二个点不用管。
所以枚举的时间复杂度是 $\mathcal O(2^(m-n+1))$，最多 $64$ 。
调试记录
- 没有判断一个点有两种限制的情况。
代码
#include <bits/stdc++.h>
using namespace std;
inline int rd(){int ch,ret,nag=0;while(!isdigit(ch=getchar()))nag=ch=='-';ret=ch-'0';while(isdigit(ch=getchar()))ret=ret*10+ch-'0';return nag?-ret:ret;}
int n, m, e=0, ans1=0, ans0=0, hed[100005], use[100005], spn[100005];
struct edge {
int to, nxt;
} edges[200005];
struct rawedge {
int x, y;
inline void rd() { x = ::rd(); y = ::rd(); }
} A[200005];
struct UnionSet {
int fa[100005];
void I(int n) {
for (int i=1; i<=n; i++) fa[i] = i;
}
int f(int x) {
return fa[x] = (x == fa[x] ? x : f(fa[x]));
}
void u(int x, int y) {
x = f(x), y = f(y);
if (x == y) return;
fa[x] = y;
}
} S;
const int P = 1000000007;
int dp[100005][2], color[100005];
vector<int> U;
inline void addedge(int x, int y) {
edges[e] = (edge){y, hed[x]};
hed[x] = e++;
}
void findGenerateTree() {
S.I(n);
for (int i=1; i<=m; i++) if (S.f(A[i].x) != S.f(A[i].y)) {
use[i] = 1, S.u(A[i].x, A[i].y), addedge(A[i].x, A[i].y), addedge(A[i].y, A[i].x);
}
}
void dfs(int x, int fa) {
dp[x][0] = dp[x][1] = 1;
for (int e=hed[x]; e!=-1; e=edges[e].nxt) {
int y = edges[e].to;
if (y != fa) {
dfs(y, x);
dp[x][0] = 1ll * dp[x][0] * (dp[y][0] + dp[y][1]) % P;
dp[x][1] = 1ll * dp[x][1] * dp[y][0] % P;
}
}
if (spn[x] == 1) dp[x][1] = 0;
else if (spn[x] == 2) dp[x][0] = 0;
}
int main() {
// freopen("akekure.in", "r",stdin);
// freopen("akekure.out", "w",stdout);
n = rd(); m = rd();
for (int i=1; i<=n; i++) hed[i] = -1;
for (int i=1; i<=m; i++) A[i].rd();
findGenerateTree();
int ans = 0;
for (int i=1; i<=m; i++) if (!use[i]) U.push_back(i);
assert(U.size() == (m - n + 1));
for (int i=0; i<(1 << (m - n + 1)); i++) {
memset(spn, 0, sizeof(spn));
bool fail = 0;
for (int j=0; j<U.size(); j++) if (i & (1 << j)) {
if (spn[A[U[j]].x] > 1) { fail = 1; break; }
spn[A[U[j]].x] = 1;
} else {
if (spn[A[U[j]].x] == 1 || spn[A[U[j]].y] > 1) { fail = 1; break; }
spn[A[U[j]].x] = 2;
spn[A[U[j]].y] = 1;
}
if (fail) continue;
dfs(1, 0);
(ans += (dp[1][0] + dp[1][1]) % P) %= P;
}
printf("%d\n", ans);
return 0;
}
