18.10.9 题目
bzoj1306 CQOI2009
这道题就是一个爆搜 然后剪枝很多 很不容易卡过去了
代码
#include <bits/stdc++.h> using namespace std; const int N = 10; int n, a[N], tot = 0, now[N], las[N], ans; struct mat { int x, y; mat(int x = 0, int y = 0): x(x), y(y) {} }m[N * N]; void Init( ) { scanf("%d",& n); for(int i = 1;i <= n;i ++) scanf("%d",& a[i]); for(int i = 1;i <= n;i ++) { for(int j = i + 1;j <= n;j ++) { m[++ tot] = mat(i, j); } las[i] = tot; } } void dfs(int pos) { if(pos == tot + 1) { for(int i = 1;i <= n;i ++) if(a[i] != now[i]) return ; ans ++; return ; } int u = m[pos].x, v = m[pos].y; if(now[u] + 3 * (las[u] - pos + 1) < a[u]) return ; if(now[v] + 3 * (las[v] - pos + 1) < a[v]) return ; for(int j = 0;j <= 1;j ++) { if(j == 1) { int t = u; u = v; v = t; } if(pos == las[u]) { if(now[u] + 3 == a[u]) {now[u] += 3; dfs(pos + 1); now[u] -= 3;} if(now[u] + 1 == a[u]) { now[u] ++; now[v] ++; if(now[v] <= a[v]) dfs(pos + 1); now[u] --; now[v] --; } if(now[u] == a[u]) {now[v] += 3; if(now[v] <= a[v]) dfs(pos + 1); now[v] -= 3;} return ; } } u = m[pos].x, v = m[pos].y; if(now[u] + 3 <= a[u]) { now[u] += 3; dfs(pos + 1); now[u] -=3; } if(now[u] + 1 <= a[u] && now[v] + 1 <= a[v]) { now[u] ++; now[v] ++; dfs(pos + 1); now[u] --; now[v] --; } if(now[v] + 3 <= a[v]) { now[v] += 3; dfs(pos + 1); now[v] -= 3; } } int main( ) { Init( ); dfs(1); printf("%d\n",ans); }
JSOI2015 洛谷P4171
一道$2sat$裸题啊 对于昨天才搞过$2sat$的本蒟蒻十分友好了
将每个食材拆成两个点 一个表示做汉菜 一个是满菜 根据约束条件$(i, j)$
连边$(-i, j),(-j, i)$ 然后$tarjan$跑一边强连通分量即可
代码
#include <bits/stdc++.h> using namespace std; const int N = 2 * 1e3 + 5; int tot, idc, head[N], nex[2 * N], tov[2 * N], dfn[N], low[N]; int n, m, stk[N], top, cnt, col[N], T; bool vis[N]; char s1[20], s2[20]; void add(int u, int v) { tot ++; nex[tot] = head[u]; tov[tot] = v; head[u] = tot; } void Add_Edge( ) { memset(col, 0, sizeof(col)); memset(head, 0 , sizeof(head)); tot = 0; memset(dfn, 0, sizeof(dfn)); idc = 0; scanf("%d%d",& n,& m); top = 0; cnt = 0; for(int i = 1;i <= m;i ++) { scanf("%s %s", s1, s2); int n1 = s1[0] == 'h' ? 0 : 1; int n2 = s2[0] == 'h' ? 0 : 1; int u = 0, v = 0, k = 1; while(s1[k] >= '0' && s1[k] <= '9') u = u * 10 + s1[k ++] - '0'; k = 1; while(s2[k] >= '0' && s2[k] <= '9') v = v * 10 + s2[k ++] - '0'; if(n1 == 0 && n2 == 0) {add(u + n, v); add(v + n, u);} if(n1 == 0 && n2 == 1) {add(u + n, v + n); add(v, u);} if(n1 == 1 && n2 == 1) {add(u, v + n); add(v, u + n);} if(n1 == 1 && n2 == 0) {add(u, v); add(v + n, u + n);} } } void tarjan(int u) { dfn[u] = low[u] = ++ idc; vis[u] = true; stk[++ top] = u; for(int i = head[u];i;i = nex[i]) { int v = tov[i]; if(! dfn[v]) { tarjan(v); low[u] = min(low[u], low[v]); } else if(vis[v]) low[u] = min(low[u], dfn[v]); } if(low[u] == dfn[u]) { cnt ++; while(1) { int x = stk[top --]; vis[x] = false; col[x] = cnt; if(x == u) break; } } } void Solve( ) { scanf("%d",& T); while(T --) { Add_Edge( ); for(int i = 1;i <= n;i ++) { if(! dfn[i]) tarjan(i); } bool tag = false; for(int i = 1;i <= n;i ++) { if(col[i] == col[i + n]) tag = true; } if(tag) printf("BAD\n"); else printf("GOOD\n"); } } int main( ) { Solve( ); }
NOI2015 洛谷P2146
又是一道裸题 线段树套树剖 将已安装的视为$1$ 未安装为$0$
安装则统计从该点到根节点的$0$个数 卸载则统计子树$1$的个数 相应修改即可
代码
#include <bits/stdc++.h> #define il inline #define rg register using namespace std; const int N = 1e5 + 5; int n, tot, head[N], nex[2 * N], tov[2 * N], fa[N], size[N]; int tag[4 * N], f[4 * N], top[N], dep[N], in[N], out[N]; int son[N], idc, q; il int read( ) { int t = 1, ans = 0; char x; x = getchar( ); while(x < '0' || x > '9') { if(x == '-') t = -1; x = getchar( ); } while(x >= '0' && x <= '9') { ans = ans * 10 + x - '0'; x = getchar( ); } return ans * t; } il void add(int u, int v) { tot ++; nex[tot] = head[u]; tov[tot] = v; head[u] = tot; } il void Add_Edge( ) { n = read( ); int v; for(rg int i = 1;i < n;i ++) { v = read( ); add(i + 1, v + 1); add(v + 1, i + 1); } } il void push_down(int o, int l, int r) { int mid = l + r >> 1; if(tag[o] != -1) { tag[2 * o] = tag[o]; tag[2 * o + 1] = tag[o]; f[2 * o] = tag[o] * (mid - l + 1); f[2 * o + 1] = tag[o] * (r - mid); tag[o] = -1; } } il void update(int o) { f[o] = f[2 * o] + f[2 * o + 1]; } il int query(int o, int l, int r, int L, int R) { if(l >= L && r <= R) return f[o]; push_down(o, l, r); int mid = l + r >> 1; int num = 0; if(L <= mid) num += query(2 * o, l, mid, L, R); if(mid < R) num += query(2 * o + 1, mid + 1, r, L, R); update(o); return num; } il void modify(int o, int l, int r, int L, int R, int del) { if(l >= L && r <= R) { f[o] = del * (r - l + 1); tag[o] = del; return ; } push_down(o, l, r); int mid = l + r >> 1; if(L <= mid) modify(2 * o, l, mid, L, R, del); if(mid < R) modify(2 * o + 1, mid + 1, r, L, R, del); update(o); } il int Query(int u, int v) { int num = 0; while(top[u] != top[v]) { if(dep[top[u]] < dep[top[v]]) swap(u, v); num += query(1, 1, n, in[top[u]], in[u]); modify(1, 1, n, in[top[u]], in[u], 1); u = fa[top[u]]; } if(dep[u] < dep[v]) swap(u, v); num += query(1, 1, n, in[v], in[u]); modify(1, 1, n, in[v], in[u], 1); return num; } il void dfs1(int u, int fat) { size[u] = 1; fa[u] = fat; for(rg int i = head[u];i;i = nex[i]) { int v = tov[i]; if(v == fat) continue; dep[v] = dep[u] + 1; dfs1(v, u); size[u] += size[v]; if(size[v] > size[son[u]]) son[u] = v; } } il void dfs2(int u, int tp) { top[u] = tp; in[u] = ++ idc; if(son[u]) dfs2(son[u], tp); for(rg int i = head[u];i;i = nex[i]) { int v = tov[i]; if(v == fa[u] || v == son[u]) continue; dfs2(v, v); } out[u] = idc; } il void Solve( ) { scanf("%d",& q); dep[1] = 1; dfs1(1, 1); dfs2(1, 1); memset(tag, -1, sizeof(tag)); for(rg int i = 1;i <= q;i ++) { char s[10]; int x; scanf("%s",s); if(s[0] == 'i') { scanf("%d",& x);x ++; int num = Query(x, 1); num = dep[x] - num; printf("%d\n",num); } else { scanf("%d",& x);x ++; int num = query(1, 1, n, in[x], out[x]); modify(1, 1, n, in[x], out[x], 0); printf("%d\n",num); } } } int main( ) { Add_Edge( ); Solve( ); }
题目大意:
给定一个矩阵P 两整数L,R 问是否存在数列a[N]与b[N] 使得L ≤ p[ i ][ j ] * a[ i ] / b[ j ] ≤ R。
这道题是一道差分约束系统的题目 也就是说将一堆不等式化为图论 通过求最短/最长路求解
对于两不等式 $a - b <= c , b - d <= e$ 建边$(b, a, c),(d, b, e)$ 通过求$b, d$间最短路得到边界条件
将式子化简得到
$L * b[j] <= p[i][j] * a[i] <= R * b[j]$
因为两边分别有未知数 所以两边同时取对数化为加减
$b[j] - a[i] <= logP[i][j] - logL$
$a[i] - b[j] <= logR - logP[i][j]$
像上述建边 然后跑最短路即可 判断有无解就是判断有无负环 因为一个负环所代表的式子相当于$0 <= x, x$是一个负数 显然不合法叻
普遍的做法是建一个超级源点向每个点连一条边权为$0$的边 无数解的情况则是求解的两个点不连通
但是由于这道题每个点都是互相连通的 所以直接跑也可以
代码
#include <bits/stdc++.h> #define oo 1e9 using namespace std; const int N = 400100; int head[805], nex[N], tov[N], n, m, l, r; int tot = 0, cnt[N], src; double val[N], dis[N], p[805][805]; bool tag, vis[N]; queue<int>Q; void Init( ) { memset(head, 0, sizeof(head)); tot = 0; memset(cnt, 0, sizeof(cnt)); tag = false; for(int i = 1;i <= n;i ++) for(int j = 1;j <= m;j ++) scanf("%lf",& p[i][j]); } void add(int u, int v, double w) { tot ++; nex[tot] = head[u]; tov[tot] = v; val[tot] = w; head[u] = tot; } void Add_Edge( ) { double L = log2(l), R = log2(r); for(int i = 1;i <= n;i ++) { for(int j = 1;j <= m;j ++) { double P = log2(p[i][j]); add(i, j + n, P - L); add(j + n, i, R - P); } } src = n + m + 1; for(int i = 1;i <= n + m;i ++) add(src, i, 0); } void spfa( ) { for(int i = 1;i <= src;i ++) dis[i] = oo; memset(vis, 0, sizeof(vis)); dis[src] = 0; Q.push(src); vis[src] = true; while(! Q.empty( )) { int u = Q.front( ); Q.pop( ); vis[u] = false; for(int i = head[u];i;i = nex[i]) { int v = tov[i]; if(dis[v] - dis[u] - val[i] > 1e-10) { dis[v] = dis[u] + val[i]; if(! vis[v]) { cnt[v] ++; if(cnt[v] > 15) { tag = true; return; } vis[v] = true; Q.push(v); } } } } } int main( ) { while(scanf("%d%d%d%d",& n,& m,& l,& r) == 4) { Init( ); Add_Edge( ); spfa( ); if(tag) printf("NO\n"); else printf("YES\n"); } }
SDOI2015 洛谷2483
这道题用$A*$水过去了..滑稽
估价函数写一下 优先队列写一下 $SPFA$写一下 美滋滋
代码
#include <bits/stdc++.h> using namespace std; const int N = 5005; double g[N], e; int n, m, cnt[N], ans; bool vis[N]; struct node { int x; double h; node(int x = 0, double h = 0): x(x),h(h) {} bool operator < (const node & a) const { return h + g[x] > a.h + g[a.x]; } }; priority_queue<node>Q; vector<node>G[N],G1[N]; queue<int>q; void Init( ) { scanf("%d%d%lf",& n,& m,& e); for(int i = 1;i <= m;i ++) { int u, v; double w; scanf("%d%d%lf",& u,& v,& w); G[u].push_back(node(v, w)); G1[v].push_back(node(u, w)); } } void spfa( ) { for(int i = 1;i <= n;i ++) g[i] = 1000000000; memset(vis, 0, sizeof(vis)); q.push(n); g[n] = 0; vis[n] = true; while(! q.empty( )) { int u = q.front( ); q.pop( ); vis[u] = false; for(int i = 0;i < G1[u].size( );i ++) { int v = G1[u][i].x; if(g[v] > g[u] + G1[u][i].h) { g[v] = g[u] + G1[u][i].h; if(! vis[v]) { q.push(v); vis[v] = true; } } } } } void A_star( ) { double k = e / g[1]; Q.push(node(1, 0)); while(! Q.empty( )) { node u = Q.top( ); Q.pop( ); int x = u.x; double h = u.h; if(h > e) return ; cnt[x] ++; if(cnt[x] > k) continue; if(x == n) { ans ++; e -= h; continue; } for(int i = 0;i < G[x].size( );i ++) { int v = G[x][i].x; Q.push(node(v, h + G[x][i].h)); } } } int main( ) { Init( ); spfa( ); A_star( ); printf("%d\n",ans); }
