hihocoder 1233 Boxes(bfs+状态压缩+hash表)
2015-09-22 16:36
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题意:
有n个卡槽,放有体积不同的n个空盒子,每次你可以移动一个空盒子到相邻卡槽,但前提是相邻卡槽若已经有空盒子,那么要移动的空盒子体积必须小于已有的空盒子,问要移动多少步才能使得从左到右,每个卡槽空盒子的体积递增。解析:
状态压缩,用一个longlong longlong的状态表示当前所有的状态,每个盘子所在的位置,每个盘子的位置用77位二进制表示,总共的状态为2472^{47},因为每次盘子只能向左放或者向右放,那么我们从结束的位置开始搜索,bfsbfs预处理出目标状态到所有状态所需要的最小步数插入hashhash表中(反方向建表),然后对于每个询问O(1)O(1)回答即可。mymy codecode
[code]#include <cstdio> #include <cstring> #include <algorithm> #include <queue> using namespace std; typedef long long ll; const int MAXSIZE = 1000003; const int N = 7; const int dir[] = {-1, 1}; int goal[] = {1, 2, 3, 4, 5, 6, 7}; int bit[65]; struct Node { ll state; int step; }; int v , save , n; struct HashTable { int head[MAXSIZE], next[MAXSIZE]; ll state[MAXSIZE], dist[MAXSIZE]; int sz; void clear() {sz = 1; memset(head, 0, sizeof(head)); } int getHash(ll state) { return state % MAXSIZE; } bool insert(ll st, ll step) { int h = getHash(st); int u = head[h]; while(u) { if(st == state[u]) return false; u = next[u]; } state[sz] = st; dist[sz] = step; next[sz] = head[h]; head[h] = sz++; return true; } int find(ll st) { int h = getHash(st); int u = head[h]; while(u) { if(st == state[u]) return dist[u]; u = next[u]; } return -1; } } table[7]; ll getState(int a[]) { ll state = 0; for(int i = 0; i < n; i++) state = (state << 7) + (1 << (a[i] - 1)); return state; } inline int lowbit(int x) { return x & (-x); }; inline ll getSlot(ll state, int pos) { return ( state >> (7 * pos) ) % 128; } inline bool move(ll &state, int cur, int next) { ll x = getSlot(state, cur); ll curTop = bit[lowbit(x)]; x = getSlot(state, next); ll nextTop = bit[lowbit(x)]; if(curTop > nextTop && nextTop != 0) return false; state = state^(1ll << (curTop - 1 + 7 * cur))^(1ll << (curTop - 1 + 7 * next)); return true; } void bfs(int id) { queue<Node> que; ll endState = getState(goal); que.push( (Node){endState, 0} ); table[id].insert(endState, 0); while(!que.empty()) { Node node = que.front(); que.pop(); for(int i = 0; i < n; i++) { if(getSlot(node.state, i) == 0) continue; for(int d = 0; d < 2; d++) { int next = i + dir[d]; if(next < 0 || next >= n) continue; Node newNode = node; if(move(newNode.state, i, next)) { newNode.step = node.step + 1; if(table[id].insert(newNode.state, newNode.step)) que.push(newNode); } } } } } void prepare() { bit[0] = 0; for(int i = 0; i < 7; i++) bit[1 << i] = i+1; for(int i = 0; i < 7; i++) { n = i+1; table[i].clear(); bfs(i); } } void discrete() { for(int i = 0; i < n; i++) save[i] = v[i]; sort(save, save+n); for(int i = 0; i < n; i++) v[i] = lower_bound(save, save+n, v[i]) - save + 1; } int main() { prepare(); int T; scanf("%d", &T); while(T--) { scanf("%d", &n); for(int i = 0; i < n; i++) scanf("%d", &v[i]); discrete(); printf("%d\n", table[n-1].find( getState(v) )); } return 0; }
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