hihocoder 1233 Boxes（bfs+状态压缩+hash表）

来源：互联网发布：蝴蝶效应知乎编辑：程序博客网时间：2024/06/04 20:04

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long long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7位二进制表示，总共的状态为247，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，bfs预处理出目标状态到所有状态所需要的最小步数插入hash表中（反方向建表），然后对于每个询问O(1)回答即可。

my 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[N], save[N], 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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