POJ 1475 Pushing Boxes 推箱子游戏_推箱子关卡boxes10-优快云博客

本文介绍了一种解决迷宫推箱子游戏问题的算法。通过使用两次广度优先搜索（BFS），该算法能够找到将箱子推到目标位置所需的最少推动次数及行走路径。文章详细解释了算法的工作原理，并提供了一个完整的C++实现示例。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

两个BFS。

尝试使用A*算法，但由于使用stl的priority_queue，效率太低，不能满足时限要求。

/*Pushing Boxes Time Limit: 2000MS Memory Limit: 131072K Total Submissions: 2966 Accepted: 1084 Special Judge Description Imagine you are standing inside a two-dimensional maze composed of square cells which may or may not be filled with rock. You can move north, south, east or west one cell at a step. These moves are called walks. One of the empty cells contains a box which can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box. Such a move is called a push. The box cannot be moved in any other way than by pushing, which means that if you push it into a corner you can never get it out of the corner again. One of the empty cells is marked as the target cell. Your job is to bring the box to the target cell by a sequence of walks and pushes. As the box is very heavy, you would like to minimize the number of pushes. Can you write a program that will work out the best such sequence? Input The input contains the descriptions of several mazes. Each maze description starts with a line containing two integers r and c (both <= 20) representing the number of rows and columns of the maze. Following this are r lines each containing c characters. Each character describes one cell of the maze. A cell full of rock is indicated by a `#' and an empty cell is represented by a `.'. Your starting position is symbolized by `S', the starting position of the box by `B' and the target cell by `T'. Input is terminated by two zeroes for r and c. Output For each maze in the input, first print the number of the maze, as shown in the sample output. Then, if it is impossible to bring the box to the target cell, print ``Impossible.''. Otherwise, output a sequence that minimizes the number of pushes. If there is more than one such sequence, choose the one that minimizes the number of total moves (walks and pushes). If there is still more than one such sequence, any one is acceptable. Print the sequence as a string of the characters N, S, E, W, n, s, e and w where uppercase letters stand for pushes, lowercase letters stand for walks and the different letters stand for the directions north, south, east and west. Output a single blank line after each test case. Sample Input 1 7 SB....T 1 7 SB..#.T 7 11 ########### #T##......# #.#.#..#### #....B....# #.######..# #.....S...# ########### 8 4 .... .##. .#.. .#.. .#.B .##S .... ###T 0 0 Sample Output Maze #1 EEEEE Maze #2 Impossible. Maze #3 eennwwWWWWeeeeeesswwwwwwwnNN Maze #4 swwwnnnnnneeesssSSS Source Southwestern European Regional Contest 1997*/ #include <stdio.h> #include <algorithm> #include <queue> #include <vector> #include "math.h" #include "string.h" using namespace std; #define MAX_MAZE_SIZE 20 #define MAX_TOTAL_CELL_NUM 400 #define POSITION_NOT_VISITED 0 #define POSITION_VISITED_FROM_BIG 1 #define POSITION_VISITED_FROM_SMALL 2 #define POSITION_VISITED_FROM_EQUL 4 #define POSITION_VISITED 7 #define INIFINITE 0x7f7f7f7f #define MOVE_SUCCESS 0 #define MOVE_FAIL -1 #define EMPTY 0 #define ROCK 1 #define MOVE_NORTH 0 #define MOVE_SOUTH 1 #define MOVE_WEST 2 #define MOVE_EAST 3 typedef struct _POSITION_ST_ { char cX; char cY; }POSITION_ST; POSITION_ST gstBoxTarget; POSITION_ST gstPersonTarget; char gacBoxVisited[MAX_MAZE_SIZE][MAX_MAZE_SIZE][4]; char gacPersonVisited[MAX_MAZE_SIZE][MAX_MAZE_SIZE]; char gacMazeMap[MAX_MAZE_SIZE][MAX_MAZE_SIZE]; int giMazeRowNum; int giMazeColumnNum; struct BOX_STATE_ST { char cPosX; char cPosY; char cMoveDiert; char cBoxOldPosX; char cBoxOldPosY; char cPerSrcPosX; char cPerSrcPosY; char cPerTgtPosX; char cPerTgtPosY; queue<char> qucMoveRecord; }; struct PERSON_STATE_ST { short cPosX; short cPosY; queue<char> qucMoveRecord; }; int Person_AStar(BOX_STATE_ST *vpstState,queue<char> *vpqucMoveRecord) { PERSON_STATE_ST stStateNorth; PERSON_STATE_ST stStateSouth; PERSON_STATE_ST stStateWest; PERSON_STATE_ST stStateEast; queue<PERSON_STATE_ST> priquPerQueue; memset(gacPersonVisited,POSITION_NOT_VISITED,MAX_MAZE_SIZE*MAX_MAZE_SIZE); /*add src state into queue*/ stStateNorth.cPosX = vpstState->cPerSrcPosX; stStateNorth.cPosY = vpstState->cPerSrcPosY; priquPerQueue.push(stStateNorth); if (vpstState->cPerSrcPosX == vpstState->cPerTgtPosX &&vpstState->cPerSrcPosY == vpstState->cPerTgtPosY) { return MOVE_SUCCESS; } gstPersonTarget.cX = vpstState->cPerTgtPosX; gstPersonTarget.cY = vpstState->cPerTgtPosY; gacMazeMap[vpstState->cBoxOldPosX][vpstState->cBoxOldPosY] = ROCK; while(!priquPerQueue.empty()) { stStateNorth = priquPerQueue.front(); if (POSITION_VISITED == gacPersonVisited[stStateNorth.cPosX][stStateNorth.cPosY]) { priquPerQueue.pop(); continue; } gacPersonVisited[stStateNorth.cPosX][stStateNorth.cPosY] = POSITION_VISITED; if (stStateNorth.cPosX == vpstState->cPerTgtPosX &&stStateNorth.cPosY == vpstState->cPerTgtPosY) { while(!stStateNorth.qucMoveRecord.empty()) { vpqucMoveRecord->push(stStateNorth.qucMoveRecord.front()); stStateNorth.qucMoveRecord.pop(); } gacMazeMap[vpstState->cBoxOldPosX][vpstState->cBoxOldPosY] = EMPTY; return MOVE_SUCCESS; } stStateSouth = priquPerQueue.front(); stStateWest = priquPerQueue.front(); stStateEast = priquPerQueue.front(); priquPerQueue.pop(); /************************************************************************/ /* north */ /************************************************************************/ if (0 < stStateNorth.cPosX) { if (EMPTY == gacMazeMap[stStateNorth.cPosX-1][stStateNorth.cPosY] &&POSITION_VISITED != gacPersonVisited[stStateNorth.cPosX-1][stStateNorth.cPosY]) { stStateNorth.cPosX--; stStateNorth.qucMoveRecord.push('n'); priquPerQueue.push(stStateNorth); } } /************************************************************************/ /* south */ /************************************************************************/ if (giMazeRowNum-1 > stStateSouth.cPosX ) { if (EMPTY == gacMazeMap[stStateSouth.cPosX+1][stStateSouth.cPosY] &&POSITION_VISITED != gacPersonVisited[stStateSouth.cPosX+1][stStateSouth.cPosY] ) { stStateSouth.cPosX++; stStateSouth.qucMoveRecord.push('s'); priquPerQueue.push(stStateSouth); } } /************************************************************************/ /* west */ /************************************************************************/ if (0 < stStateWest.cPosY ) { if (EMPTY == gacMazeMap[stStateWest.cPosX][stStateWest.cPosY-1] &&POSITION_VISITED != gacPersonVisited[stStateWest.cPosX][stStateWest.cPosY-1]) { stStateWest.cPosY--; stStateWest.qucMoveRecord.push('w'); priquPerQueue.push(stStateWest); } } /************************************************************************/ /* east */ /************************************************************************/ if (giMazeColumnNum-1 > stStateEast.cPosY ) { if (EMPTY == gacMazeMap[stStateEast.cPosX][stStateEast.cPosY+1] &&POSITION_VISITED != gacPersonVisited[stStateEast.cPosX][stStateEast.cPosY+1]) { stStateEast.cPosY++; stStateEast.qucMoveRecord.push('e'); priquPerQueue.push(stStateEast); } } } gacMazeMap[vpstState->cBoxOldPosX][vpstState->cBoxOldPosY] = EMPTY; return MOVE_FAIL; } int CheckMove(char vcPosVisited,char vcPerPos,char vcBoxPos) { if ((vcPerPos > vcBoxPos &&POSITION_VISITED_FROM_BIG != (vcPosVisited&POSITION_VISITED_FROM_BIG)) ||(vcPerPos < vcBoxPos &&POSITION_VISITED_FROM_SMALL != (vcPosVisited&POSITION_VISITED_FROM_SMALL)) ||(vcPerPos == vcBoxPos &&POSITION_VISITED_FROM_EQUL != (vcPosVisited&POSITION_VISITED_FROM_EQUL))) { return MOVE_SUCCESS; } return MOVE_FAIL; } void MarkMove(char *vpcPosVisited,char vcPerPos,char vcBoxPos) { if (vcPerPos > vcBoxPos) { *vpcPosVisited |= POSITION_VISITED_FROM_BIG; } else if(vcPerPos < vcBoxPos) { *vpcPosVisited |= POSITION_VISITED_FROM_SMALL; } else { *vpcPosVisited |= POSITION_VISITED_FROM_EQUL; } return; } int PushingBoxes_BFS(POSITION_ST *vpstSrcBoxPos,POSITION_ST *vpstSrcPerPos,int viMazeId) { int iReturnVal; char cDirection; char cPerPos; char cBoxPos; int iFlag = 0; BOX_STATE_ST stStateNorth; BOX_STATE_ST stStateSouth; BOX_STATE_ST stStateWest; BOX_STATE_ST stStateEast; queue<char> qucMoveRecord; queue<BOX_STATE_ST> priquBoxQueue; memset(gacBoxVisited,POSITION_NOT_VISITED,MAX_MAZE_SIZE*MAX_MAZE_SIZE*4); /*add src state into queue*/ stStateNorth.cPosX = vpstSrcBoxPos->cX; stStateNorth.cPosY = vpstSrcBoxPos->cY; stStateNorth.cBoxOldPosX = vpstSrcBoxPos->cX; stStateNorth.cBoxOldPosY = vpstSrcBoxPos->cY; stStateNorth.cPerSrcPosX = vpstSrcPerPos->cX; stStateNorth.cPerSrcPosY = vpstSrcPerPos->cY; stStateNorth.cPerTgtPosX = vpstSrcPerPos->cX; stStateNorth.cPerTgtPosY = vpstSrcPerPos->cY; priquBoxQueue.push(stStateNorth); while(!priquBoxQueue.empty()) { stStateNorth = priquBoxQueue.front(); stStateSouth = priquBoxQueue.front(); stStateWest = priquBoxQueue.front(); stStateEast = priquBoxQueue.front(); priquBoxQueue.pop(); if (0 != iFlag) { if (MOVE_SOUTH == stStateNorth.cMoveDiert) { cDirection = 'S'; cPerPos = stStateNorth.cPerSrcPosX; cBoxPos = stStateNorth.cBoxOldPosX; } else if (MOVE_NORTH == stStateNorth.cMoveDiert) { cDirection = 'N'; cPerPos = stStateNorth.cPerSrcPosX; cBoxPos = stStateNorth.cBoxOldPosX; } else if (MOVE_EAST == stStateNorth.cMoveDiert) { cDirection = 'E'; cPerPos = stStateNorth.cPerSrcPosY; cBoxPos = stStateNorth.cBoxOldPosY; } else if(MOVE_WEST == stStateNorth.cMoveDiert) { cDirection = 'W'; cPerPos = stStateNorth.cPerSrcPosY; cBoxPos = stStateNorth.cBoxOldPosY; } if (POSITION_VISITED == gacBoxVisited[stStateNorth.cPosX][stStateNorth.cPosY][stStateNorth.cMoveDiert]) { continue; } while(!qucMoveRecord.empty()) { qucMoveRecord.pop(); } iReturnVal = Person_AStar(&stStateNorth,&qucMoveRecord); if (MOVE_SUCCESS == iReturnVal) { stStateNorth.cPerSrcPosX = stStateNorth.cBoxOldPosX ; stStateNorth.cPerSrcPosY = stStateNorth.cBoxOldPosY ; stStateSouth.cPerSrcPosX = stStateNorth.cBoxOldPosX ; stStateSouth.cPerSrcPosY = stStateNorth.cBoxOldPosY ; stStateEast.cPerSrcPosX = stStateNorth.cBoxOldPosX ; stStateEast.cPerSrcPosY = stStateNorth.cBoxOldPosY ; stStateWest.cPerSrcPosX = stStateNorth.cBoxOldPosX ; stStateWest.cPerSrcPosY = stStateNorth.cBoxOldPosY ; while(!qucMoveRecord.empty()) { stStateNorth.qucMoveRecord.push(qucMoveRecord.front()); stStateSouth.qucMoveRecord.push(qucMoveRecord.front()); stStateEast.qucMoveRecord.push(qucMoveRecord.front()); stStateWest.qucMoveRecord.push(qucMoveRecord.front()); qucMoveRecord.pop(); } stStateNorth.qucMoveRecord.push(cDirection); stStateSouth.qucMoveRecord.push(cDirection); stStateEast.qucMoveRecord.push(cDirection); stStateWest.qucMoveRecord.push(cDirection); } else { MarkMove(&gacBoxVisited[stStateNorth.cPosX][stStateNorth.cPosY][stStateNorth.cMoveDiert],cPerPos,cBoxPos); continue; } gacBoxVisited[stStateNorth.cPosX][stStateNorth.cPosY][stStateNorth.cMoveDiert] = POSITION_VISITED; } iFlag =1; if (stStateNorth.cPosX == gstBoxTarget.cX &&stStateNorth.cPosY == gstBoxTarget.cY) { printf("Maze #%d/n",viMazeId); while(!stStateNorth.qucMoveRecord.empty()) { printf("%c",stStateNorth.qucMoveRecord.front()); stStateNorth.qucMoveRecord.pop(); } printf("/n/n"); return MOVE_SUCCESS; } if (0 < stStateNorth.cPosX && giMazeRowNum - 1 > stStateNorth.cPosX &&EMPTY == gacMazeMap[stStateNorth.cPosX-1][stStateNorth.cPosY] &&EMPTY == gacMazeMap[stStateNorth.cPosX+1][stStateNorth.cPosY]) { /************************************************************************/ /* north */ /************************************************************************/ if (POSITION_VISITED != gacBoxVisited[stStateNorth.cPosX-1][stStateNorth.cPosY][MOVE_NORTH]) { if (MOVE_SUCCESS == CheckMove(gacBoxVisited[stStateNorth.cPosX-1][stStateNorth.cPosY][MOVE_NORTH],stStateNorth.cPerSrcPosX,stStateNorth.cPosX)) { stStateNorth.cPerTgtPosX = stStateNorth.cPosX+1; stStateNorth.cPerTgtPosY = stStateNorth.cPosY; stStateNorth.cBoxOldPosX = stStateNorth.cPosX; stStateNorth.cBoxOldPosY = stStateNorth.cPosY; stStateNorth.cMoveDiert = MOVE_NORTH; stStateNorth.cPosX--; priquBoxQueue.push(stStateNorth); } } /************************************************************************/ /* south */ /************************************************************************/ if (POSITION_VISITED != gacBoxVisited[stStateSouth.cPosX+1][stStateSouth.cPosY][MOVE_SOUTH]) { if (MOVE_SUCCESS == CheckMove(gacBoxVisited[stStateSouth.cPosX+1][stStateSouth.cPosY][MOVE_SOUTH],stStateSouth.cPerSrcPosX,stStateSouth.cPosX)) { stStateSouth.cPerTgtPosX = stStateSouth.cPosX-1; stStateSouth.cPerTgtPosY = stStateSouth.cPosY; stStateSouth.cBoxOldPosX = stStateSouth.cPosX; stStateSouth.cBoxOldPosY = stStateSouth.cPosY; stStateSouth.cMoveDiert = MOVE_SOUTH; stStateSouth.cPosX++; priquBoxQueue.push(stStateSouth); } } } if (0 < stStateWest.cPosY && giMazeColumnNum-1 > stStateWest.cPosY &&EMPTY == gacMazeMap[stStateWest.cPosX][stStateWest.cPosY-1] &&EMPTY == gacMazeMap[stStateWest.cPosX][stStateWest.cPosY+1]) { /************************************************************************/ /* west */ /************************************************************************/ if (POSITION_VISITED != gacBoxVisited[stStateWest.cPosX][stStateWest.cPosY-1][MOVE_WEST]) { if (MOVE_SUCCESS == CheckMove(gacBoxVisited[stStateWest.cPosX][stStateWest.cPosY-1][MOVE_WEST],stStateWest.cPerSrcPosY,stStateWest.cPosY)) { stStateWest.cPerTgtPosX = stStateWest.cPosX; stStateWest.cPerTgtPosY = stStateWest.cPosY+1; stStateWest.cBoxOldPosX = stStateWest.cPosX; stStateWest.cBoxOldPosY = stStateWest.cPosY; stStateWest.cMoveDiert = MOVE_WEST; stStateWest.cPosY--; priquBoxQueue.push(stStateWest); } } /************************************************************************/ /* east */ /************************************************************************/ if (POSITION_VISITED != gacBoxVisited[stStateEast.cPosX][stStateEast.cPosY+1][MOVE_EAST]) { if (MOVE_SUCCESS == CheckMove(gacBoxVisited[stStateEast.cPosX][stStateEast.cPosY+1][MOVE_EAST],stStateEast.cPerSrcPosY,stStateEast.cPosY)) { stStateEast.cPerTgtPosX = stStateEast.cPosX; stStateEast.cPerTgtPosY = stStateEast.cPosY-1; stStateEast.cBoxOldPosX = stStateEast.cPosX; stStateEast.cBoxOldPosY = stStateEast.cPosY; stStateEast.cMoveDiert = MOVE_EAST; stStateEast.cPosY++; priquBoxQueue.push(stStateEast); } } } } return MOVE_FAIL; } int main(void) { int iLoopRow; int iLoopColumn; int iMazeId = 1; char acBuff[MAX_MAZE_SIZE+1]; POSITION_ST stSrcBoxPos; POSITION_ST stSrcPerPos; while (1) { scanf("%d %d",&giMazeRowNum,&giMazeColumnNum); if (0 == giMazeRowNum && 0 == giMazeColumnNum) { break; } memset(gacMazeMap,EMPTY,MAX_MAZE_SIZE*MAX_MAZE_SIZE); for (iLoopRow = 0; iLoopRow < giMazeRowNum; iLoopRow++) { scanf("%s",acBuff); for (iLoopColumn = 0; iLoopColumn < giMazeColumnNum; iLoopColumn++) { if ('#' == acBuff[iLoopColumn]) { gacMazeMap[iLoopRow][iLoopColumn] = ROCK; } else if ('.' == acBuff[iLoopColumn]) { continue; } else if ('T' == acBuff[iLoopColumn]) { gstBoxTarget.cX = iLoopRow; gstBoxTarget.cY = iLoopColumn; } else if ('B' == acBuff[iLoopColumn]) { stSrcBoxPos.cX = iLoopRow; stSrcBoxPos.cY = iLoopColumn; } else if ('S' == acBuff[iLoopColumn]) { stSrcPerPos.cX = iLoopRow; stSrcPerPos.cY = iLoopColumn; } } } if(MOVE_SUCCESS != PushingBoxes_BFS(&stSrcBoxPos,&stSrcPerPos,iMazeId++)) { printf("Maze #%d/nImpossible./n/n",iMazeId-1); } } return 0; } /*========================END OF FILE=================================================*/