三人三鬼过河问题

三人三鬼过河问题：

三个人和三个鬼在河边，都想要到河的对岸去；河边有一只船，只能搭载两个人、或者两个鬼、或者一人一鬼；如果在岸上或者在船上，鬼的数目多于人的数目，鬼就会把人吃掉。
怎样安排人和鬼的组合上船过河，才能使三个人和三个鬼都安全到河的对岸去呢？

程序思路：

人鬼过河问题实际上可以考虑为状态之间的迁移，或者是构建一个有向图，然后在图中寻找可行的路径。

我们把当前岸边作为左岸，河的对岸作为右岸。

那么状态包含两个因素，一个是左岸上人鬼的数量(右岸人鬼的数量可以由左岸人鬼数量计算得出)，另一个是船在左岸还是在右岸。

迁移表现为从人鬼从左岸渡船到右岸，或者人鬼从右岸渡船到左岸。

因为鬼多于人的时候会吃人，所以不是任意的人和鬼的数量的组合都是合理的状态。

程序中首先找到所有合理的状态，然后再找到所有状态到状态可行的迁移，最后深度搜索所有迁移，寻找到从开始状态到结束状态间的可行路径。

程序的输出也是按照这个步骤，分成了三个部分，分别是可行状态、可行迁移，可行路径。

H-human人

G-ghost鬼

B-boat船

LB-left boat船在左边

RB-right boat船在右边

#include <stdio.h>#include <stdlib.h>#include <string.h>#define LBOAT '*'#define RBOAT ' 'typedef struct HGB_struct{int H;int G;int B;} HGB;int ARR_LEN;int state_count;HGB *state; //[ARR_LEN];int *transfer; // [ARR_LEN][ARR_LEN];int stack_sp;HGB *stack; // [ARR_LEN];#define transfer_ref(i, j) (transfer[i * ARR_LEN + j])#define stack_init() (stack_sp = 0)#define stack_push(hgb) (stack[stack_sp++] = (hgb))#define stack_pop() (stack[--stack_sp])#define stack_top(hgb) (stack[stack_sp - 1])#define stack_find(hgb, result) for(result = stack_sp - 1; result >= 0; result--) { if(stack[result].H == hgb.H && stack[result].G == hgb.G && stack[result].B == hgb.B) break; }#define state_find(hgb, result) for(result = state_count - 1; result >= 0; result--) { if(state[result].H == hgb.H && state[result].G == hgb.G && state[result].B == hgb.B) break; }int search(HGB hgb, int n){int i, index;int found;if((hgb.H == 0) && (hgb.G == 0) && (hgb.B == RBOAT)){stack_push(hgb);printf("=======================================================================================================\n");for(i = 0; i < stack_sp; i++)printf("H%dG%d[%c] ", stack[i].H, stack[i].G, stack[i].B);printf("\n");printf("-------------------------------------------------------------------------------------------------------\n");printf( "H%dG%d             H%dG%d\n",stack[0].H, stack[0].G,n - stack[0].H, n - stack[0].G);for(i = 0; i < stack_sp - 1; i++){if(i % 2){printf( "       <-H%dG%d--\n""H%dG%d             H%dG%d\n",stack[i + 1].H - stack[i].H, stack[i + 1].G - stack[i].G,stack[i + 1].H, stack[i + 1].G,n - stack[i + 1].H, n - stack[i + 1].G);}else{printf( "       --H%dG%d->\n""H%dG%d             H%dG%d\n",stack[i].H - stack[i + 1].H, stack[i].G - stack[i + 1].G,stack[i + 1].H, stack[i + 1].G,n - stack[i + 1].H, n - stack[i + 1].G);}}printf("=======================================================================================================\n");stack_pop();return -1;}else{stack_find(hgb, index);if(index >= 0){return 0;}state_find(hgb, index);stack_push(hgb);for(i = 0; i < state_count; i++){if(transfer_ref(index, i)){search(state[i], n);}}stack_pop();return 0;}}void human_ghost(int human_ghost_count, int boat_capacity){int i, j;int HL, GL, HR, GR;int tmp;int result;stack = NULL; // [ARR_LEN];state = NULL; //[ARR_LEN];transfer = NULL; // [ARR_LEN][ARR_LEN];ARR_LEN = (2 * (human_ghost_count + 1) * (human_ghost_count + 1));do{state = (HGB *)malloc(ARR_LEN * sizeof(HGB));if(state == NULL) break;stack = (HGB *)malloc(ARR_LEN * sizeof(HGB));if(stack == NULL) break;transfer = (int *)malloc(ARR_LEN * ARR_LEN * sizeof(int));if(transfer == NULL) break;printf("human_ghost:%d boat_capacity:%d\n", human_ghost_count, boat_capacity);state_count = 0;for(i = 0; i < (human_ghost_count + 1) * (human_ghost_count + 1); i++){HR = i / (human_ghost_count + 1);GR = i % (human_ghost_count + 1);HL = human_ghost_count - HR;GL = human_ghost_count - GR;if((HL > 0) && (HL < GL)) continue;if((HR > 0) && (HR < GR)) continue;printf("H%dG%d:H%dG%d L\n", HL, GL, HR, GR);printf("H%dG%d:H%dG%d R\n", HL, GL, HR, GR);state[state_count].H = HL;state[state_count].G = GL;state[state_count].B = LBOAT;state_count++;state[state_count].H = HL;state[state_count].G = GL;state[state_count].B = RBOAT;state_count++;}printf("         ");for(j = 0; j < state_count; j++){printf("H%dG%d[%c] ", state[j].H, state[j].G, state[j].B);}printf("\n");for(i = 0; i < state_count; i++){printf("H%dG%d[%c] |", state[i].H, state[i].G, state[i].B);for(j = 0; j < state_count; j++){transfer_ref(i, j) = 1;if(state[i].B == LBOAT){if(state[j].B == LBOAT) transfer_ref(i, j) = 0;if(state[i].H < state[j].H) transfer_ref(i, j) = 0;if(state[i].G < state[j].G) transfer_ref(i, j) = 0;tmp = (state[i].H + state[i].G) - (state[j].H + state[j].G);if(tmp <= 0 || tmp > boat_capacity) transfer_ref(i, j) = 0;}else{if(state[j].B == RBOAT) transfer_ref(i, j) = 0;if(state[i].H > state[j].H) transfer_ref(i, j) = 0;if(state[i].G > state[j].G) transfer_ref(i, j) = 0;tmp = (state[j].H + state[j].G) - (state[i].H + state[i].G);if(tmp <= 0 || tmp > boat_capacity) transfer_ref(i, j) = 0;}if(transfer_ref(i, j)){printf(" H%dG%d%c |", state[j].H, state[j].G, state[j].B);}else{printf("       |");}}printf("\n");}stack_init();search(state[0], human_ghost_count);} while(0);if(stack) free(stack);if(state) free(state);if(transfer) free(transfer);}int main(int argc, char *argv[]){int human_ghost_count = 0;int boat_capacity = 0;human_ghost(3, 2);return 0;}

程序的输出结果：

human_ghost:3 boat_capacity:2H3G3:H0G0 LH3G3:H0G0 RH3G2:H0G1 LH3G2:H0G1 RH3G1:H0G2 LH3G1:H0G2 RH3G0:H0G3 LH3G0:H0G3 RH2G2:H1G1 LH2G2:H1G1 RH1G1:H2G2 LH1G1:H2G2 RH0G3:H3G0 LH0G3:H3G0 RH0G2:H3G1 LH0G2:H3G1 RH0G1:H3G2 LH0G1:H3G2 RH0G0:H3G3 LH0G0:H3G3 R         H3G3[*] H3G3[ ] H3G2[*] H3G2[ ] H3G1[*] H3G1[ ] H3G0[*] H3G0[ ] H2G2[*] H2G2[ ] H1G1[*] H1G1[ ] H0G3[*] H0G3[ ] H0G2[*] H0G2[ ] H0G1[*] H0G1[ ] H0G0[*] H0G0[ ] H3G3[*] |       |       |       | H3G2  |       | H3G1  |       |       |       | H2G2  |       |       |       |       |       |       |       |       |       |       |H3G3[ ] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H3G2[*] |       |       |       |       |       | H3G1  |       | H3G0  |       | H2G2  |       |       |       |       |       |       |       |       |       |       |H3G2[ ] | H3G3* |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H3G1[*] |       |       |       |       |       |       |       | H3G0  |       |       |       | H1G1  |       |       |       |       |       |       |       |       |H3G1[ ] | H3G3* |       | H3G2* |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H3G0[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H3G0[ ] |       |       | H3G2* |       | H3G1* |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H2G2[*] |       |       |       |       |       |       |       |       |       |       |       | H1G1  |       |       |       | H0G2  |       |       |       |       |H2G2[ ] | H3G3* |       | H3G2* |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H1G1[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       | H0G1  |       | H0G0  |H1G1[ ] |       |       |       |       | H3G1* |       |       |       | H2G2* |       |       |       |       |       |       |       |       |       |       |       |H0G3[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       | H0G2  |       | H0G1  |       |       |H0G3[ ] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H0G2[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       | H0G1  |       | H0G0  |H0G2[ ] |       |       |       |       |       |       |       |       | H2G2* |       |       |       | H0G3* |       |       |       |       |       |       |       |H0G1[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       | H0G0  |H0G1[ ] |       |       |       |       |       |       |       |       |       |       | H1G1* |       | H0G3* |       | H0G2* |       |       |       |       |       |H0G0[*] |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |       |H0G0[ ] |       |       |       |       |       |       |       |       |       |       | H1G1* |       |       |       | H0G2* |       | H0G1* |       |       |       |=======================================================================================================H3G3[*] H3G1[ ] H3G2[*] H3G0[ ] H3G1[*] H1G1[ ] H2G2[*] H0G2[ ] H0G3[*] H0G1[ ] H1G1[*] H0G0[ ] -------------------------------------------------------------------------------------------------------H3G3             H0G0       --H0G2->H3G1             H0G2       <-H0G1--H3G2             H0G1       --H0G2->H3G0             H0G3       <-H0G1--H3G1             H0G2       --H2G0->H1G1             H2G2       <-H1G1--H2G2             H1G1       --H2G0->H0G2             H3G1       <-H0G1--H0G3             H3G0       --H0G2->H0G1             H3G2       <-H1G0--H1G1             H2G2       --H1G1->H0G0             H3G3==============================================================================================================================================================================================================H3G3[*] H3G1[ ] H3G2[*] H3G0[ ] H3G1[*] H1G1[ ] H2G2[*] H0G2[ ] H0G3[*] H0G1[ ] H0G2[*] H0G0[ ] -------------------------------------------------------------------------------------------------------H3G3             H0G0       --H0G2->H3G1             H0G2       <-H0G1--H3G2             H0G1       --H0G2->H3G0             H0G3       <-H0G1--H3G1             H0G2       --H2G0->H1G1             H2G2       <-H1G1--H2G2             H1G1       --H2G0->H0G2             H3G1       <-H0G1--H0G3             H3G0       --H0G2->H0G1             H3G2       <-H0G1--H0G2             H3G1       --H0G2->H0G0             H3G3==============================================================================================================================================================================================================H3G3[*] H2G2[ ] H3G2[*] H3G0[ ] H3G1[*] H1G1[ ] H2G2[*] H0G2[ ] H0G3[*] H0G1[ ] H1G1[*] H0G0[ ] -------------------------------------------------------------------------------------------------------H3G3             H0G0       --H1G1->H2G2             H1G1       <-H1G0--H3G2             H0G1       --H0G2->H3G0             H0G3       <-H0G1--H3G1             H0G2       --H2G0->H1G1             H2G2       <-H1G1--H2G2             H1G1       --H2G0->H0G2             H3G1       <-H0G1--H0G3             H3G0       --H0G2->H0G1             H3G2       <-H1G0--H1G1             H2G2       --H1G1->H0G0             H3G3==============================================================================================================================================================================================================H3G3[*] H2G2[ ] H3G2[*] H3G0[ ] H3G1[*] H1G1[ ] H2G2[*] H0G2[ ] H0G3[*] H0G1[ ] H0G2[*] H0G0[ ] -------------------------------------------------------------------------------------------------------H3G3             H0G0       --H1G1->H2G2             H1G1       <-H1G0--H3G2             H0G1       --H0G2->H3G0             H0G3       <-H0G1--H3G1             H0G2       --H2G0->H1G1             H2G2       <-H1G1--H2G2             H1G1       --H2G0->H0G2             H3G1       <-H0G1--H0G3             H3G0       --H0G2->H0G1             H3G2       <-H0G1--H0G2             H3G1       --H0G2->H0G0             H3G3=======================================================================================================