哈密顿回路汇编语言实现（有小bug）

Posted 2020-11-16 buaa-wander

C++实现
#include <iostream>
#include <cstdio>
#include <bits/stdc++.h>
/*邻接矩阵存储图，从起点开始，直接深搜，打标记，一直搜到不可以再搜，看看是不是走了n步，并且头尾相连*/ 
int graph[30][30];
int sign[30];
int n,m,ans=0;
void DFS(int now,int step);
int main() {
    int u,v;
    scanf("%d %d",&n,&m); //不妨图的顶点序号从1开始 
    for(int i=0;i<m;i++){
        scanf("%d %d",&u,&v);
        graph[u][v]=graph[v][u]=1;
    }
    sign[1]=1;
    DFS(1,1);
    printf("%d
",ans);
    return 0;
}
void DFS(int now,int step){
    if(step==n){
        if(graph[1][now]){
            ans=1;    
        }
        return;
    }
    for(int i=1;i<=n;i++){
        if(!sign[i] && i!=now && graph[now][i]){
            sign[i]=1;
            DFS    (i,step+1);
            sign[i]=0;
        }
    }
    return; 
}

汇编实现：（有小bug，似乎会被卡单点或者两点，但特判之后反而错得更多了）
代码已做特殊处理
.macro    done
    li    $v0,10
    syscall
.end_macro
#############################################################
.macro     initial
    li    $t0,0
for_1:
    beq    $t0,$s0,for_1_end
    sll    $t1,$t0,2    #t1=t0*4(int is 4 byte)
    add    $t1,$t1,$s3
    sw    $0,0($t1)    #sign[t1]=0
    addi    $t0,$t0,1    #t0=t0+1
    j    for_1
for_1_end:
.end_macro
#############################################################
.macro    getindex(%ans,%i,%j)
    mult    %i,$t6    #i*10
    mflo    $t4    #t4=i*10
    add    %ans,$t4,%j    #t4=i*10+j
    sll    %ans,%ans,2    #ans=ans*4
.end_macro
#############################################################
.data
matrix:        .space 400
sign:        .space 40

#########################################################
.text
main:
    la    $s2,matrix
    la    $s3,sign
    li    $t6,10        #tmp
    li    $t7,1        #tmp
    li    $s7,0        #s7 is answer
    li    $v0,5
    syscall
    move    $s0,$v0        #s0 is n
    li    $v0,5
    syscall
    move    $s1,$v0        #s1 is m
    initial
    li    $t0,0        #t0 is i
for_create:
    beq    $t0,$s1,for_create_end    #if i==m,stop add edge
    li    $v0,5
    syscall
    move    $t1,$v0        #t1 is u
    li    $v0,5
    syscall
    move    $t2,$v0        #t2 is v
    getindex($t3,$t1,$t2)    #get the address in matrix
    add    $t3,$t3,$s2    #get address in matrix,t3 is address
    sw    $t7,0($t3)    #add edge (u,v)
    getindex($t3,$t2,$t1)
    add    $t3,$t3,$s2    
    sw    $t7,0($t3)    #add edge (v,u)
    addi    $t0,$t0,1    #i++
    j    for_create
for_create_end:
    sw    $t7,4($s3)    #sign[1]=1
    li    $a0,1        #a0 is now position
    li    $a1,1        #a1 is step
    jal    dfs        #the return address is in $31
    li    $v0,1
    li    $a0,0
    syscall
    done
    
dfs:    
    sw    $31,0($sp)
    addi    $sp,$sp,-4
    blt        $a1,$s0,dfs_else
    getindex($t3,$t7,$a0)
    add    $t3,$t3,$s2    #t3 is address in matrix
    lw    $t4,0($t3)    #t4=graph[1][now]
    beq    $t4,1,arrive_ans
    addi    $sp,$sp,4
    lw    $31,0($sp)
    jr    $31        #if we don‘t find the ans,return
    #omit something…………
dfs_else:
    jal    dfs_work
    addi    $sp,$sp,4
    lw    $31,0($sp)
    jr    $31
then:
    jr    $31        #you have jumped to main succesfully
    
arrive_ans:
    li    $s7,1
    li    $a0,1
    li    $v0,1        #print answer
    syscall
    done
    j    then        
dfs_work:
#then ,we should do something 
    li    $t0,1        #t0 is i
    sw    $31,0($sp)    #save return address
    addi    $sp,$sp,-4
for_dfs1:
    bgt     $t0,$s0,for_dfs1_end
    bge    $a1,$s0,for_dfs1_end
    sw    $a0,0($sp)    #save now
    addi    $sp,$sp,-4
    sw    $a1,0($sp)    #save step
    addi    $sp,$sp,-4    #all the info was saved sucessfully
    sll    $t1,$t0,2    #t1=t0*4
    add    $t1,$t1,$s3    #t1 is the address in array_sign
    lw    $t2,0($t1)    #t2 is sign[i]
    getindex($t3,$a0,$t0)    #t3 is [now][i]
    lw    $t3,0($t3)    #t3 is graph[now][i]
    beq    $t2,1,else    #if sign[i]==1,return
    beq    $t0,$a0,else    #if i==now,return 
    beq    $t3,0,else    #if graph[now][i]==0,return 
    sw    $t7,0($t1)    #sign[i]=1;
    sw    $t0,0($sp)    #save tmpi in stack
    addi    $sp,$sp,-4
    sw    $t1,0($sp)    #save the address in array_sign
    addi    $sp,$sp,-4
    move    $a0,$t0        #now=i
    addi    $a1,$a1,1    #step++
    jal    dfs        #next recursion
    
    addi    $sp,$sp,4
    lw    $t1,0($sp)    #fetch the address in array_sign
    addi    $sp,$sp,4
    lw    $t0,0($sp)    #fetch i
    sw    $t7,0($t1)    #sign[i]=0
    addi    $sp,$sp,4
    lw    $a1,0($sp)
    addi    $sp,$sp,4
    lw    $a0,0($sp)    #fetch all the things
    addi    $t0,$t0,1    #i++
    j    for_dfs1

for_dfs1_end:
    addi    $sp,$sp,4
    lw    $31,0($sp)    #fetch the leeway
    jr    $31


else:
    addi    $t0,$t0,1
    addi    $sp,$sp,4
    lw    $a1,0($sp)
    addi    $sp,$sp,4
    lw    $a0,0($sp)    #fetch all the things
    j    for_dfs1

 

用汇编语言写递归程序的经验教训：

1.值的进栈与出栈：这个一定要注意，每次调用其他过程的时候，都要想想是不是要把退路保存下来，把原来的变量保存下来，有些甚至不止保存一次，有些甚至会因为分支而要在各个分支中进栈出栈。递归的还得多练，这次居然写了六个小时还被卡了一个点，由此可见我P2大概率会被干掉。

2.判断条件的书写：很多时候用相等判断beq并不够（因为自己写的程序太混乱，值会超过预期），我们需要能判断大于等于，小于等于，严格小，严格大的指令，至于到底使用哪种，一定要在写代码的时候想好。循环退出的条件一般写在循环的最前面。最好每个条件判断后面都写上清晰的注释。

3.别怕。汇编程序看着长，实际上重复的部分有很多是进栈出栈，以后写的时候不能再抓狂到砸东西了！