用mips彙編實現哈密爾頓迴路

用mips彙編實現哈密爾頓迴路.

哈密頓迴路是一個非常經典的問題

題目難度不大，雖然是np的但是隻需要你寫一個非多項式的實現算法。

我們先回顧一下怎麼用c++實現

#include <bits/stdc++.h>

#define REP(I,A,B) for (int I=(A),I##_END_=(B);I<=I##_END_;I++)
#define FOR(I,A,B) for (int I=(A),I##_END_=(B);I<I##_END_;I++)
#define REPD(I,A,B) for (int I=(A),I##_END_=(B);I>=I##_END_;I--)

int n,m;
int cnt[101];

using namespace std;

int get_id(int x,int y){
	return (x-1)*n+y;
}

int mark;
int a[101];
int all=0;


void dfs(int p){
	if (p==n+1)
	{
		all |= cnt[ get_id( a[n],a[1] ) ];
		return ;
	}
	else
		for (int i=1;i<=n;i++)
			if (((mark>>i)&1)==0 && cnt[ get_id( a[p-1] , i) ] )
			{
				mark ^= 1<<i;
				a[p]=i;
				dfs(p+1);
				mark ^= 1<<i;
			}
}

int main(){
	scanf("%d%d",&n,&m);
	int x,y;
	REP(i,1,m)
	{
		scanf("%d%d",&x,&y);
		cnt[get_id(x,y)]=cnt[get_id(y,x)]=1;
	}

	mark=2;
	a[1]=1;
	dfs(2);
	printf("%d\n",all);

	return 0;
}

基本實現如下

.data
	array_had: .space 800
	array_a: .space 80
	char_space: .asciiz " "
	char_endl: .asciiz "\n"


.text

main:
	la $s0,array_had
	la $s1,array_a
#la $s2,int_n
#la $s3,int_m
#la $s4,int_all
#la $s5,int_mark
	li $s4,0
	li $s5,2
#one
	li $s6,1 

	li $v0,5
	syscall
	move $s2,$v0

	li $v0,5
	syscall
	move $s3,$v0

# for m
	li $t1,0
	for_m_st:
		beq $t1,$s3,for_m_ed
		nop

		li $v0,5
		syscall
		move $t6,$v0

		li $v0,5
		syscall
		move $t7,$v0

		move $a0,$t6
		move $a1,$t7
		
		jal get_id
		mul $v0,$v0,4
		add $t2,$s0,$v0 
		sw $s6,0($t2)

		#swap
		move $a0,$t7
		move $a1,$t6

		jal get_id
		mul $v0,$v0,4
		add $t2,$s0,$v0
		sw $s6,0($t2)

		addi $t1,$t1,1
		j for_m_st
		nop
	for_m_ed:

	sw $s6,4($s1)
	li $a0,2
	jal dfs

	move $a0,$s4
	li $v0,1
	syscall

	li $v0,10
	syscall

get_id:
	mul $a0,$a0,$s2
	add $v0,$a0,$a1
	jr $31

dfs:

	sw $ra,0($sp)
	subi $sp,$sp,4
	sw $a0,0($sp)
	subi $sp,$sp,4

	bgt $a0,$s2,if_check_then
	nop
	j if_check_end

	if_check_then:
		
		li $t1 1
		mul $t1,$t1,4
		add $t1,$t1,$s1
		lw $t1,0($t1)
		move $a0,$t1

		move $t1,$s2
		mul $t1,$t1,4
		add $t1,$t1,$s1
		lw $t1,0($t1)
		move $a1,$t1

		jal get_id
		mul $v0,$v0,4
		add $t1,$s0,$v0
		lw $t1,0($t1)
		or $s4,$s4,$t1

		addi $sp,$sp,4
		addi $sp,$sp,4
		lw $ra,0($sp)
		jr $31

	if_check_end:

	bne $a0,$0,dfs_work

	dfs_work:
		#for_dfs
		li $t1,1
		for_dfs_st:
			bgt $t1,$s2,for_dfs_ed
			nop

				sllv $t2,$s6,$t1
				and $t2,$s5,$t2
				seq $t2,$t2,0

				addi $sp,$sp,4
				lw $t3,0($sp)
				subi $sp,$sp,4
				sub $t3,$t3,1

				mul $t3,$t3,4
				add $t3,$t3,$s1
				lw $t3,0($t3)
				move $a0,$t3
				move $a1,$t1

				jal get_id
				mul $v0,$v0,4
				add $t3,$v0,$s0
				lw $t3,0($t3)
				
				and $t2,$t2,$t3

				beq $t2,$s6,if_mark_then
				nop
				j if_mark_end

				if_mark_then:

					# t3  = a0
					addi $sp,$sp,4
					lw $t3,0($sp)
					subi $sp,$sp,4

					sw $s5,0($sp)
					subi $sp,$sp,4

					sllv $t2,$s6,$t1
					or $s5,$s5,$t2

					mul $t2,$t3,4
					add $t2,$s1,$t2
					sw $t1,0($t2)

					sw $t1,0($sp)
					subi $sp,$sp,4

					addi $a0,$t3,1
					jal dfs

					addi $sp,$sp,4
					lw $t1,0($sp)

					addi $sp,$sp,4
					lw $s5,0($sp)

				if_mark_end:

			addi $t1,$t1,1
			j for_dfs_st
		for_dfs_ed:

			addi $sp,$sp,4
			addi $sp,$sp,4
			lw $ra,0($sp)
			jr $31