最长公共子序列问题，打印路径总结了两个方法，一个是递归指向，就像前面做的01背包问题如：
for(int i = 1; i < n; i ++)
for(int j = 0; j < n-i; j ++)
for(int k = j; k < i+j; k ++)
{
if(k == j)
{
f[j][i+j] = f[j][k]+f[k+1][i+j]+A[j][0]*A[k][1]*A[i+j][1];
part1[j][i+j] = k;//赋值
}
if(f[j][k]+f[k+1][i+j]+A[j][0]*A[k][1]*A[j+i][1] < f[j][i+j])
{
f[j][i+j] = f[j][k]+f[k+1][i+j]+A[j][0]*A[k][1]*A[j+i][1];
part1[j][i+j] = k;//赋值
}
}
void printpath(int a, int b)//输出
{
if(a == b)
{
printf("A%d", a + 1);
return ;
}
printf("(");
printpath(a, part1[a][b]);
printf(" x ");
printpath(part1[a][b] + 1, b);
printf(")");
}
例如：
for(int i = 1; i <= cdnum; i ++)
for(int j = 0; j <= tap; j ++)
{
f[i][j] = f[i-1][j];
p[i][j] = j;//赋值
if(j>=num[i]&&f[i-1][j-num[i]]+num[i] > f[i][j])
{
f[i][j] = f[i-1][j-num[i]]+num[i]; p[i][j] = j-num[i];//赋值
}
}
void print(int i, int j)//打印路径
{
if(i == 0)
return;
print(i - 1, p[i][j]);
if(p[i][j] < j)
printf("%d ", num[i]);
}
这第二种就是今天用到的 赋值遍历打印路径；
for(int i = 1; i <= m; i ++)
for(int j = 1; j <= n; j ++)
if(!strcmp(a[i], b[j]))
{
f[i][j] = f[i-1][j-1] + 1;
p[i][j] = 1;//赋值
}
else if(f[i-1][j]>f[i][j-1])
{
f[i][j] = f[i-1][j];
p[i][j] = 0;//赋值
}
else
{
f[i][j] = f[i][j-1];
p[i][j] = -1;//赋值
}
void print(int i , int j)//输出
{
if(!i || !j)
return ;
if(p[i][j] == 1)
{
print(i-1,j-1);
if(flag)
printf(" ");
else
flag = 1;
printf("%s", a[i]);
}
else if(p[i][j] == 0)
print(i-1,j);
else print(i,j-1);
}
代码如下：#include<stdio.h>
#include<string.h>
#define MAXN 100 + 5
char a[MAXN][35], b[MAXN][35], f[MAXN][MAXN], p[MAXN][MAXN];
int m, n, flag;
void print(int i , int j)
{
if(!i || !j)
return ;
if(p[i][j] == 1)
{
print(i-1,j-1);
if(flag)
printf(" ");
else
flag = 1;
printf("%s", a[i]);
}
else if(p[i][j] == 0)
print(i-1,j);
else print(i,j-1);
}
void solve()
{
memset(f,0,sizeof(f));
for(int i = 1; i <= m; i ++)
for(int j = 1; j <= n; j ++)
if(!strcmp(a[i], b[j]))
{
f[i][j] = f[i-1][j-1] + 1;
p[i][j] = 1;
}
else if(f[i-1][j]>f[i][j-1])
{
f[i][j] = f[i-1][j];
p[i][j] = 0;
}
else
{
f[i][j] = f[i][j-1];
p[i][j] = -1;
}
print(m,n);
printf("\n");
}
void input()
{
while(scanf("%s",a[1]) == 1)
{
flag = 0;
m = 1;
n = 0;
if(a[1][0] != '#')
for(int j = 2; ;j ++)
{
scanf("%s",a[j]);
if(a[j][0] == '#') break;
m ++;
}
for(int i = 1; ; i ++)
{
scanf("%s",b[i]);
if(b[i][0] == '#') break;
n ++;
}
solve();
}
}
int main()
{
input();
return 0;
}