UVA 116 -- Unidirectional TSP
题意：
求从第一列到最后一列的一个字典序最小的最短路，要求不仅输出最短路长度，还要输出字典序最小的路径。
解题思路：
设d(i,j)为从格子(i,j)出发，到最后一列的最小开销。因为不仅要输出解，还要输出字典序最小的序列，所以需要再计算d(i,j)的同时记录“下一列的行号”的最小值
For each specification the number of rows will be between 1 and 10 inclusive; the number of columns will be between 1 and 100 inclusive. No path’s weight will exceed integer values representable using 30 bits.
1 #include<iostream> 2 #include<algorithm> 3 using namespace std; 4 const int INF = 0x3f3f3f3f; 5 const int maxi = 10+5; 6 const int maxj = 100+5; 7 int d[maxi][maxj]; 8 int a[maxi][maxj]; 9 int c[maxi][maxj];///记录路径 10 11 int main() 12 { 13 int m,n; 14 while(cin>>m>>n){ 15 for(int i=0;i<m;i++) 16 for(int j=0;j<n;j++) 17 cin>>a[i][j]; 18 int ans = INF,first = 0; 19 for(int j=n-1;j>=0;j--){//列 20 for(int i=0;i<m;i++){ 21 if(j == n-1){//最右边一列 22 d[i][j] = a[i][j]; 23 } 24 else{ 25 int rows[3] = {i,i-1,i+1}; 26 if(i == 0) rows[1] = m-1;//第0行“上面”是第m-1行 27 if(i == m-1) rows[2] = 0;//最后一行“下面”是第0行 28 sort(rows,rows+3);//重新排序，以便找到字典序最小的 29 d[i][j] = INF; 30 for(int k = 0;k<3;k++){ 31 int v = d[rows[k]][j+1] + a[i][j]; 32 if(v < d[i][j]) { 33 d[i][j] = v;c[i][j] = rows[k]; 34 } 35 } 36 } 37 if(j == 0 && d[i][j]<ans){ 38 ans = d[i][j];first = i; 39 } 40 } 41 } 42 43 cout<<first+1; 44 for(int i=c[first][0],j=1;j<n;i = c[i][j],j++) 45 cout<<" "<<i+1; 46 cout<<endl<<ans<<endl; 47 } 48 49 return 0; 50 }
测试样例： 5 6 3 4 1 2 8 6 6 1 8 2 7 4 5 9 3 9 9 5 8 4 1 3 2 6 3 7 2 8 6 4 5 6 3 4 1 2 8 6 6 1 8 2 7 4 5 9 3 9 9 5 8 4 1 3 2 6 3 7 2 1 2 3 2 2 9 10 9 10 10 14 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 4 7 1 2 -3 4 -2 1 5 -1 3 5 -2 6 -3 4 2 1 3 -2 -1 3 1 3 -3 4 2 -3 4 3 5 6 3 4 1 2 8 6 6 1 8 2 7 4 5 9 3 9 9 5 8 4 1 3 2 6 3 7 2 8 6 4 5 6 3 4 1 2 8 6 6 1 8 2 7 4 5 9 3 9 9 5 8 4 1 3 2 6 3 7 2 1 2 3 2 2 9 10 9 10 5 6 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 5 1 5 10 6 3 5 1 8 4 11 10 12 5 2 9 7 3 20 5 8 4 1 5 12 6 5 10 11 53 34 73 18 53 99 52 31 54 4 72 24 6 46 17 63 82 89 25 67 22 10 97 99 64 33 45 81 76 24 71 46 62 18 11 54 40 17 51 99 8 57 76 7 51 90 92 51 21 5 10 11 53 1 73 18 53 99 52 31 54 4 72 54 6 46 17 63 82 89 25 67 22 80 97 99 64 33 45 81 76 24 71 46 62 18 11 54 40 17 51 99 8 57 76 7 51 90 92 51 21 5 6 -3 -4 -1 -2 -8 -6 -6 -1 -8 -2 -7 -4 -5 -9 -3 -9 -9 -5 -8 -4 -1 -3 -2 -6 -3 -7 -2 -8 -6 -4 10 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 29 1 -1 0 0 1 -1 -1 -1 1 1 0 1 -1 -1 -1 0 -1 -1 1 -1 1 0 0 -1 0 -1 1 1 0 -1 1 0 -1 -1 0 1 0 -1 -1 -1 -1 1 1 0 -1 -1 0 -1 -1 1 -1 1 0 -1 1 0 1 -1 0 0 1 0 -1 1 0 0 1 1 0 -1 1 1 -1 -1 1 0 0 1 1 0 -1 1 0 -1 -1 1 1 1 -1 -1 -1 -1 -1 0 0 0 1 -1 0 0 0 -1 -1 0 -1 0 1 0 -1 1 0 1 1 -1 0 1
1 1
1
结果： 1 2 3 4 4 5 16 1 2 1 5 4 5 11 1 1 19 1 2 3 4 5 6 7 8 9 10 1 1 1 2 14 1 4 1 2 1 2 3 -11 1 2 3 4 4 5 16 1 2 1 5 4 5 11 1 1 19 1 1 1 1 1 1 6 1 1 1 1 10 1 2 3 2 1 14 2 3 3 2 1 2 3 4 4 5 188 1 5 1 2 1 2 3 4 4 5 172 4 3 2 3 3 4 -49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 100 2 1 4 4 3 4 1 1 2 2 2 2 1 1 1 2 1 1 2 1 4 4 1 1 2 1 4 1 2 -25
1
1
