UVa 116
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[edit] 116 - Unidirectional TSP
[edit] Summary
A standard Dynamic Programming problem.
[edit] Explanation
Let f(x,y) be the optimal (minimum) sum that ends at grid point x and y, and v(x,y) be the value of grid point x and y.
Then f(x,y) is simply: f(x,y) = min(f(x - 1,y - 1),f(x,y - 1),f(x + 1,y - 1)) + v(x,y)
[edit] Gotcha's
- Negative numbers.
- If there is more than one path of minimal weight the path that is lexicographically smallest should be output.
[edit] Input
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 12 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 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 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
[edit] Output
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 11 12 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
