C. Track
Time Limit : 10000/5000ms (Java/Other) Memory Limit : 524288/262144K (Java/Other)
Total Submission(s) : 0 Accepted Submission(s) : 0
You already know that Valery's favorite sport is biathlon. Due to your help, he learned to shoot without missing, and his skills are unmatched at the shooting range. But now a smaller task is to be performed, he should learn to complete the path fastest.
The track's map is represented by a rectangle n¡Ám in size divided into squares. Each square is marked with a lowercase Latin letter (which means the type of the plot), with the exception of the starting square (it is marked with a capital Latin letters S) and the terminating square (it is marked with a capital Latin letter T). The time of movement from one square to another is equal to 1 minute. The time of movement within the cell can be neglected. We can move from the cell only to side-adjacent ones, but it is forbidden to go beyond the map edges. Also the following restriction is imposed on the path: it is not allowed to visit more than k different types of squares (squares of one type can be visited an infinite number of times). Squares marked with S and T have no type, so they are not counted. But S must be visited exactly once at the very beginning, and T must be visited exactly once at the very end.
Your task is to find the path from the square S to the square T that takes minimum time. Among all shortest paths you should choose the lexicographically minimal one. When comparing paths you should lexicographically represent them as a sequence of characters, that is, of plot types.
5 3 2<br />Sba<br />ccc<br />aac<br />ccc<br />abT<br />3 4 1<br />Sxyy<br />yxxx<br />yyyT<br />
bcccc<br />xxxx<br />