Submit solution

Points: 17
Time limit: 0.6s
Memory limit: 64M

Problem type

Allowed languages
C , C++

Pepe the frog needs to jump across a river while only stepping on some stones! He needs to jump from column 1 to column N (left to right in the input). Rock i means the rock on row i. However, jumping from row i to j takes (i-j)^2 time.


The first line of the input contains two integers, N and C, the number of columns and the number of positions of rocks.

Each subsequent C lines of the input contains of a string of N 0s and 1s. A 1 on line i (starting from 2nd line) on column j (both 0-indexed) indicates the rock j is present in column i, a 0 indicates that rock j is not present.


Output the minimum amount of time taken to jump to the end.

You are guaranteed there is at least one possible way to jump to the end.


Subtask 1 (10%) 1\le N,C\le7

Subtask 2 (5%) 1\le N,C\le100

Subtask 3 (20%) 1\le N,C\le500

Subtask 4 (20%) 1\le N,C\le750

Subtask 5 (45%) 1\le N,C\le2000

Sample Input 1

5 3

Sample Output 1


Sample Input 1 Explanation

You don't need to jump, just use rock 3 throughout.

Sample Input 2

5 5

Sample Output 2


Sample Input 2 Explanation

Start from rock 0, change to rock 1, change to rock 2, etc. Each of them takes 1 time because they are adjacent.


  • 0
    Cueball1234  commented on Sept. 3, 2017, 9:31 p.m. edited


    My solution has an execution time of O(NClogC), which should be fast enough. However, I am TLEing. Is there maybe a reason for this occurring? Thank you!

    Edit: I changed a couple parts to reduce the execution time and it worked, but it is still really weird why my initial O(NClogC) TLEd. Some suggestions on why my initial solution TLEd would be much appreciated. Thanks!

    • 1
      Xue_Alex  commented on Sept. 4, 2017, 9:35 a.m. edited

      With a sub 1 second time limit on the problem, it's a possibility that you got a slow judge on some submissions and a fast judge on other submissions. Normally that wouldn't be the difference between an AC and TLE, the tight time limit probably caused that, even though there was nothing wrong with your code.

      • 0
        Cueball1234  commented on Sept. 4, 2017, 12:49 p.m.

        Ah yes, very true. But it is still weird, since NClogC is on the order of magnitude of 40 million operations. I am not too sure about this, but can't a computer do about 1 billion operations in a second? Thank you!

  • 1
    Cueball1234  commented on Aug. 31, 2017, 1:41 p.m.

    Sorry, just to clarify, does the frog have to visit every column or is the frog technically allowed to jump from a rock in column 1 directly to a rock in column N?


    1 0 1
    0 1 0

    Is the answer 2 or 0?


    • 1
      Xue_Alex  commented on Sept. 1, 2017, 4:52 p.m. edited

      The input

      3 2



      Gave me 2, so I think the frog does need to visit each column.

      Edit: format

      • 1
        Cueball1234  commented on Sept. 1, 2017, 5:25 p.m.

        Awesome, thank you for the confirmation!

  • 0
    kobortor  commented on Jan. 7, 2017, 2:03 p.m.
    Time limit

    The time constraint for this question is quite strict. It is not guaranteed to be solvable by languages other than C++. Even then you will need quite a bit of constant optimization to pass (assuming you have the optimal time complexity).

  • 0
    gloomcore  commented on Jan. 7, 2017, 3:30 a.m. edited
    Some clarification will be helpful

    Can frog jump back or just forward? And can frog move between different stones within the same column?


    Is answer for this test is 2?

    • 0
      bruce  commented on Jan. 7, 2017, 9:25 a.m.

      Based on my submission, the frog can only jump forward. The case you provided is the same as


      and the answer is 2.

      • 0
        gloomcore  commented on Jan. 9, 2017, 11:03 a.m. edited

        Thanks, a lot Bruce, it will help me clarify task. I wanted to check if frog can jump between diffrent rows on the same column. I mean, that if frog can jump between different rows on the same colum, then as for test:


        the answer is 6, when frog will jump between different rows in the same column.

        In other case, if frog should always move one column forward and cannot make jumps within the same column, then the best answer in this case is 18. (Jump from row 1 to row 4 and from row 4 to row 7).

        Can you help, which way is correct?

        • 0
          bruce  commented on Jan. 9, 2017, 6:50 p.m.

          The frog cannot jump between different rows in the same column. Agree with ZQFMGB12. 18 is the best answer for your case.

        • 0
          ZQFMGB12  commented on Jan. 9, 2017, 12:57 p.m.

          The latter is correct.