As I know all correct input data have only one possible solution.
As for 1010 question is where to take input sample for 1010?

I can't create a generator of random solution, which can be used for random generating test.
I can't find regularity and think up an quick algorithm.
Now it takes about 50-300Ms for one new correct random clues. I think it is not enought for tests.
But I can generate in advance any amout of solutions
For example https://github.com/ekaruk/codewars/blob/master/Scrapers.txt
As I understand, these are right examples of Skyscrapers and clues with one solution.
I use little brute force for generation, so time of generation is not fixed.

You can add hundred solutions and use any random 5-10 from these fixed solutions for every test

Such problems are very well solved step by step.
Decision one.
Therefore on each step we can improve the last decision without brute force.

Interesting Kat series (44; 66; 77).
I am proud of myself :)
The first solution for 44 works with the minimum changes in indexes both on 66 and on 77.
For the size 7*7 calculation lasts on PC 54 milliseconds so possible will work also for the bigger size.
Plus 1 Kyu for one solution :)

One of options.
It is possible to add 20 in advance generated tests, but to check every time, for example, any random 5 of them.

Java translation done

Interesting approach. Two identical kata with different complexity
At first I solved it in easier version https://www.codewars.com/kata/52756e5ad454534f220001ef
The solution of a Performance version kata was much shorter and 50 times faster, than the decision it in easier version

Thank you.
The first time I haven't understood the instructions correctly

I have get in Java version result of test
expected: <a[c]> but was:<a[]>
Result must be String. What does it mean a[c]? String "a" or "c" ?
Correct wrong result usually look like this : expected:<[ab]> but was:<[abc]>

Very interesting Kata.
My first solution was too long.
It has given a reason to think again and write other solution.
Thank you :)

Now I isn't get this error.
I think it is fixed;
Now I get error "Execution Timed Out (20000 ms)". It is problem of my algoritm, not problem of test.

Thanks for an explanation.
It seems that error of tests really such. Missed not every time point last before finish. Different points.
Zero distances not a problem. They shouldn't influence calculation in any way.

I have test again
result of test
your path: [up, up, right, up, up, up, up, left, left, left, up, left, up, up, up, up, up, up, up, up, up, up, up, left, left, left, up, up, up, up, up, up, up, left, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, left, left, up, left, left, up, left, left, left, left, up, left, left, up, up, up, up, up, up, up, up, up, up, right, up, right, up, right],
cost=2288 should be somehting like
[up, up, right, up, up, up, up, left, left, left, up, left, up, up, up, up, up, up, up, up, up, up, up, left, left, left, up, up, up, up, up, up, up, left, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, up, left, up, up, left, left, left, left, left, left],
cost=2263 expected:<2263> but was:<2288>

Real cost of 2 ways 2312
My way has more steps but same cost
(last part is different in sample)

up:5;up:22;right:16;up:7;up:38;up:49;up:14;left:23;left:45;left:34;up:8;left:1;up:10;up:33;up:20;up:20;up:35;up:76;
up:20;up:33;up:28;up:76;up:13;left:18;left:17;left:41;up:4;up:84;up:2;up:6;up:4;up:37;up:34;left:14;up:22;up:38;up:62;
up:24;up:33;up:93;up:42;up:32;up:4;up:51;up:40;up:28;up:30;up:37;up:76;up:53;up:19;up:0;up:24;
left:36;left:5;up:29;left:20;left:30;up:53;left:20;left:2;left:53;left:19;up:16;left:15;left:27;up:10;up:11;up:44;up:31;up:3;up:78;up:24;up:22;up:33;up:0;right:23;up:78;right:0;up:4;right:31;
2312

up:5;up:22;right:16;up:7;up:38;up:49;up:14;left:23;left:45;left:34;up:8;left:1;up:10;up:33;up:20;up:20;up:35;up:76;
up:20;up:33;up:28;up:76;up:13;left:18;left:17;left:41;up:4;up:84;up:2;up:6;up:4;up:37;up:34;left:14;up:22;up:38;up:62;
up:24;up:33;up:93;up:42;up:32;up:4;up:51;up:40;up:28;up:30;up:37;up:76;up:53;up:19;up:0;up:24;
up:81;up:6;up:39;up:11;up:50;up:5;up:4;up:68;up:4;up:66;up:18;up:7;up:21;left:39;up:35;up:41;left:39;left:20;left:81;left:22;left:29;left:31;
2312

(sample of date on the same githab with first sample)

'''java
int[][] tollMap3 = {
{50,58,98,44,88,31,33,14,30,58,79,40,28,80,35,9,54,30,78,74,42,37,32,16,93,71,86,56,71,78,61,51,2,86,43,},
{19,87,95,18,59,17,25,14,86,98,4 ,93,20,64,8, 34,29,13,57,81,14,32,36,87,31,57,6,21,91,55,95,99,67,84,31,},
{68,46,93,17,69,75,89,33,0 ,33,57,72,23,15,22,11,85,67,63,57,29,38,81,57,41,83,40,40,22,9,80,88,27,7,99,},
{23,64,77,63,48,54,49,52,62,0 ,93,95,20,92,25,24,80,89,74,50,24,57,88,46,89,75,33,48,54,68,18,46,22,30,83,},
{37,4 ,41,76,85,63,2 ,47,69,44,19,23,25,11,58,66,98,8,49,86,24,34,7,94,46,37,53,59,58,58,88,23,3,7,15,}};
Point start3 = new Point(1, 17), finish3 = new Point(4, 13);
System.out.println(cheapestPath(tollMap3, start3, finish3));
'''

In Java version may be incorrect calculating of tests result
Check, please.

Sample from Test result
your path: [left, left, left, down, left, left, down, down, right], cost=164
29 34 8 22 15 23 20 25 11
should be somehting like
[left, left, left, down, down, down, left], cost=131 expected:<131> but was:<164>
29 34 8 22 25 58 11
Both cases sum 187, not 131 and not 164
Full array of data
https://github.com/ekaruk/codewars/blob/master/Finder.txt