10891 - Game of Sum

[zobayer]

@kbr_iut, I am very much eager to no how did you solve it in O(n^2). I can not think of any way faster than O(n^3). Which dimension did you reduce?

[zobayer]

All the test cases from this thread:

Code: Select all

2
7 -2
3
2 7 3
5
1000 -1000 -1000 1000 1000
9
-823 912 -345 100000 867 -222 -991 -3 -40000
7
-23 35 -12 100000 99234 -86123 -3245
8
-23 35 12 100000 99234 -86123 -3245 -1
47
7 7 7 -7 7 -7 80 7 7 7 -7 7 -7 -7 7 -7 7 -7 7 -7 -7 7 -7 -7 -7 7 7 7 -7 7 -7 7 -7 7 7 7 -7 7 -7 7 -7 7 -7 -7 7 -7 7
48
-7 -7 -7 -7 -7 7 7 -80 7 -7 -7 -7 -7 7 -7 -7 -7 -7 7 7 -7 -7 -7 7 7 7 -7 7 -7 -7 -7 7 -7 -7 7 7 7 -7 7 -7 7 7 7 7 7 7 7 7
22
91 56 -23 45 87 -65 45 -45 78 23 -20 -41 17 -54 51 51 94 -62 -74 -42 76 -76
18
92834 -95461 15911 -56189 6369 -80545 31811 51263 30076 68867 -36905 -32499 -59799 334 -82991 46636 -98741 -66601
1
-129
20
-35463 -88121 4362 -94457 86235 83680 72686 6003 93069 -2015 -10436 2139 93162 -30380 19067 76335 -78941 48620 -55887 15679
17
19335 97643 11468 86267 -79718 -59584 12129 52642 -86575 62307 -11545 -52658 72377 39986 74850 -1992 -86928
5
-91883 -97793 -54567 -64714 -98624
43
98473 41866 71129 -65936 -42626 9194 -46718 96921 -45613 47677 -8763 54634 -47259 -71448 9918 22666 -32711 -21692 40207 -2017 -23040 -86083 77809 15472 30718 -39085 -87911 54827 -41686 -28354 37203 6548 -74184 -3043 -43961 -95189 1238 -22002 93507 63546 32527 -42778 -31614
50
1 -2 -3 -4 -5 -6 7 -8 -9 -10 -11 -12 13 -14 -15 -16 -17 -18 19 20 -21 -22 23 24 25 26 -27 28 -29 -30 31 32 33 34 -35 36 37 38 -39 -40 41 -42 -43 -44 -45 -46 -47 -48 -49 -50
50
1 1 -1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 1 1 1 -1 1 1 -1 1 1 -1 1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 1 1 -1
50
1 -2 -3 -4 5 -6 -7 -8 -9 11 11 11 -11 -11 111 -11 -11 11 11 11 -11 -11 11 -11 -11 11 -11 11 11 11 112 -312 312 123 -123 -123 123 -123 -123 -123 -123 -123 123 -123 -123 -123 123 -231 -31 -312
50
-1234 -1233 -12 312 -32 23 434 12 -312 -45 -1234 1233 -12 -312 32 -23 -434 -12 312 45 -1234 1233 12 312 32 23 -434 -12 312 -45 -1234 1233 -12 312 32 -23 -434 -12 312 -45 -1234 -1233 12 -312 -32 -23 -434 -12 312 45
34
1 2 -3 -3 3 -3 3 3 -3 3 3 3 -3 3 -3 3 3 -3 3 3 -3 3 3 3 3 3 -3 -3 3 3 3 3 -3 -3
4
9 100 -1 8
50
-1 -2 -3 4 5 -6 -7 8 -9 -8 7 66 5 4 3 -4 5 -6 7 8 -9 -8 -7 -6 6 -5 -4 5 -6 -3 -4 -4 -5 -6 -3 -4 -5 -6 3 -4 -5 6 -3 4 -5 6 3 4 5 -6
50
-1 -2 3 -4 -5 -6 7 -8 9 10 -1 2 3 -4 5 1 -2 -3 -4 -65 -67 -2 3 -4 -7 2 3 4 6 6 -7 2 3 4 -7 78 8 82 2 3 -4 7 -2 2 34 -4 6 -7 -3 2
3
-100 -10 10
1
1
50
1 2 -3 -4 5 6 7 8 9 -10 -1 2 3 4 -5 -6 -7 -8 9 10 1 2 3 -4 5 6 7 8 9 10 -2 -4 -3 -5 4 6 -7 -5 -6 10 2 -5 -4 -3 -4 -5 6 -7 -9 -10
6
6 4 3 -5 -8 -8
5
1 5 20 2 -1
48
1 2 3 -4 -5 -6 -6 7 8 767 -765 111 76576 -5 64 654 64 -7 7657 -76575 64 -65 6454 -64 -654 -65464 7 -5435 65 -746 -7 546 -7 654 7 -5435 -547 6 6 7 -6547 7654 -6 754 -54353 -65 -7 8
5
-2147483648 2147483647 -2147483648 2147483647 -2147483648
5
2147483647 2147483647 2147483647 2147483647 2147483647
4
4 -10 -20 7
4
1 2 3 4
4
-20 8 -1 -2
6
15 -16 17 18 -19 13
1
654654
0

Correct output:

Code: Select all

9
12
1000
139395
116356
116381
108
73
364
93092
-129
443781
323860
-14747
102465
117
6
408
655
33
116
60
210
100
1
70
18
29
114995
2147483646
10737418235
7
10
25
28
654654

Hope this helps...

[Shafaet_du]

Nice problem . Take a number and call the recursive function for rest of the array. A will try to maximize the difference,B will do the opposite. I used 3state dp.

[plamplam]

Why do you need 3 states? Can be easily solved with 2....nvm ac is ac.
But yeah quite awesome problem....enjoyed solving it 10891 FTW