![???せ
? N??????????A[i]????
? ?k??┠????x???????ィM?????
???????????????????Q?????
? ??
? 1
≤
N
≤
2000
? 1
≤
M
≤
2000
? 1
≤
Q
≤
500000](https://image.slidesharecdn.com/review-140830083058-phpapp02/85/AtCoder-Regular-Contest-028-15-320.jpg)
![10?ゎ?
(N,M,Q≤100)
? ?????????DP????
? DP[i][j]=i??┠???j????????
? ????
? DP[i][j]
=
ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j]
? ??????????O(1)???????](https://image.slidesharecdn.com/review-140830083058-phpapp02/85/AtCoder-Regular-Contest-028-16-320.jpg)
![??ゎ?
? ?????O(1)????????????
? ??i???????????DP?????????
????????i????????????
? ??
? ???????????
? DP?????DP[i-?‐1]????(??)????](https://image.slidesharecdn.com/review-140830083058-phpapp02/85/AtCoder-Regular-Contest-028-19-320.jpg)
![??DP
? DP[i]??DP[i-?‐1]??????
? DP[i][j]
=
ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j]
? →
? DP[i-?‐1][j]
=
DP[i][j]-?‐ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j-?‐1]
? O(M)???????
? ?????????????????????
DP[N]??????i???????????DP???
????i???????????](https://image.slidesharecdn.com/review-140830083058-phpapp02/85/AtCoder-Regular-Contest-028-20-320.jpg)
AtCoder Regular Contest 028 解説
- 1. A?? ?▼??????
- 2. ???せ ? ??N???▼??????? ? Ant???Bug???Ant??...???????????? ? Ant???A????Bug???B????▼???? ? ?????????????????????? ? ?? ? 1 ≤ N, A, B ≤ 1000
- 3. ゎ? ? ?????????????? ? ????????????????A?B????? ????? ? ?????0?????????????????? ????????
- 4. B?? ???
- 5. ???せ ? ??????????N????????? ? i?????????????┠???????? ??? ? 1??j??????K?┠?????????K~N ?j????????? ? ?? ? 1 ≤ N ≤ 10^5
- 6. 40?ゎ? (N≤1000) ? ?????????????? ? 1???j???????????????K?┠?せ ??ぢ??
- 7. ??ゎ? ? j??????????????????????? ???? ? ?????K+1?┠?????????????K ?┠???????? ? ????????? – K+1?┠????????????? – K?┠???????⿵?????⿵???????? ??????⿵??????? ? ???⿵????????????????????
- 8. ??ゎ? ? ??????????????????せ??せ ????? – せ?????? – せ??????????????? ? priority queue???????queue? ? ????O(log せ??)??????????? ? ゝㄒ????????????????????? ????????
- 10. ???せ ? ???N????????? ? ??v???????????????????? ??????????v???????? ? ?? ? 1 ≤ N ≤ 10^5
- 11. 30?ゎ? (N≤1000) ? ?????????????? ? ?????????????? ? DFS?????????
- 12. ??ゎ? ? ???????????????? ? DFS?????DP??????????????? ???????????? ? ????ぶ?????????????????? ???? ? →N-?‐1-?‐(?????????????) ???????
- 13. ??? ? ヲ??????┬????? ? ?????????????????????? ????????????????
- 14. D?? ?????????
- 15. ???せ ? N??????????A[i]???? ? ?k??┠????x???????ィM????? ???????????????????Q????? ? ?? ? 1 ≤ N ≤ 2000 ? 1 ≤ M ≤ 2000 ? 1 ≤ Q ≤ 500000
- 16. 10?ゎ? (N,M,Q≤100) ? ?????????DP???? ? DP[i][j]=i??┠???j???????? ? ???? ? DP[i][j] = ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j] ? ??????????O(1)???????
- 17. 30?ゎ? (N,M≤100) ? ???????????????????? ? ??i???????????DP????????? ????????i?????????? ? ????O(N^2M) ? ?????O(M) ? ????30???????????
- 18. 80?ゎ?(N,M≤2000,Q≤1000) ? ?i???????DP???┤??????↓??? ? ? 0~j?????????DP????? ? j~N?????????DP???? ? ???????(せ?????????DP????) ? ???????????DP????????????? O(M)??????????????
- 19. ??ゎ? ? ?????O(1)???????????? ? ??i???????????DP????????? ????????i???????????? ? ?? ? ??????????? ? DP?????DP[i-?‐1]????(??)????
- 20. ??DP ? DP[i]??DP[i-?‐1]?????? ? DP[i][j] = ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j] ? → ? DP[i-?‐1][j] = DP[i][j]-?‐ΣDP[i-?‐1][j-?‐a[i]]~DP[i-?‐1][j-?‐1] ? O(M)??????? ? ????????????????????? DP[N]??????i???????????DP??? ????i???????????