I am stuck in the ELEVATOR problem in cses dp section. I tried to find the solution online but couldn`t find any reliable source. PROBLEM LINK — https://cses.fi/problemset/task/1653. It would be a great help if someone can explain the idea behind it.

See here: Competitive Programmer's Handbook pdf page 103-104

Thanks a lot.

I cant understand what the bit operations are doing. Can you explain them?

we have the same pfp

I solved in this way I have two fields DP and Moves

Moves[Mask] — the minimum number of elevator rides

DP[Mask] — Minimum Weight Sum of People for the last Move

We know that we have moves in the priority so the transitions were

newDp = (DP[mask ^ (1 << j)] + w[j]) % x

newMoves = (Moves[mask ^ (1 << j)] + (newDp > Dp[mask ^ (1 << j]))

It means that if newDp is bigger that x then new Move is added, and we change the Moves and DP, if Moves > newMoves or (newDp < DP and Moves = newMoves)

Is I cann't done it with recursion + dp

I got tle

don't you think in else part there should be option.second=min(option.second,weight[p])?????

no option.second=min(option.second,weight[p]) is incorrect, because we are considering last ride. It means (let the current ride be nth ride), --> we have already completed (n — 1)th ride, so we cannot go back to some kth ride which is obviously (1 <= k < n) and update it.

can you tell me why for input {2,3,4,5,9} and lift capaicty as 12 the above algorithm prints:-

best[31].first as 1 and best[31].second as 11

don't you think (best[31].first) which is actually minimum no of rides should print 2, not 1.

best[mask].first is the number of complete rides, and best[mask].second is the weigth of the current ride.

If best[mask].second == 0, thus the minimum number of rides for mask is best[mask].first, else this number is best[mask].first + 1 (+1 because of the incomplete ride)

For a mask, for a set bit b, we are checking whether it can fit in the group already formed with least sum, at this time it is possible that for current mask the minimum sum group will not be (weight[b]+dp_sum[remaining]) and we should now change this dp_sum[current_mask] to sum of the group with least sum. Why we are not doing that? For ex: we have 8,6,4 and max_wt=10, and dp_sum[(8,6)] = 6 and rides[{8,6}] = 2 and on checking for weight 4, dp_sum[{8,6}]+4=10, we are actually doing dp_sum[{8,6,4}]=10 but should not we do dp_sum[{8,6,4}] = 8; as from {8}, {6,4} these groups, 8 has minimum sum group.

Can anyone suggest a good problem similar to this one for practice?

The idea is to calculate for each subset of people two values: the minimum number of rides needed and the minimum weight of people who ride in the last group.

Above is the whole Idea for given problem, but I am not understanding that why we only need to check for last ride?