You might be surprised to know that 2013 is the first year since 1987 with distinct digits. The years 2014, 2015, 2016, 2017, 2018, 2019 each have distinct digits. 2012 does not have distinct digits, since the digit 2 is repeated.
Given a year, what is the next year with distinct digits?
The input consists of one integer \(Y\) (\(0 \leq Y \leq 10000\)), representing the starting year.
The output will be the single integer \(D\), which is the next year after \(Y\) with distinct digits.
198720139991023A train of railway cars attempts to cross a bridge. The length of each car is 10m but their weights might be different. The bridge is 40m long (thus can hold 4 train cars at one time). The bridge will crack if the total weight of the cars on it at one time is greater than a certain weight. The cars are numbered starting at 1, going up to \(N\), and they cross the bridge in that order (i.e., 1 immediately followed by 2, which is immediately followed by 3, and so on).
What is the largest number \(T\) of railway cars such that the train of cars \(1...T\) (in order) can cross the bridge?
The first line of input is the maximum weight \(W\) (\(1 \leq W \leq 100000\)) that the bridge can hold at any particular time. The second line of input is the number \(N\) (\(1 \leq N \leq 100000\)) which is the number of railway cars that we wish to move across the bridge. On each of the next \(N\) lines of input, there will be a positive integer \(w_i\) (\(1 \leq i \leq N\), \(1 \leq w_i \leq 100000\)) which represents the weight of the \(i\)th railway car in the sequence.
Your output should be a non-negative integer representing the maximum number of railway cars that can be brought across the bridge in the order specified.
100
6
50
30
10
10
40
505The first four railway cars have total weight \(50+30+10+10=100\), which is not greater than what the bridge can hold. When the first railway car leaves, and the next comes on, we have a total weight of \(30+10+10+40=90\), which is not greater than what the bridge can hold. The last four cars would cause the bridge to break, since \(10+10+40+50=110\) which is greater than the bridge can hold. So, only the first 5 railway cars can be taken across the bridge.
100
3
150
1
10When the first railway car enters the bridge, its weight of \(150\) will exceed the maximum weight the bridge can hold. Thus, we cannot bring any railway cars across the bridge.
You want to determine the chances that your favourite team will be the champion of a small tournament.
There are exactly four teams. At the end of the tournament, a total of six games will have been played with each team playing every other team exactly once. For each game, either one team wins (and the other loses), or the game ends in a tie. If the game does not end in a tie, the winning team is awarded three points and the losing team is awarded zero points. If the game ends in a tie, each team is awarded one point.
Your favourite team will only be the champion if it ends the tournament with strictly more total points than every other team (i.e., a tie for first place is not good enough for your favourite team).
The tournament is not over yet but you know the scores of every game that has already been played. You want to consider all possible ways points could be awarded in the remaining games that have not yet been played and determine in how many of these cases your favourite team will be the tournament champion.
The first line of input will contain an integer \(T\) which is your favourite team (\(1 \leq T \leq 4\)).
The second line will contain an integer \(G\), the number of games already played (\(0 \leq G \leq 5\)).
The next \(G\) lines will give the results of games that have already been played. Each of these lines will consist of four integers \(A\), \(B\), \(S_A\), \(S_B\) separated by single spaces where \(1\leq A < B \leq 4\), and \(S_A, S_B \geq 0\) . This corresponds to a game between team \(A\) (which had score \(S_A\)) and team \(B\) (which had score \(S_B\)) where team \(A\) won if \(S_A>S_B\), team \(B\) won if \(S_A<S_B\) and the game ended in a tie if \(S_A=S_B\). The pairs \(A\) and \(B\) on the input lines are distinct, since no pair of teams plays twice.
The output will consist of a single integer which is the number of times that team \(T\) is the champion over all possible awarding of points in the remaining games in the tournament.
3
3
1 3 7 5
3 4 0 8
2 4 2 20Team 3 has lost two of its three games, and team 4 has tied one and won one, which gives 4 points to team 4. Even if team 3 wins its final game, it cannot have more points than team 4, and thus, will not be champion.
3
4
1 3 5 7
3 4 8 0
2 4 2 2
1 2 5 59After these games, we know the following:
| Team | Points |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 1 |
There are two remaining games (team 3 plays team 2; team 1 plays team 4). Teams 1, 2 or 4 cannot achieve 6 points, since even if they win their final games, their final point totals will be 4, 5 and 4 respectively. Thus, out of the 9 possible outcomes (2 matches with 3 different possible results per match), team 3 will be the champion in all 9 outcomes.
You have a few minutes before your class starts, and you decide to compare the heights of your classmates. You don’t have an accurate measuring device, so you just compare relative heights between two people: you stand two people back-to-back, and determine which one of the two is taller. Conveniently, none of your classmates are the same height, and you always compare correctly (i.e., you never make a mistake in your comparisons).
After you have done all of your comparisons, you would like to determine who the tallest person is between two particular classmates.
The first line contains two integers \(N\) and \(M\) separated by one space. \(N\), the number of people in the class, is an integer with \(1 \le N \le 1000000\). \(M\), the number of comparisons that have already been done, is an integer with \(1 \le M \le 10000000\). Each of the next \(M\) lines contains two distinct integers \(x\) and \(y\) (\(1 \leq x, y \leq N\)) separated by a space, indicating that person number \(x\) was determined to be taller than person number \(y\). Finally, the last line contains two distinct integers \(p\) and \(q\) (\(1 \leq p, q \leq N\)) separated by one space: your goal is to determine, if possible, whether person \(p\) is taller than person \(q\). Note that it may be the case that neither \(p\) nor \(q\) occur in the input concerning measurements between classmates, and each measurement between any two particular people will be recorded exactly once.
The output is one line, containing one of three possible strings:
yes (if \(p\) is taller than \(q\)),
no (if \(q\) is taller than \(p\)),
unknown (if there is not enough
information to determine the relative heights of \(p\) and \(q\)).
10 3
8 4
3 8
4 2
3 2yes10 3
3 8
2 8
3 4
3 2unknownIn the game of Factor Solitaire, you start with the number 1, and try to change it to some given target number \(n\) by repeatedly using the following operation. In each step, if \(c\) is your current number, you split it into two positive factors \(a\), \(b\) of your choice such that \(c=a*b\). You then add \(a\) to your current number \(c\) to get your new current number. Doing this costs you \(b\) points. You continue doing this until your current number is \(n\), and you try to achieve this at the cost of a minimum total number of points.
For example, here is one way to get to 15:
start with 1,
change 1 to 1+1 = 2 — cost so far is 1,
change 2 to 2+1 = 3 — cost so far is 1+2,
change 3 to 3+3 = 6 — cost so far is 1+2+1,
change 6 to 6+6 = 12 — cost so far is 1+2+1+1,
change 12 to 12+3 = 15 — done, total cost is 1+2+1+1+4=9.
In fact, this is the minimum possible total cost to get 15. You want to compute the minimum total cost for other target end numbers.
The input consists of a single integer \(N \ge 1\). In at least half of the cases \(N \le 50000\), in at least another quarter of the cases \(N \le 500000\), and in the remaining cases \(N \le 5000000\).
Compute the minimum cost that gets you to \(N\).
15
9
2013
91
For example, start with 1, then get to 2, 4, 5, 10, 15, 30, 60, 61, 122, 244, 305, 610, 671, 1342, and then 2013.