Description

The Huaxia 60 supersonic fighter jet is one of the most maneuverable fighters in the world today. A key issue in combat is how to climb/dive from the current flight altitude and speed to a designated altitude and achieve a designated speed in the shortest time to gain a superior combat position.

Assume that the Huaxia 60 is allowed to perform only the following three basic maneuvers, and a new basic maneuver can only start after the previous one is completed. Thus, a flight can be represented as a sequence composed of these three basic maneuvers.

(1) Maintain the current speed and perform a constant-speed climb until the flight altitude increases by $\Delta h$ feet.

(2) Perform horizontal acceleration until the speed increases by 1 Mach (1 Mach $\approx 1200$ km/h).

(3) Perform a vertical dive by $\Delta h$ feet, during which the flight speed increases by 1 Mach.

Also assume that the initial flight speed and the speed at the beginning of each basic maneuver are integer multiples of 1 Mach and do not exceed 6 Mach; the initial flight altitude and the altitude at the beginning of each basic maneuver are integer multiples of $\Delta h$ feet (where $\Delta h$ is an integer).

Experimental studies show that the time required to complete the above three basic maneuvers varies with different altitudes $H$ and initial speeds $V$. Tables 1–3 give the required times when $\Delta h = 15000$ feet and the maximum flight altitude is $75000$ feet.

Based on the data in Tables 1–3, the shortest time for the Huaxia 60 to reach the flight state $H=75000$ feet, $V=6$ Mach starting from $H=0$ feet, $V=1$ Mach is 79 seconds, and the corresponding sequence of maneuvers is:

(1) Constant-speed climb to $H=15000$ feet, $V=1$ Mach.

(2) Perform two consecutive horizontal accelerations to $H=15000$ feet, $V=3$ Mach.

(3) Perform four consecutive constant-speed climbs to $H=75000$ feet, $V=3$ Mach.

(4) Horizontal acceleration to $H=75000$ feet, $V=4$ Mach.

(5) Perform two consecutive vertical dives to $H=45000$ feet, $V=6$ Mach.

(6) Perform two consecutive constant-speed climbs to $H=75000$ feet, $V=6$ Mach.

Now Xiao Ming is flying the Huaxia 60 at $V_1$ Mach at altitude $H_1$ feet. The squadron commander orders him to fly at $V_2$ Mach at altitude $H_2$ feet. Please write a program to decide how to fly so that the order is completed in the least time.

Input Format

Output Format

The output contains two lines.

• The first line contains the time required by your optimal plan.
• The second line contains the action sequence of the optimal plan (use R for constant-speed climb, A for horizontal acceleration, and D for vertical dive). No extra characters (including whitespace) are allowed on the second line.

0 1 75000 6 15000 75000
12 12 12 11 12 14
11 10 8 9 10 11
9 8 6 7 8 8
8 7 6 6 6 5
8 6 6 6 6 5
11 11 11 13 15
10 10 9 9 10
10 9 9 10 10
9 8 9 9 10
7 8 8 9 9
7 7 7 8 8
5 4 3 3 2
4 3 3 2 2
3 3 2 2 2
3 3 2 2 2

79
RAARRRRADDRR

Hint

Translated by ChatGPT 5