**Problem:**

Please find the problem here.

**Solution:**

Finally some problem that makes me think - the others are just so classic so far. In this problem we will use the same idea of 'achievable' state idea as in my previous solution for UVa Problem 562 - Dividing coins.

Some greediness helps here. If a song can fit in a current disk, there is no point to use a new disk. Using the current disk can be as least as good as recording this in the next disk. We basically used the same search. We use a two dimensional array to track the current disk and the current time left, each state is marked with whether it is reachable or not, and the number of used disks.

For each song, we examine each existing reachable state and try to add that song - one might be able to fit the disk in the current disk or need to open a disk, in either case that reach a new state, if the new state is already reachable, we choose the state with more song count.

At the end of the algorithm, we inspect each state, and find the maximum song count, that's it.

**Code:**

#include "stdafx.h" // http://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=414 #include "UVa473.h" #include <iostream> #include <vector> #include <algorithm> using namespace std; struct UVa473_State { public: int songs_recorded; bool reachable; }; int UVa473() { int number_of_test_cases; cin >> number_of_test_cases; for (int c = 0; c < number_of_test_cases; c++) { int number_of_songs; int time_per_disk; int number_of_disks; cin >> number_of_songs; cin >> time_per_disk; cin >> number_of_disks; vector<int> song_duration; for (int s = 0; s < number_of_songs; s++) { int song_time; cin >> song_time; song_duration.push_back(song_time); if (s != number_of_songs - 1) { char comma; cin >> comma; } } vector<vector<UVa473_State> > last_max_songs; vector<vector<UVa473_State> > max_songs; last_max_songs.resize(number_of_disks + 1); max_songs.resize(number_of_disks + 1); for (int d = 0; d <= number_of_disks; d++) { last_max_songs[d].resize(time_per_disk + 1); max_songs[d].resize(time_per_disk + 1); } // Initialization - the only achievable state at the beginning is all disk not recorded for (int d = 0; d <= number_of_disks; d++) { for (int t = 0; t <= time_per_disk; t++) { last_max_songs[d][t].songs_recorded = 0; last_max_songs[d][t].reachable = (d == number_of_disks) && (t == time_per_disk); } } for (int s = 0; s < number_of_songs; s++) { int current_song_duration = song_duration[s]; // Initializing the max_songs with the not choosing the current song for (int d = 0; d <= number_of_disks; d++) { for (int t = 0; t <= time_per_disk; t++) { max_songs[d][t].reachable = last_max_songs[d][t].reachable; max_songs[d][t].songs_recorded = last_max_songs[d][t].songs_recorded; } } for (int d = 0; d <= number_of_disks; d++) { for (int t = 0; t <= time_per_disk; t++) { if (last_max_songs[d][t].reachable) { int current_disk = d; int current_disk_remaining_time = t; int current_song_recorded = last_max_songs[d][t].songs_recorded; // Step 1: Consider if the current song can fit on the current disk if (current_disk != 0 && current_disk_remaining_time >= current_song_duration) { // Yes it can, let see if that's a better deal int new_disk = current_disk; int new_current_disk_remaining_time = current_disk_remaining_time - current_song_duration; int new_song_recorded = current_song_recorded + 1; if (!max_songs[new_disk][new_current_disk_remaining_time].reachable || max_songs[new_disk][new_current_disk_remaining_time].songs_recorded < new_song_recorded) { max_songs[new_disk][new_current_disk_remaining_time].reachable = true; max_songs[new_disk][new_current_disk_remaining_time].songs_recorded = new_song_recorded; } } // Step 2: Consider if the current song can fit on the next disk else if (current_disk > 1 && current_song_duration <= time_per_disk) { // Yes it can, let see if that's a better deal int new_disk = current_disk - 1; int new_current_disk_remaining_time = time_per_disk - current_song_duration; int new_song_recorded = current_song_recorded + 1; if (!max_songs[new_disk][new_current_disk_remaining_time].reachable || max_songs[new_disk][new_current_disk_remaining_time].songs_recorded < new_song_recorded) { max_songs[new_disk][new_current_disk_remaining_time].reachable = true; max_songs[new_disk][new_current_disk_remaining_time].songs_recorded = new_song_recorded; } } } } } for (int d = 0; d <= number_of_disks; d++) { for (int t = 0; t <= time_per_disk; t++) { last_max_songs[d][t].reachable = max_songs[d][t].reachable; last_max_songs[d][t].songs_recorded = max_songs[d][t].songs_recorded; } } } int max_songs_recorded = -1; for (int t = 0; t <= time_per_disk; t++) { max_songs_recorded = max(max_songs_recorded, max_songs[1][t].songs_recorded); } if (c != 0) { cout << endl; } cout << max_songs_recorded << endl; } return 0; }

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