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thecodingwizardthecodingwizard
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5.5.3
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‎README.md

+2
Original file line numberDiff line numberDiff line change
@@ -72,6 +72,7 @@ Solutions to USACO training and USACO contest problems.
7272
| 5.4.3 | [TeleCowmunication][5.4.3] | Max Flow Min Cut, Split Nodes |
7373
| 5.5.1 | [Picture][5.5.1] | Line Sweep |
7474
| 5.5.2 | [Hidden Passwords][5.5.2] | String Processing |
75+
| 5.5.3 | [Two Five][5.5.3] | DP |
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7677
### Silver USACO Contests:
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| Contest Date | Problem ID | Problem Name | Solution Notes |
@@ -309,6 +310,7 @@ Solutions to USACO training and USACO contest problems.
309310
[5.4.3]: usaco-training/Chapter%205/5.4.3%20-%20TeleCowmunication.cpp
310311
[5.5.1]: usaco-training/Chapter%205/5.5.1%20-%20Picture.cpp
311312
[5.5.2]: usaco-training/Chapter%205/5.5.2%20-%20Hidden%20Passwords.cpp
313+
[5.5.3]: usaco-training/Chapter%205/5.5.3%20-%20Two%20Five.cpp
312314

313315
[reststops]: usaco-contests/2018feb/silver/reststops.cpp
314316
[revegetate]: usaco-contests/2019feb/silver/revegetate.cpp

‎main.cpp

+110-14
Original file line numberDiff line numberDiff line change
@@ -1,3 +1,9 @@
1+
/*
2+
ID: nathan.18
3+
TASK: twofive
4+
LANG: C++
5+
*/
6+
17
#include <iostream>
28
#include <string>
39
#include <utility>
@@ -70,23 +76,113 @@ void setupIO(const string &PROB) {
7076

7177
/* ============================ */
7278

79+
int grid[5][5];
80+
int memo[6][6][6][6][6];
81+
bool used[26];
82+
83+
int run(int a, int b, int c, int d, int e, int val) {
84+
if (e == 5) return 1;
85+
while (val <= 25 && used[val]) val++;
86+
if (val > 25) return 0;
87+
88+
if (memo[a][b][c][d][e] != -1) return memo[a][b][c][d][e];
89+
90+
int ans = 0;
91+
if (a != 5 && (a == 0 || grid[0][a-1] < val)) ans += run(a+1, b, c, d, e, val+1);
92+
if (b != 5 && b < a && grid[0][b] < val && (b == 0 || grid[1][b - 1] < val)) ans += run(a, b+1, c, d, e, val+1);
93+
if (c != 5 && c < b && grid[1][c] < val && (c == 0 || grid[2][c - 1] < val)) ans += run(a, b, c+1, d, e, val+1);
94+
if (d != 5 && d < c && grid[2][d] < val && (d == 0 || grid[3][d - 1] < val)) ans += run(a, b, c, d+1, e, val+1);
95+
if (e != 5 && e < d && grid[3][e] < val && (e == 0 || grid[4][e - 1] < val)) ans += run(a, b, c, d, e+1, val+1);
96+
97+
/* cout << a << " " << b << " " << c << " " << d << " " << e << " " << val << " " << ans << endl; */
98+
99+
return memo[a][b][c][d][e] = ans;
100+
}
101+
102+
73103
int main() {
74-
int n; cin >> n;
75-
if (n == 1) cout << 1 << endl;
76-
else if (n < 4) cout << "NO SOLUTION" << endl;
77-
else {
78-
vi toPrint;
79-
F0R1(i, n) {
80-
if (i & 1) continue;
81-
toPrint.pb(i);
104+
setupIO("twofive");
105+
106+
/* SET2D(grid, -1, 5, 5); */
107+
/* SET(used, false, 26); */
108+
/* F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1; */
109+
/* run(0, 0, 0, 0, 0, 0); */
110+
111+
/* return 0; */
112+
113+
char c; cin >> c;
114+
if (c == 'N') {
115+
int m; cin >> m;
116+
SET2D(grid, -1, 5, 5);
117+
SET(used, false, 26);
118+
F0R(i, 5) {
119+
F0R(j, 5) {
120+
int sum = 0;
121+
F0R(k, 25) {
122+
if (used[k]) continue;
123+
if (j > 0 && grid[i][j - 1] >= k) continue;
124+
if (i > 0 && grid[i - 1][j] >= k) continue;
125+
grid[i][j] = k;
126+
used[k] = true;
127+
128+
F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1;
129+
130+
int val;
131+
if (i == 0) val = run(j+1, 0, 0, 0, 0, 0);
132+
if (i == 1) val = run(5, j+1, 0, 0, 0, 0);
133+
if (i == 2) val = run(5, 5, j+1, 0, 0, 0);
134+
if (i == 3) val = run(5, 5, 5, j+1, 0, 0);
135+
if (i == 4) val = run(5, 5, 5, 5, j+1, 0);
136+
/* cout << val << endl; */
137+
sum += val;
138+
if (sum >= m) {
139+
sum -= val;
140+
m -= sum;
141+
break;
142+
}
143+
used[k] = false;
144+
}
145+
}
82146
}
83-
F0R1(i, n) {
84-
if (!(i & 1)) continue;
85-
toPrint.pb(i);
147+
148+
string ans = "";
149+
F0R(i, 5) F0R(j, 5) ans += ('A' + grid[i][j]);
150+
cout << ans << endl;
151+
} else {
152+
char realGrid[5][5];
153+
F0R(i, 5) F0R(j, 5) cin >> realGrid[i][j];
154+
SET2D(grid, -1, 5, 5);
155+
SET(used, false, 26);
156+
157+
int ans = 0;
158+
F0R(i, 5) {
159+
F0R(j, 5) {
160+
F0R(k, 25) {
161+
if (used[k]) continue;
162+
if (j > 0 && grid[i][j - 1] >= k) continue;
163+
if (i > 0 && grid[i - 1][j] >= k) continue;
164+
grid[i][j] = k;
165+
used[k] = true;
166+
if (k == realGrid[i][j] - 'A') break;
167+
168+
F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1;
169+
170+
int val;
171+
if (i == 0) val = run(j+1, 0, 0, 0, 0, 0);
172+
if (i == 1) val = run(5, j+1, 0, 0, 0, 0);
173+
if (i == 2) val = run(5, 5, j+1, 0, 0, 0);
174+
if (i == 3) val = run(5, 5, 5, j+1, 0, 0);
175+
if (i == 4) val = run(5, 5, 5, 5, j+1, 0);
176+
177+
ans += val;
178+
179+
used[k] = false;
180+
}
181+
}
86182
}
87-
cout << toPrint[0];
88-
FOR(i, 1, toPrint.size()) cout << " " << toPrint[i];
89-
cout << endl;
183+
184+
ans++;
185+
cout << ans << endl;
90186
}
91187

92188
return 0;

‎usaco-training/Chapter 5/5.5.3 - Two Five.cpp

+189
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,189 @@
1+
/*
2+
ID: nathan.18
3+
TASK: twofive
4+
LANG: C++
5+
*/
6+
7+
#include <iostream>
8+
#include <string>
9+
#include <utility>
10+
#include <sstream>
11+
#include <algorithm>
12+
#include <stack>
13+
#include <vector>
14+
#include <queue>
15+
#include <map>
16+
#include <set>
17+
#include <bitset>
18+
#include <cmath>
19+
#include <cstring>
20+
#include <iomanip>
21+
#include <fstream>
22+
#include <cassert>
23+
#include <unordered_set>
24+
#include <ctime>
25+
#include <list>
26+
27+
using namespace std;
28+
29+
template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
30+
31+
#define FOR(i, a, b) for (int i=a; i<(b); i++)
32+
#define F0R(i, a) for (int i=0; i<(a); i++)
33+
#define F0R1(i, a) for (int i=1; i<=(a); i++)
34+
#define FORd(i, a, b) for (int i = (b)-1; i >= a; i--)
35+
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
36+
#define F0Rd1(i, a) for (int i=a; i>0; i--)
37+
#define SORT(vec) sort(vec.begin(), vec.end())
38+
#define MIN(a, b) a = min(a, b)
39+
#define MAX(a, b) a = max(a, b)
40+
41+
#define INF 1000000010
42+
#define LL_INF 4500000000000000000
43+
#define LSOne(S) (S & (-S))
44+
#define EPS 1e-9
45+
#define pA first
46+
#define pB second
47+
#define mp make_pair
48+
#define pb push_back
49+
#define PI acos(-1.0)
50+
#define ll long long
51+
#define MOD (int)(2e+9+11)
52+
#define SET(vec, val, size) for (int i = 0; i < size; i++) vec[i] = val;
53+
#define SET2D(arr, val, dim1, dim2) F0R(i, dim1) F0R(j, dim2) arr[i][j] = val;
54+
#define SET3D(arr, val, dim1, dim2, dim3) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) arr[i][j][k] = val;
55+
#define SET4D(arr, val, dim1, dim2, dim3, dim4) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) F0R(l, dim4) arr[i][j][k][l] = val;
56+
#define READGRID(arr, dim) F0R(i, dim) F0R(j, dim) cin >> arr[i][j];
57+
#define all(x) (x).begin(), (x).end()
58+
59+
typedef pair<int, int> ii;
60+
typedef pair<int, ii> iii;
61+
typedef pair<ll, ll> pll;
62+
typedef vector<int> vi;
63+
typedef vector<ii> vii;
64+
typedef vector<iii> viii;
65+
typedef vector<ll> vl;
66+
67+
void setupIO(const string &PROB) {
68+
ios::sync_with_stdio(false);
69+
cin.tie(nullptr);
70+
ifstream infile(PROB + ".in");
71+
if (infile.good()) {
72+
freopen((PROB + ".in").c_str(), "r", stdin);
73+
freopen((PROB + ".out").c_str(), "w", stdout);
74+
}
75+
}
76+
77+
/* ============================ */
78+
79+
int grid[5][5];
80+
int memo[6][6][6][6][6];
81+
bool used[26];
82+
83+
int run(int a, int b, int c, int d, int e, int val) {
84+
if (e == 5) return 1;
85+
while (val <= 25 && used[val]) val++;
86+
if (val > 25) return 0;
87+
88+
if (memo[a][b][c][d][e] != -1) return memo[a][b][c][d][e];
89+
90+
int ans = 0;
91+
if (a != 5 && (a == 0 || grid[0][a-1] < val)) ans += run(a+1, b, c, d, e, val+1);
92+
if (b != 5 && b < a && grid[0][b] < val && (b == 0 || grid[1][b - 1] < val)) ans += run(a, b+1, c, d, e, val+1);
93+
if (c != 5 && c < b && grid[1][c] < val && (c == 0 || grid[2][c - 1] < val)) ans += run(a, b, c+1, d, e, val+1);
94+
if (d != 5 && d < c && grid[2][d] < val && (d == 0 || grid[3][d - 1] < val)) ans += run(a, b, c, d+1, e, val+1);
95+
if (e != 5 && e < d && grid[3][e] < val && (e == 0 || grid[4][e - 1] < val)) ans += run(a, b, c, d, e+1, val+1);
96+
97+
/* cout << a << " " << b << " " << c << " " << d << " " << e << " " << val << " " << ans << endl; */
98+
99+
return memo[a][b][c][d][e] = ans;
100+
}
101+
102+
103+
int main() {
104+
setupIO("twofive");
105+
106+
/* SET2D(grid, -1, 5, 5); */
107+
/* SET(used, false, 26); */
108+
/* F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1; */
109+
/* run(0, 0, 0, 0, 0, 0); */
110+
111+
/* return 0; */
112+
113+
char c; cin >> c;
114+
if (c == 'N') {
115+
int m; cin >> m;
116+
SET2D(grid, -1, 5, 5);
117+
SET(used, false, 26);
118+
F0R(i, 5) {
119+
F0R(j, 5) {
120+
int sum = 0;
121+
F0R(k, 25) {
122+
if (used[k]) continue;
123+
if (j > 0 && grid[i][j - 1] >= k) continue;
124+
if (i > 0 && grid[i - 1][j] >= k) continue;
125+
grid[i][j] = k;
126+
used[k] = true;
127+
128+
F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1;
129+
130+
int val;
131+
if (i == 0) val = run(j+1, 0, 0, 0, 0, 0);
132+
if (i == 1) val = run(5, j+1, 0, 0, 0, 0);
133+
if (i == 2) val = run(5, 5, j+1, 0, 0, 0);
134+
if (i == 3) val = run(5, 5, 5, j+1, 0, 0);
135+
if (i == 4) val = run(5, 5, 5, 5, j+1, 0);
136+
/* cout << val << endl; */
137+
sum += val;
138+
if (sum >= m) {
139+
sum -= val;
140+
m -= sum;
141+
break;
142+
}
143+
used[k] = false;
144+
}
145+
}
146+
}
147+
148+
string ans = "";
149+
F0R(i, 5) F0R(j, 5) ans += ('A' + grid[i][j]);
150+
cout << ans << endl;
151+
} else {
152+
char realGrid[5][5];
153+
F0R(i, 5) F0R(j, 5) cin >> realGrid[i][j];
154+
SET2D(grid, -1, 5, 5);
155+
SET(used, false, 26);
156+
157+
int ans = 0;
158+
F0R(i, 5) {
159+
F0R(j, 5) {
160+
F0R(k, 25) {
161+
if (used[k]) continue;
162+
if (j > 0 && grid[i][j - 1] >= k) continue;
163+
if (i > 0 && grid[i - 1][j] >= k) continue;
164+
grid[i][j] = k;
165+
used[k] = true;
166+
if (k == realGrid[i][j] - 'A') break;
167+
168+
F0R(i, 6) F0R(j, 6) F0R(k, 6) F0R(l, 6) F0R(m, 6) memo[i][j][k][l][m] = -1;
169+
170+
int val;
171+
if (i == 0) val = run(j+1, 0, 0, 0, 0, 0);
172+
if (i == 1) val = run(5, j+1, 0, 0, 0, 0);
173+
if (i == 2) val = run(5, 5, j+1, 0, 0, 0);
174+
if (i == 3) val = run(5, 5, 5, j+1, 0, 0);
175+
if (i == 4) val = run(5, 5, 5, 5, j+1, 0);
176+
177+
ans += val;
178+
179+
used[k] = false;
180+
}
181+
}
182+
}
183+
184+
ans++;
185+
cout << ans << endl;
186+
}
187+
188+
return 0;
189+
}

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