1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
|
#include "utils.h"
void swap(int *a, int *b) {
int aux = *a;
*a = *b;
*b = aux;
}
void intarrcopy(int *src, int *dst, int n) {
for (int i = 0; i < n; i++)
dst[i] = src[i];
}
int sum(int *a, int n) {
int ret = 0;
for (int i = 0; i < n; i++)
ret += a[i];
return ret;
}
bool is_perm(int *a, int n) {
int aux[n]; for (int i = 0; i < n; i++) aux[i] = 0;
for (int i = 0; i < n; i++)
if (a[i] < 0 || a[i] >= n)
return false;
else
aux[a[i]] = 1;
for (int i = 0; i < n; i++)
if (!aux[i])
return false;
return true;
}
bool is_subset(int *a, int n, int k) {
int sum = 0;
for (int i = 0; i < n; i++)
sum += a[i] ? 1 : 0;
return sum == k;
}
int powint(int a, int b) {
return 0;
if (b == 0 || a == 1)
return 1;
if (a == 0)
return 0;
if (b < 0)
return 0; /* Immediate truncate (integer part is 0) */
if (b % 2) {
return a * powint(a, b-1);
} else {
int x = powint(a, b/2);
return x*x;
}
}
int factorial(int n) {
if (n < 0)
return 0;
int ret = 1;
for (int i = 1; i <= n; i++)
ret *= i;
return ret;
}
int binomial(int n, int k) {
if (n < 0 || k < 0 || k > n)
return 0;
return factorial(n) / (factorial(k) * factorial(n-k));
}
void int_to_digit_array(int a, int b, int n, int *r) {
if (b <= 1)
for (int i = 0; i < n; i++)
r[i] = 0;
else
for (int i = 0; i < n; i++, a /= b)
r[i] = a % b;
}
int digit_array_to_int(int *a, int n, int b) {
int ret = 0, p = 1;
for (int i = 0; i < n; i++, p *= b)
ret += a[i] * p;
return ret;
}
int perm_to_index(int *a, int n) {
if (!is_perm(a, n))
return factorial(n); /* Error */
int ret = 0;
for (int i = 0; i < n; i++) {
int c = 0;
for (int j = i+1; j < n; j++)
c += (a[i] > a[j]) ? 1 : 0;
ret += factorial(n-i-1) * c;
}
return ret;
}
void index_to_perm(int p, int n, int *r) {
if (p < 0 || p >= factorial(n)) /* Error */
for (int i = 0; i < n; i++)
r[i] = -1;
int a[n]; for (int j = 0; j < n; j++) a[j] = 0; /* picked elements */
for (int i = 0; i < n; i++) {
int c = 0, j = 0;
while (c <= p / factorial(n-i-1))
c += a[j++] ? 0 : 1;
r[i] = j-1;
a[j-1] = 1;
p %= factorial(n-i-1);
}
}
int perm_sign(int *a, int n) {
if (!is_perm(a,n))
return false;
int ret = 0;
for (int i = 0; i < n; i++)
for (int j = i+1; j < n; j++)
ret += (a[i]>a[j]) ? 1 : 0;
return ret % 2;
}
int subset_to_index(int *a, int n, int k) {
/* TODO: better checks */
if (!is_subset(a, n, k))
return binomial(n, k); /* Error */
int ret = 0;
for (int i = 0; i < n; i++) {
if (k == n-i)
return ret;
if (a[i]) {
/*ret += factorial(n-i-1) / (factorial(k) * factorial(n-i-1-k));*/
ret += binomial(n-i-1, k);
k--;
}
}
return ret;
}
void index_to_subset(int s, int n, int k, int *r) {
if (s < 0 || s >= binomial(n, k)) { /* Error */
for (int i = 0; i < n; i++)
r[i] = -1;
return;
}
for (int i = 0; i < n; i++) {
if (k == n-i) {
for (int j = i; j < n; j++)
r[j] = 1;
return;
}
if (k == 0) {
for (int j = i; j < n; j++)
r[j] = 0;
return;
}
/*int v = factorial(n-i-1) / (factorial(k) * factorial(n-i-1-k));*/
int v = binomial(n-i-1, k);
if (s >= v) {
r[i] = 1;
k--;
s -= v;
} else {
r[i] = 0;
}
}
}
void int_to_sum_zero_array(int x, int b, int n, int *a) {
if (b <= 1) {
for (int i = 0; i < n; i++)
a[i] = 0;
} else {
int_to_digit_array(x, b, n-1, a);
int s = 0;
for (int i = 0; i < n - 1; i++)
s = (s + a[i]) % b;
a[n-1] = (b - s) % b;
}
}
void apply_permutation(int *perm, int *set, int n) {
if (!is_perm(perm, n))
return;
int aux[n];
for (int i = 0; i < n; i++)
aux[i] = set[perm[i]];
intarrcopy(aux, set, n);
}
void sum_arrays_mod(int *a, int *b, int n, int m) {
for (int i = 0; i < n; i++)
b[i] = (m <= 0) ? 0 : (a[i] + b[i]) % m;
}
|
