# |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
650589 |
2022-10-14T08:47:09 Z |
alvinpiter |
Bank (IZhO14_bank) |
C++17 |
|
180 ms |
8496 KB |
/*
dp[mask] -> The maximum number of prefix of salaries that we can pay using the banknotes represented by "mask".
Transition:
Brute force on the last used banknotes. Assume the last used banknote is the i-th:
* The number of paid salaries so far is k = dp[mask ^ (1 << i)]
* The next salary to pay is the (k + 1)-th one
* After paying the first k salaries, there might be leftover. Use this leftover together with the
i-th banknote to pay for (k + 1)-th salary
Total complexity is O(m * 2^m)
*/
#include<bits/stdc++.h>
using namespace std;
int n, m, a[22], b[22], asum[22], bsum[(1 << 20) + 3];
int dp[(1 << 20) + 2];
int main() {
cin >> n >> m;
for (int i = 0; i < n; i++) {
cin >> a[i];
}
for (int i = 0; i < m; i++) {
cin >> b[i];
}
asum[0] = a[0];
for (int i = 1; i < n; i++) {
asum[i] = asum[i - 1] + a[i];
}
for (int mask = 0; mask < (1 << m); mask++) {
bsum[mask] = 0;
for (int i = 0; i < m; i++) {
if (mask & (1 << i)) {
bsum[mask] += b[i];
}
}
}
dp[0] = 0;
for (int mask = 1; mask < (1 << m); mask++) {
dp[mask] = 0;
for (int i = 0; i < m; i++) {
if (mask & (1 << i)) {
int prevMask = mask ^ (1 << i);
// The current subset of bank notes must be at least as good
// as the previous subset of bank notes.
dp[mask] = max(dp[mask], dp[prevMask]);
int leftOver = bsum[prevMask] - (dp[prevMask] > 0 ? asum[dp[prevMask] - 1] : 0);
if (leftOver + b[i] == a[dp[prevMask]]) {
dp[mask] = max(dp[mask], dp[prevMask] + 1);
dp[mask] = min(dp[mask], n);
}
}
}
}
cout << (dp[(1 << m) - 1] == n ? "YES" : "NO") << endl;
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
212 KB |
Output is correct |
2 |
Correct |
1 ms |
212 KB |
Output is correct |
3 |
Correct |
1 ms |
212 KB |
Output is correct |
4 |
Correct |
5 ms |
468 KB |
Output is correct |
5 |
Correct |
148 ms |
8412 KB |
Output is correct |
6 |
Correct |
1 ms |
212 KB |
Output is correct |
7 |
Correct |
1 ms |
212 KB |
Output is correct |
8 |
Correct |
166 ms |
8440 KB |
Output is correct |
9 |
Correct |
150 ms |
8436 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
212 KB |
Output is correct |
2 |
Correct |
1 ms |
212 KB |
Output is correct |
3 |
Correct |
1 ms |
212 KB |
Output is correct |
4 |
Correct |
1 ms |
212 KB |
Output is correct |
5 |
Correct |
1 ms |
212 KB |
Output is correct |
6 |
Correct |
1 ms |
212 KB |
Output is correct |
7 |
Correct |
1 ms |
212 KB |
Output is correct |
8 |
Correct |
1 ms |
212 KB |
Output is correct |
9 |
Correct |
1 ms |
212 KB |
Output is correct |
10 |
Correct |
1 ms |
212 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
3 ms |
340 KB |
Output is correct |
2 |
Correct |
2 ms |
340 KB |
Output is correct |
3 |
Correct |
2 ms |
340 KB |
Output is correct |
4 |
Correct |
3 ms |
388 KB |
Output is correct |
5 |
Correct |
3 ms |
356 KB |
Output is correct |
6 |
Correct |
3 ms |
340 KB |
Output is correct |
7 |
Correct |
2 ms |
340 KB |
Output is correct |
8 |
Correct |
3 ms |
340 KB |
Output is correct |
9 |
Correct |
3 ms |
340 KB |
Output is correct |
10 |
Correct |
2 ms |
340 KB |
Output is correct |
11 |
Correct |
3 ms |
340 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
212 KB |
Output is correct |
2 |
Correct |
1 ms |
212 KB |
Output is correct |
3 |
Correct |
1 ms |
212 KB |
Output is correct |
4 |
Correct |
5 ms |
468 KB |
Output is correct |
5 |
Correct |
148 ms |
8412 KB |
Output is correct |
6 |
Correct |
1 ms |
212 KB |
Output is correct |
7 |
Correct |
1 ms |
212 KB |
Output is correct |
8 |
Correct |
166 ms |
8440 KB |
Output is correct |
9 |
Correct |
150 ms |
8436 KB |
Output is correct |
10 |
Correct |
1 ms |
212 KB |
Output is correct |
11 |
Correct |
1 ms |
212 KB |
Output is correct |
12 |
Correct |
1 ms |
212 KB |
Output is correct |
13 |
Correct |
1 ms |
212 KB |
Output is correct |
14 |
Correct |
1 ms |
212 KB |
Output is correct |
15 |
Correct |
1 ms |
212 KB |
Output is correct |
16 |
Correct |
1 ms |
212 KB |
Output is correct |
17 |
Correct |
1 ms |
212 KB |
Output is correct |
18 |
Correct |
1 ms |
212 KB |
Output is correct |
19 |
Correct |
1 ms |
212 KB |
Output is correct |
20 |
Correct |
3 ms |
340 KB |
Output is correct |
21 |
Correct |
2 ms |
340 KB |
Output is correct |
22 |
Correct |
2 ms |
340 KB |
Output is correct |
23 |
Correct |
3 ms |
388 KB |
Output is correct |
24 |
Correct |
3 ms |
356 KB |
Output is correct |
25 |
Correct |
3 ms |
340 KB |
Output is correct |
26 |
Correct |
2 ms |
340 KB |
Output is correct |
27 |
Correct |
3 ms |
340 KB |
Output is correct |
28 |
Correct |
3 ms |
340 KB |
Output is correct |
29 |
Correct |
2 ms |
340 KB |
Output is correct |
30 |
Correct |
3 ms |
340 KB |
Output is correct |
31 |
Correct |
160 ms |
8484 KB |
Output is correct |
32 |
Correct |
163 ms |
8484 KB |
Output is correct |
33 |
Correct |
148 ms |
8476 KB |
Output is correct |
34 |
Correct |
156 ms |
8416 KB |
Output is correct |
35 |
Correct |
148 ms |
8408 KB |
Output is correct |
36 |
Correct |
144 ms |
8408 KB |
Output is correct |
37 |
Correct |
137 ms |
8488 KB |
Output is correct |
38 |
Correct |
140 ms |
8368 KB |
Output is correct |
39 |
Correct |
151 ms |
8368 KB |
Output is correct |
40 |
Correct |
147 ms |
8424 KB |
Output is correct |
41 |
Correct |
144 ms |
8492 KB |
Output is correct |
42 |
Correct |
152 ms |
8484 KB |
Output is correct |
43 |
Correct |
140 ms |
8404 KB |
Output is correct |
44 |
Correct |
151 ms |
8436 KB |
Output is correct |
45 |
Correct |
149 ms |
8496 KB |
Output is correct |
46 |
Correct |
156 ms |
8368 KB |
Output is correct |
47 |
Correct |
139 ms |
8368 KB |
Output is correct |
48 |
Correct |
162 ms |
8388 KB |
Output is correct |
49 |
Correct |
138 ms |
8376 KB |
Output is correct |
50 |
Correct |
157 ms |
8488 KB |
Output is correct |
51 |
Correct |
139 ms |
8484 KB |
Output is correct |
52 |
Correct |
137 ms |
8396 KB |
Output is correct |
53 |
Correct |
147 ms |
8476 KB |
Output is correct |
54 |
Correct |
180 ms |
8484 KB |
Output is correct |
55 |
Correct |
168 ms |
8436 KB |
Output is correct |
56 |
Correct |
146 ms |
8392 KB |
Output is correct |
57 |
Correct |
143 ms |
8472 KB |
Output is correct |
58 |
Correct |
151 ms |
8484 KB |
Output is correct |