/
maxplus_convolution.hpp
57 lines (53 loc) · 1.75 KB
/
maxplus_convolution.hpp
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
#include "convex/monotone_minima.hpp"
template <typename T>
vc<T> maxplus_convolution_concave_concave(vc<T>& A, vc<T>& B) {
int n = len(A), m = len(B);
if (n == 0 && m == 0) return {};
vc<T> C(n + m - 1, -infty<T>);
while (n > 0 && A[n - 1] == -infty<T>) --n;
while (m > 0 && B[m - 1] == -infty<T>) --m;
if (n == 0 || m == 0) return C;
int a = 0, b = 0;
while (a < n && A[a] == -infty<T>) ++a;
while (b < m && B[b] == -infty<T>) ++b;
C[a + b] = A[a] + B[b];
for (int i = a + b + 1; i < n + m - 1; ++i) {
if (b == m - 1 || (a != n - 1 && A[a + 1] + B[b] > A[a] + B[b + 1])) {
chmax(C[i], A[++a] + B[b]);
} else {
chmax(C[i], A[a] + B[++b]);
}
}
return C;
}
template <typename T>
vc<T> maxplus_convolution_arbitrary_concave(vc<T>& A, vc<T>& B) {
int n = len(A), m = len(B);
if (n == 0 && m == 0) return {};
vc<T> C(n + m - 1, -infty<T>);
while (m > 0 && B[m - 1] == -infty<T>) --m;
if (m == 0) return C;
int b = 0;
while (b < m && B[b] == -infty<T>) ++b;
auto select = [&](int i, int j, int k) -> bool {
if (i < k) return false;
if (i - j >= m - b) return true;
return A[j] + B[b + i - j] <= A[k] + B[b + i - k];
};
vc<int> J = monotone_minima(n + m - b - 1, n, select);
FOR(i, n + m - b - 1) {
T x = A[J[i]], y = B[b + i - J[i]];
if (x > -infty<T> && y > -infty<T>) C[b + i] = x + y;
}
return C;
}
template <typename T, bool conA, bool conB>
vc<T> maxplus_convolution(vc<T>& A, vc<T>& B) {
static_assert(conA || conB);
if constexpr (conA && conB) return maxplus_convolution_concave_concave(A, B);
if constexpr (conA && !conB)
return maxplus_convolution_arbitrary_concave(B, A);
if constexpr (conB && !conA)
return maxplus_convolution_arbitrary_concave(A, B);
return {};
}