|
8 | 8 | * https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/
|
9 | 9 | */
|
10 | 10 |
|
11 |
| -#include <bits/stdc++.h> |
| 11 | +#include "tests.h" |
| 12 | +#include "graphs.h" |
12 | 13 |
|
13 |
| -using namespace std; |
14 |
| - |
15 |
| -/* =========================================================================== |
16 |
| - * Data structures |
17 |
| - * =========================================================================== |
18 |
| - */ |
19 |
| -// Edge is a pair of nodes with weight [u, v, w] |
20 |
| -using Edge = array<int, 3>; |
21 |
| - |
22 |
| -// Graph is a pair of V nodes & array of E edges |
23 |
| -using Graph = pair<int, vector<Edge>>; |
24 |
| - |
25 |
| -/* =========================================================================== |
26 |
| - * Test helpers |
27 |
| - * =========================================================================== |
28 |
| - */ |
29 |
| -class _00_test |
30 |
| -{ |
31 |
| -public: |
32 |
| - _00_test(const string &name) : name(name) {} |
33 |
| - |
34 |
| - string getName(void) const { return name; } |
35 |
| - |
36 |
| - virtual vector<int> shortestPaths(const Graph &g, int src = 0) = 0; |
37 |
| - |
38 |
| -private: |
39 |
| - string name; |
40 |
| -}; |
| 14 | +using namespace Graphs; |
41 | 15 |
|
42 | 16 | /* ===========================================================================
|
43 | 17 | * Algorithms implementation
|
44 | 18 | * ===========================================================================
|
45 | 19 | */
|
| 20 | +#define _bf_desc "Bellman-Ford - Single source shortest path to all nodes" |
46 | 21 |
|
47 | 22 | /* TC : Best O(E), Average O(V*E), Worst O(V*E) => O(n^3) when E = V^2
|
48 | 23 | * For a complete graph E = V(V-1)/2 => O(E) = O(V^2).
|
49 | 24 | * SC : O(V) => O(n)
|
50 | 25 | */
|
51 |
| -class _01_bellman_ford : public _00_test |
| 26 | +vi_t shortestPaths(int nodes, const vi2_t &edges, int source) |
52 | 27 | {
|
53 |
| -public: |
54 |
| - _01_bellman_ford() |
55 |
| - : _00_test("Bellman-Ford single source shortest path to all " |
56 |
| - "nodes") |
57 |
| - { |
| 28 | + int ne = size(edges); |
| 29 | + vi_t d(nodes, X); |
| 30 | + d[source] = 0; |
| 31 | + fii (i, (nodes - 1)) { |
| 32 | + fii (j, ne) { |
| 33 | + int u = edges[j][0]; |
| 34 | + int v = edges[j][1]; |
| 35 | + int w = edges[j][2]; |
| 36 | + if (d[u] != X) d[v] = min(d[v], d[u] + w); |
| 37 | + } |
58 | 38 | }
|
59 |
| - |
60 |
| - vector<int> shortestPaths(const Graph &g, int src = 0) override |
61 |
| - { |
62 |
| - const int n = g.first; |
63 |
| - vector<int> d(n, INT_MAX); |
64 |
| - d[src] = 0; |
65 |
| - for (int i = 0; i < n - 1; i++) |
66 |
| - for (auto [u, v, w] : g.second) |
67 |
| - if (d[u] != INT_MAX) |
68 |
| - d[v] = min(d[v], d[u] + w); |
69 |
| - // Detect negative cycle |
70 |
| - for (auto [u, v, w] : g.second) |
71 |
| - if (d[u] != INT_MAX && d[v] > d[u] + w) |
72 |
| - return {INT_MIN}; |
73 |
| - return d; |
| 39 | + // Detect negative cycle |
| 40 | + fii (j, ne) { |
| 41 | + int u = edges[j][0]; |
| 42 | + int v = edges[j][1]; |
| 43 | + int w = edges[j][2]; |
| 44 | + if (d[u] != X && d[v] > d[u] + w) return {NX}; |
74 | 45 | }
|
75 |
| -}; |
| 46 | + return d; |
| 47 | +} |
76 | 48 |
|
77 | 49 | /* ===========================================================================
|
78 | 50 | * Test code
|
79 | 51 | * ===========================================================================
|
80 | 52 | */
|
81 |
| -template <class Container = vector<int>> |
82 |
| -string _vec2str(const Container &vec) |
83 |
| -{ |
84 |
| - ostringstream oss; |
85 |
| - using T = Container::value_type; |
86 |
| - oss << "{"; |
87 |
| - copy(vec.begin(), vec.end() - 1, ostream_iterator<T>(oss, ", ")); |
88 |
| - oss << vec.back(); |
89 |
| - oss << "}"; |
90 |
| - return oss.str(); |
91 |
| -} |
92 |
| - |
93 |
| -string _g2str(const Graph &g) |
| 53 | +#define _bf_check(n, ed, s, e) \ |
| 54 | + vi_t a = shortestPaths(n, ed, s); \ |
| 55 | + string _pre("distances"), im, am; \ |
| 56 | + im += to_string(n, ed); \ |
| 57 | + im += format(", source = {}", s); \ |
| 58 | + am = format("{} = {}", _pre, to_string(a)); \ |
| 59 | + CHECK_EQ(e, a); \ |
| 60 | + SHOW_OUTPUT(im, am); |
| 61 | + |
| 62 | +TEST(shortestPaths, _bf_desc) |
94 | 63 | {
|
95 |
| - ostringstream oss; |
96 |
| - oss << "{"; |
97 |
| - for (int i = 0; auto e : g.second) { |
98 |
| - if (i++) oss << ", "; |
99 |
| - oss << _vec2str<Edge>(e); |
100 |
| - } |
101 |
| - oss << "}"; |
102 |
| - return oss.str(); |
103 |
| -} |
104 |
| - |
105 |
| -void test_impl(const vector<pair<Graph, int>> &ip, |
106 |
| - const vector<vector<int>> &op, shared_ptr<_00_test> f) |
107 |
| -{ |
108 |
| - for (size_t i = 0; i < ip.size(); i++) { |
109 |
| - vector<int> t = f->shortestPaths(ip[i].first, ip[i].second); |
110 |
| - if (t != op[i]) { |
111 |
| - cerr << f->getName() << " test failed: " |
112 |
| - << "expected " << _vec2str(op[i]) << ", actual " |
113 |
| - << _vec2str(t) << "." << endl; |
114 |
| - exit(1); |
115 |
| - } |
116 |
| - |
117 |
| - if (getenv("SHOW_TEST_OUTPUT")) |
118 |
| - cout << " test-" << i << ": " |
119 |
| - << "input: graph = " << _g2str(ip[i].first) |
120 |
| - << ", source = " << ip[i].second |
121 |
| - << " output: nums = " << _vec2str(t) << "\n"; |
122 |
| - } |
123 |
| -} |
124 |
| - |
125 |
| -int main(int, char **) |
126 |
| -{ |
127 |
| - Graph g1{4, {{2, 1, -10}, {3, 2, 3}, {0, 3, 5}, {0, 1, 4}}}; |
128 |
| - Graph g2{5, |
129 |
| - {{0, 1, -1}, |
130 |
| - {0, 2, 3}, |
131 |
| - {1, 2, 3}, |
132 |
| - {1, 3, 2}, |
133 |
| - {1, 4, 2}, |
134 |
| - {3, 2, 5}, |
135 |
| - {3, 1, 1}, |
136 |
| - {4, 3, -3}}}; |
137 |
| - Graph ng1(g1); |
138 |
| - ng1.second.push_back({1, 3, 5}); // Negative cycle graph |
139 |
| - |
140 |
| - vector<pair<Graph, int>> ip{ |
141 |
| - {g1, 0}, |
142 |
| - {g2, 0}, |
143 |
| - {ng1, 0}, |
144 |
| - }; |
145 |
| - |
146 |
| - vector<vector<int>> op{ |
| 64 | + vi_t _nodes = {4, 5, 5}; |
| 65 | + vi_t _sources = {0, 0, 0}; |
| 66 | + vector<vi2_t> _edges; |
| 67 | + _edges.push_back({{2, 1, -10}, {3, 2, 3}, {0, 3, 5}, {0, 1, 4}}); |
| 68 | + _edges.push_back({{0, 1, -1}, |
| 69 | + {0, 2, 3}, |
| 70 | + {1, 2, 3}, |
| 71 | + {1, 3, 2}, |
| 72 | + {1, 4, 2}, |
| 73 | + {3, 2, 5}, |
| 74 | + {3, 1, 1}, |
| 75 | + {4, 3, -3}}); |
| 76 | + vi2_t nge = _edges[0]; |
| 77 | + nge.push_back({1, 3, 5}); // Negative cycle edge in graph |
| 78 | + _edges.push_back(nge); |
| 79 | + |
| 80 | + vi2_t _distances = { |
147 | 81 | {0, -2, 8, 5},
|
148 | 82 | {0, -1, 2, -2, 1},
|
149 |
| - {INT_MIN}, // Indicate negative cycle is detected in graph |
| 83 | + {NX}, // When graph has negative cycle |
150 | 84 | };
|
151 | 85 |
|
152 |
| - vector<shared_ptr<_00_test>> impls{ |
153 |
| - make_shared<_01_bellman_ford>(), |
154 |
| - }; |
155 |
| - |
156 |
| - for (size_t i = 0; i < impls.size(); i++) { |
157 |
| - if (getenv("SHOW_TEST_OUTPUT")) |
158 |
| - cout << "Testing implementation " << i + 1 << " " |
159 |
| - << impls[i]->getName() << "\n"; |
160 |
| - |
161 |
| - test_impl(ip, op, impls[i]); |
| 86 | + int n = size(_nodes); |
| 87 | + fii (i, n) { |
| 88 | + _bf_check(_nodes[i], _edges[i], _sources[i], _distances[i]); |
162 | 89 | }
|
163 |
| - |
164 |
| - cout << "Executed " << impls.size() << " implementations" |
165 |
| - << " with " << ip.size() << " tests." << endl; |
166 |
| - return 0; |
167 | 90 | }
|
| 91 | + |
| 92 | +INIT_TEST_MAIN(); |
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