-
Notifications
You must be signed in to change notification settings - Fork 0
/
Chap17.cpp
214 lines (202 loc) · 5.48 KB
/
Chap17.cpp
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
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
#include <vector>
#include <iostream>
#include <string>
#include <algorithm>
#include <unordered_set>
using namespace std;
int GetScoreCombinationNumber(const vector<int> &w, int score)
{
vector<int> NbComb(score + 1, 0);
NbComb[0] = 1;
for (int i = 0; i <= score; ++i)
{
for (int j = 0; j < w.size(); ++j)
{
if (i >= w[j])
NbComb[i] += NbComb[i - w[j]];
}
}
return NbComb[score];
}
void Prob17_1D()
{
vector<int> w; w.push_back(2); w.push_back(3); w.push_back(7);
unsigned int score = 12;
cout << GetScoreCombinationNumber(w,score)<< " possible combinations to reach " << score << endl;
}
int EditCost(const string &a, const string &b)
{
vector<vector<int> > edit_costs(a.size() + 1, vector<int>(b.size() + 1, 0));
for (int i = 0; i < b.size() + 1; ++i)
edit_costs[0][i] = i;
for (int i = 0; i < a.size() + 1; ++i)
edit_costs[i][0] = i;
for (int i = 1; i <= a.size(); ++i)
{
for (int j = 1; j <= b.size(); ++j)
{
int swapCost = (a[i-1] == b[j-1] ? edit_costs[i - 1][j - 1] : edit_costs[i - 1][j - 1] + 1);
int InsertCost = 1 + edit_costs[i][j - 1];
int DeleteCost = 1 + edit_costs[i - 1][j];
edit_costs[i][j] = min(swapCost, min(InsertCost, DeleteCost));
}
}
/*
for (int i = 0; i <= a.size(); ++i)
{
for (int j = 0; j <= b.size(); ++j)
{
cout << edit_costs[i][j];
}
cout << endl;
}*/
return edit_costs[a.size() ][b.size() ];
}
void Prob17_2D()
{
string a = "meilenstein";
string b = "levenshtein";
cout << "Edit distance " << a << "->" << b << " = " << EditCost(a, b);
}
int GetMazeTraversalCounts(unsigned int n, unsigned int m)
{
vector<vector<int> > counts(n+1, vector<int>(m+1, 0));
for (unsigned int i = 0; i <= m ; ++i)
counts[0][i] = 0;
for (unsigned int i = 0; i <= n; ++i)
counts[i][0] = 0;
counts[1][1] = 0;
for (unsigned int i = 1; i <= n; ++i)
{
for (unsigned int j = 1; j <= m; ++j)
{
counts[i][j] = counts[i - 1][j] + counts[i][j - 1] ;
}
}
return counts[n][m];
}
void Prob17_4D()
{
unsigned int n = 3;
unsigned int m = 3;
cout << "In a "<<n<<"x"<<m<<" maze, the nb of valid paths is:"<<GetMazeTraversalCounts(n, m)<<endl;
}
bool IsAConcatenation(string url,const unordered_set<string> &dic){
vector<bool> validPrefix(url.size()+1,false);
validPrefix[0]=true;
for (unsigned int i=1; i<=url.size(); ++i)
{
for(unsigned int j=0;j<=i;++j)
{
if((validPrefix[j] && dic.find(url.substr(j,i-j))!=dic.end() ))
{
validPrefix[i]=true;
break;
}
}
}
return validPrefix[url.size()];
}
void Prob17_12D(){
unordered_set<string> dic;
dic.emplace("beyond"); dic.emplace("hand"); dic.emplace("and"); dic.emplace("bed"); dic.emplace("bath");
string url="bedbathandbeyond";
cout<<IsAConcatenation(url, dic);
}
pair<int,int> KadaneMaxSubArraySum(vector<int> v,int start_i,int end_i)
{
int max_so_far_i = 0, total_max_i = 0, idx_max_i = 0;
for (int i = start_i; i <= end_i; ++i)
{
max_so_far_i = max(0, max_so_far_i + v[i]);
if (max_so_far_i>total_max_i)
{
total_max_i = max_so_far_i;
idx_max_i = i;
}
}
return make_pair(idx_max_i,total_max_i);
}
int Prob17_11(vector<int> v)
{
vector<int> WrappedSubsums(v.size(),0);
pair<int, int> max_starting_here_i, max_ending_here_i;
int global_max_i = 0;
for (int i = 0; i < v.size(); ++i)
{
max_ending_here_i = KadaneMaxSubArraySum(v, 0, i);
max_starting_here_i = KadaneMaxSubArraySum(v, i + 1, v.size() - 1);
WrappedSubsums[i] = max_ending_here_i.second + (max_starting_here_i.first == v.size() - 1 ? max_starting_here_i.second:0);
global_max_i = max(global_max_i, WrappedSubsums[i]);
}
return global_max_i;
}
void Prob17_11D()
{
vector<int> v;
//v.push_back(904); v.push_back(40); v.push_back(523); v.push_back(12); v.push_back(-335); v.push_back(-385); v.push_back(-124); v.push_back(481); v.push_back(-31);
v.push_back(10); v.push_back(-4); v.push_back(5); v.push_back(-4); v.push_back(10);
cout <<"Max subset sum in circular array:"<< Prob17_11(v)<<endl;
}
int Prob17_12(const vector<int> &A)
{
int global_max_i = 1;
vector<int> len(A.size(), 0);
len[0] = 1;
for (int i = 1; i < A.size(); ++i)
{
for (int j = 0; j < i; ++j)
{
if (A[i]>=A[j])
{
len[i] = max(len[i], len[j] + 1);
global_max_i = max(global_max_i, len[i]);
}
}
}
return global_max_i;
}
void Prob17_21D()
{
vector<int> A;
A.push_back(0); A.push_back(8); A.push_back(4); A.push_back(12); A.push_back(2); A.push_back(10); A.push_back(6); A.push_back(14); A.push_back(1); A.push_back(9);
cout << "longest Nondecreasing seq has length " << Prob17_12(A) << endl;
}
int Prob17_12(const vector<int> &v, const vector<int> &w,int max_capacity_i)
{
vector<vector<int> > maxBenef(v.size()+1, vector<int>(max_capacity_i+1, 0));
for (int i = 1; i <= v.size(); ++i)
{
for (int j = 1; j <= max_capacity_i; ++j)
{
if (j >= w[i - 1])
{
maxBenef[i][j] = max(maxBenef[i - 1][j], maxBenef[i-1][j - w[i - 1]] + v[i - 1]);
}
else
maxBenef[i][j] =maxBenef[i - 1][j];
}
}
/*for (int i = 1; i <= v.size(); ++i)
{
for (int j = 1; j <= max_capacity_i; ++j)
{
cout << maxBenef[i][j]<<" ";
}
cout << endl;
}*/
return maxBenef[v.size()][max_capacity_i];
}
void Prob17_7D()
{
vector<int> v,w;
v.push_back(4); v.push_back(2); v.push_back(2); v.push_back(1); v.push_back(10);
w.push_back(12); w.push_back(1); w.push_back(2); w.push_back(1); w.push_back(4);
cout<< "max value is "<<Prob17_12(v, w, 15)<<endl;
}
int main(int argc, char** argv)
{
Prob17_1D();
getchar();
return 0;
}