Introduction-To-Algorithms-Cpp-code/docs/ch15/15_2.cpp at master · EeeUnS/Introduction-To-Algorithms-Cpp-code · GitHub

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
#include <iostream>
#include<vector>

typedef std::pair<std::vector<std::vector<int>>,std::vector<std::vector<int>>> Set;


Set MATRIX_CHAIN_ORDER(const std::vector<int> &p)
{
	const int INF = 1000000000;
	const int n = p.size()-1;
	std::vector<std::vector<int>> m(n+1, std::vector<int>(n+1, 0));
	std::vector<std::vector<int>> s(n+1, std::vector<int>(n+1, 0));
	for (int l = 2; l <= n; l++)
	{
		for (int i = 1; i <= n - l + 1; i++)
		{
			int j = i + l - 1;
			m[i][j] = INF;
			for (int k = i; k <= j - 1; k++)
			{
				int  q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
				if (q < m[i][j])
				{

					m[i][j] = q;
					s[i][j] = k;
				}
			}
		}
	}
	return std::make_pair(m, s);
}


void PRINT_OPTIMAL_PARENS(const std::vector<std::vector<int>> &s, int i, int j)
{
	if (i == j)
	{
		std::cout << "A" << i;
	}
	else
	{
		std::cout << '(';
		PRINT_OPTIMAL_PARENS(s, i, s[i][j]);
		PRINT_OPTIMAL_PARENS(s, s[i][j] + 1, j);
		std::cout << ')';
	}
}


int RECURSIVE_MATRIX_CHAIN(const std::vector<int> &p, int i, int j)
{
	const int INF = 1000000000;
	const int n = p.size() -1 ;
	std::vector<std::vector<int>> m(n+1, std::vector<int>(n+1, 0));
	if (i == j)
	{
		return 0;
	}
	m[i][j] = INF;
	for (int k = i; k <= j - 1; k++)
	{
		int q = RECURSIVE_MATRIX_CHAIN(p, i, k) +
			RECURSIVE_MATRIX_CHAIN(p, k + 1, j) + p[i - 1] * p[k] * p[j];

		if (q < m[i][j])
		{
			m[i][j] = q;
		}
	}
	return m[i][j];
}

int LOOKUP_CHAIN(std::vector<std::vector<int>> &m,const std::vector<int> &p,int i,int j)
{
	const int INF = 1000000000;

	if (m[i][j] < INF)
	{
		return m[i][j];
	}
	if (i == j)
	{
		m[i][j] = 0;
	}
	else for (int k = i ; k <= j - 1; k++)
	{
		int q = LOOKUP_CHAIN(m, p, i, k)
			+ LOOKUP_CHAIN(m, p, k + 1, j) + p[i - 1] * p[k] * p[j];
		if (q < m[i][j])
		{
			m[i][j] = q;
		}
	}
	return m[i][j];
}


int MEMORIZED_MATRIX_CHAIN(const std::vector<int> &p)
{
	const int INF = 1000000000;
	const int n = p.size() - 1;
	std::vector<std::vector<int>> m(n+1, std::vector<int>(n+1, 0));
	for (int i = 1; i <= n; i++)
	{

		for (int j = 1; j <= n; j++)
		{
			m[i][j] = INF;
		}
	}
	return LOOKUP_CHAIN(m, p, 1, n);
}

std::vector<int> p = {30,35,15,5,10,20,25};


int main()
{
	Set ms = MATRIX_CHAIN_ORDER(p);// m, s
	std::cout << RECURSIVE_MATRIX_CHAIN(p, 1, 6) << std::endl;
	std::cout <<  MEMORIZED_MATRIX_CHAIN(p) << std::endl;


	//PRINT_OPTIMAL_PARENS(ms.second, 1, 6);


	return 0;
}