65 lines
2.1 KiB
C++
65 lines
2.1 KiB
C++
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#include<stdio.h>
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#include<limits.h>
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#include<iostream>
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using namespace std;
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// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
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int MatrixChainOrder(int p[], int n)
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{
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/* For simplicity of the program, one extra row and one extra column are
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allocated in m[][]. 0th row and 0th column of m[][] are not used */
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int m[n][n];
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int s[n][n];
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int i, j, k, L, q;
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/* m[i,j] = Minimum number of scalar multiplications needed to compute
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the matrix A[i]A[i+1]...A[j] = A[i..j] where dimention of A[i] is
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p[i-1] x p[i] */
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// cost is zero when multiplying one matrix.
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for (i = 1; i < n; i++)
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m[i][i] = 0;
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// L is chain length.
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for (L = 2; L < n; L++)
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{
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for (i = 1; i <= n - L + 1; i++)
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{
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j = i + L - 1;
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m[i][j] = INT_MAX;
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for (k = i; k <= j - 1; k++)
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{
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// q = cost/scalar multiplications
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q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
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if (q < m[i][j])
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{
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m[i][j] = q;
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s[i][j] = k;
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}
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}
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}
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}
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return m[1][n - 1];
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}
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int main()
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{
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cout
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<< "Enter the array p[], which represents the chain of matrices such that the ith matrix Ai is of dimension p[i-1] x p[i]";
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cout << "Enter the total length:";
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int n;
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cin >> n;
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int array[n];
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cout << "Enter the dimensions: ";
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for (int var = 0; var < n; ++var)
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{
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cin >> array[var];
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}
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cout << "Minimum number of multiplications is: " << MatrixChainOrder(array,
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n);
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return 0;
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}
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/*
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Enter the array p[], which represents the chain of matrices such that the ith matrix Ai is of dimension p[i-1] x p[i]Enter the total length:4
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Enter the dimensions: 2 4 3 5
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Minimum number of multiplications is: 54
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