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https://github.com/TheAlgorithms/C-Plus-Plus.git
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87 lines
2.6 KiB
C++
87 lines
2.6 KiB
C++
/**
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* @file cut_rod.cpp
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* @brief Implementation of cutting a rod problem
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*
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* @details
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* Given a rod of length n inches and an array of prices that
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* contains prices of all pieces of size<=n. Determine
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* the maximum profit obtainable by cutting up the rod and selling
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* the pieces.
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*
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* @author [Anmol](https://github.com/Anmol3299)
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* @author [Pardeep](https://github.com/Pardeep009)
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*
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*/
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#include <array>
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#include <cassert>
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#include <climits>
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#include <iostream>
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template <size_t T>
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/**
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* This function cuts the rod in different pieces and stores the maximum profit
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* for each piece of the rod.
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* @param n size of the rod in inches
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* @param price an array of prices that contains prices of all pieces of size<=n
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* @return maximum profit obtainable for @param n inch rod.
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*/
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int cut_rod(const std::array<int, T> &price, const int n) {
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// profit[i] will hold maximum profit for i inch rod
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int *profit = new int[n + 1];
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// if length of rod is zero, then no profit
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profit[0] = 0;
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// outer loop will select size of rod, starting from 1 inch to n inch rod.
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// inner loop will evaluate the maximum profit we can get for i inch rod by
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// making every possible cut on it and will store it in profit[i].
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for (size_t i = 1; i <= n; i++) {
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int q = INT_MIN;
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for (size_t j = 1; j <= i; j++) {
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q = std::max(q, price[j - 1] + profit[i - j]);
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}
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profit[i] = q;
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}
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int ans = profit[n];
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delete[] profit;
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return ans; /** return maximum profit obtainable for @param n inch rod */
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}
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/**
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* Function to test above algorithm
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*/
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void test() {
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// Test 1
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const int n1 = 8; // size of rod
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std::array<int, n1> price1 = {1, 5, 8, 9, 10, 17, 17, 20}; // price array
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const int max_profit1 = cut_rod(price1, n1);
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const int expected_max_profit1 = 22;
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assert(max_profit1 == expected_max_profit1);
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std::cout << "Maximum profit with " << n1 << " inch road is " << max_profit1
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<< std::endl;
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// Test 2
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const int n2 = 30; // size of rod
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std::array<int, n2> price2 = {
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1, 5, 8, 9, 10, 17, 17, 20, 24, 30, // price array
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31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
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41, 42, 43, 44, 45, 46, 47, 48, 49, 50};
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const int max_profit2 = cut_rod(price2, n2);
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const int expected_max_profit2 = 90;
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assert(max_profit2 == expected_max_profit2);
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std::cout << "Maximum profit with " << n2 << " inch road is " << max_profit2
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<< std::endl;
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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// Testing
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test();
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return 0;
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}
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