Adding dynamic programming solution for unique paths problem #2992
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singhsayan
requested review from
Panquesito7 and
realstealthninja
as code owners
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Hi @Panquesito7 @realstealthninja |
dynamic_programming/unique_paths.cpp
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| #include <iostream> | ||
| #include <vector> | ||
| #include <cassert> | ||
| using namespace std; |
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| using namespace std; |
dynamic_programming/unique_paths.cpp
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| * @namespace dp | ||
| * @brief Dynamic Programming algorithms | ||
| */ | ||
| namespace dp { |
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| namespace dp { | |
| namespace dynamic_programming { |
dynamic_programming/unique_paths.cpp
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| if (i >= m || j >= n) return 0; | ||
| if (i == m - 1 && j == n - 1) return 1; | ||
| if (dp[i][j] != -1) return dp[i][j]; | ||
| dp[i][j] = solveMem(i + 1, j, m, n, dp) + solveMem(i, j + 1, m, n, dp); |
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| dp[i][j] = solveMem(i + 1, j, m, n, dp) + solveMem(i, j + 1, m, n, dp); | |
| dp.at(i).at(j) = solveMem(i + 1, j, m, n, dp) + solveMem(i, j + 1, m, n, dp); |
dynamic_programming/unique_paths.cpp
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| * @param dp Memoization table | ||
| * @return int Number of unique paths from (i, j) to (m-1, n-1) | ||
| */ | ||
| int solveMem(int i, int j, int m, int n, vector<vector<int>> &dp) { |
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this is bad design, the user should not have to worry about supplying a memoization table, This is design details that should be handled internally
dynamic_programming/unique_paths.cpp
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| * @brief Self-test implementations | ||
| */ | ||
| static void test() { | ||
| assert(dp::uniquePaths(3, 7) == 28); |
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these tests only test the tabular form and not the memoized form
dynamic_programming/unique_paths.cpp
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| * @return int Total number of unique paths | ||
| */ | ||
| int uniquePaths(int m, int n) { | ||
| vector<vector<int>> dp(m + 1, vector<int>(n + 1, -1)); |
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Maybe this should be turned into a class? with a private member of dp, and multiple behaviours, solvetabular() or solvememoised()
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Hi @realstealthninja, I've made the requested changes. Could you please review again ? Thanks ! |
| * Dynamic Programming (Memoization + Tabulation). | ||
| * @details | ||
| * A robot is located at the top-left corner of an m x n grid. | ||
| * The robot can move either down or right at any point in time. |
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could add a brief comparison between memoization and tabulation?
dynamic_programming/unique_paths.cpp
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| /** | ||
| * @brief Get number of unique paths using Memoization | ||
| */ | ||
| int uniquePathsMemo() { return solveMem(0, 0); } |
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oslve mem isnt used anywhere why not replace the uniqupath memo function definitino with the one with solvemem and remove solvemem entirely?
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@realstealthninja Could you please review the latest changes and let me know if everything looks fine? Thanks for your time! |
dynamic_programming/unique_paths.cpp
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| */ | ||
| class UniquePathsSolver { | ||
| private: | ||
| std::vector<std::vector<int>> dp; ///< Memoization table |
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this variable name is too short, its nondescript/confusing. maybe rename it to memoization_table or something similar
dynamic_programming/unique_paths.cpp
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| /** | ||
| * @brief Get number of unique paths using Tabulation (Bottom-Up) | ||
| */ | ||
| int uniquePathsTab() { return solveTab(); } |
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you could do the same thing for this function as well
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@realstealthninja Done |
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Hi @realstealthninja, can you take a quick look at my PR and merge if it looks fine? |
Added Unique Paths algorithm using Dynamic Programming (unique_paths.cpp) with both memoization and tabulation approaches. Includes self-tests with assert().
Type of Change
• New feature
Tests
• Verified with multiple test cases (3x7, 3x2, 1x1, 2x2)
• All tests passed
Checklist
• Code compiles locally
• Tests included and passing
• Naming conventions followed
• Doxygen-style comments added