Adding dynamic programming solution for unique paths problem #2992

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singhsayan wants to merge 8 commits into TheAlgorithms:master

from singhsayan:feat/grid_unique_path

Open

Adding dynamic programming solution for unique paths problem #2992

singhsayan wants to merge 8 commits into TheAlgorithms:master from singhsayan:feat/grid_unique_path

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singhsayan

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@singhsayan singhsayan commented Sep 2, 2025

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

@singhsayan


 Adding dynamic programming solution for unique paths problem

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@singhsayan singhsayan requested review from Panquesito7 and realstealthninja as code owners

September 2, 2025 04:41

@singhsayan


 Update unique_paths.cpp

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singhsayan commented Sep 2, 2025

Hi @Panquesito7 @realstealthninja
I’ve added the Unique Paths solution with both memoization and tabulation, including self-tests. Could you please review when you get a chance? Thanks!

realstealthninja

realstealthninja requested changes

Sep 4, 2025

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dynamic_programming/unique_paths.cpp Outdated

#include <iostream>

#include <vector>

#include <cassert>

using namespace std;

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Suggested change

using namespace std;

dynamic_programming/unique_paths.cpp Outdated

* @namespace dp

* @brief Dynamic Programming algorithms

namespace dp {

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Suggested change

namespace dp {

namespace dynamic_programming {

dynamic_programming/unique_paths.cpp Outdated

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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Suggested change

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 Outdated

* @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 Outdated

* @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 Outdated

* @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()

@singhsayan


 Refactor Unique Paths as requested in code review

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singhsayan commented Sep 4, 2025

Hi @realstealthninja, I've made the requested changes. Could you please review again ? Thanks !

singhsayan added 2 commits

September 4, 2025 08:54

@singhsayan


 Update unique_paths.cpp

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 Updated code

548c500

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Sep 4, 2025

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dynamic_programming/unique_paths.cpp

* 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 Outdated

/**

* @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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 Updated_code

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singhsayan commented Sep 4, 2025

@realstealthninja Could you please review the latest changes and let me know if everything looks fine? Thanks for your time!

realstealthninja

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Sep 5, 2025

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dynamic_programming/unique_paths.cpp Outdated

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 Outdated

/**

* @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

singhsayan added 2 commits

September 5, 2025 15:48

@singhsayan


 Merge branch 'master' into feat/grid_unique_path

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 Update unique_paths.cpp

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singhsayan commented Sep 5, 2025

@realstealthninja Done

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@singhsayan singhsayan commented Sep 2, 2025

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singhsayan commented Sep 4, 2025

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singhsayan commented Sep 4, 2025

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singhsayan commented Sep 5, 2025

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