121 lines
3.9 KiB
Rust
121 lines
3.9 KiB
Rust
/*
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* File: min_path_sum.rs
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* Created Time: 2023-07-09
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* Author: codingonion (coderonion@gmail.com)
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*/
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/* Minimum path sum: Brute force search */
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fn min_path_sum_dfs(grid: &Vec<Vec<i32>>, i: i32, j: i32) -> i32 {
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// If it's the top-left cell, terminate the search
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if i == 0 && j == 0 {
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return grid[0][0];
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}
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// If the row or column index is out of bounds, return a +∞ cost
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if i < 0 || j < 0 {
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return i32::MAX;
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}
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// Calculate the minimum path cost from the top-left to (i-1, j) and (i, j-1)
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let up = min_path_sum_dfs(grid, i - 1, j);
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let left = min_path_sum_dfs(grid, i, j - 1);
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// Return the minimum path cost from the top-left to (i, j)
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std::cmp::min(left, up) + grid[i as usize][j as usize]
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}
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/* Minimum path sum: Memoized search */
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fn min_path_sum_dfs_mem(grid: &Vec<Vec<i32>>, mem: &mut Vec<Vec<i32>>, i: i32, j: i32) -> i32 {
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// If it's the top-left cell, terminate the search
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if i == 0 && j == 0 {
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return grid[0][0];
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}
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// If the row or column index is out of bounds, return a +∞ cost
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if i < 0 || j < 0 {
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return i32::MAX;
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}
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// If there is a record, return it
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if mem[i as usize][j as usize] != -1 {
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return mem[i as usize][j as usize];
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}
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// The minimum path cost from the left and top cells
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let up = min_path_sum_dfs_mem(grid, mem, i - 1, j);
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let left = min_path_sum_dfs_mem(grid, mem, i, j - 1);
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// Record and return the minimum path cost from the top-left to (i, j)
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mem[i as usize][j as usize] = std::cmp::min(left, up) + grid[i as usize][j as usize];
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mem[i as usize][j as usize]
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}
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/* Minimum path sum: Dynamic programming */
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fn min_path_sum_dp(grid: &Vec<Vec<i32>>) -> i32 {
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let (n, m) = (grid.len(), grid[0].len());
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// Initialize dp table
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let mut dp = vec![vec![0; m]; n];
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dp[0][0] = grid[0][0];
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// State transition: first row
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for j in 1..m {
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dp[0][j] = dp[0][j - 1] + grid[0][j];
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}
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// State transition: first column
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for i in 1..n {
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dp[i][0] = dp[i - 1][0] + grid[i][0];
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}
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// State transition: the rest of the rows and columns
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for i in 1..n {
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for j in 1..m {
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dp[i][j] = std::cmp::min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
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}
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}
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dp[n - 1][m - 1]
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}
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/* Minimum path sum: Space-optimized dynamic programming */
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fn min_path_sum_dp_comp(grid: &Vec<Vec<i32>>) -> i32 {
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let (n, m) = (grid.len(), grid[0].len());
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// Initialize dp table
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let mut dp = vec![0; m];
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// State transition: first row
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dp[0] = grid[0][0];
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for j in 1..m {
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dp[j] = dp[j - 1] + grid[0][j];
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}
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// State transition: the rest of the rows
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for i in 1..n {
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// State transition: first column
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dp[0] = dp[0] + grid[i][0];
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// State transition: the rest of the columns
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for j in 1..m {
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dp[j] = std::cmp::min(dp[j - 1], dp[j]) + grid[i][j];
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}
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}
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dp[m - 1]
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}
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/* Driver Code */
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pub fn main() {
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let grid = vec![
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vec![1, 3, 1, 5],
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vec![2, 2, 4, 2],
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vec![5, 3, 2, 1],
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vec![4, 3, 5, 2],
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];
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let (n, m) = (grid.len(), grid[0].len());
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// Brute force search
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let res = min_path_sum_dfs(&grid, n as i32 - 1, m as i32 - 1);
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println!("The minimum path sum from the top left corner to the bottom right corner is {res}");
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// Memoized search
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let mut mem = vec![vec![0; m]; n];
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for row in mem.iter_mut() {
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row.fill(-1);
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}
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let res = min_path_sum_dfs_mem(&grid, &mut mem, n as i32 - 1, m as i32 - 1);
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println!("The minimum path sum from the top left corner to the bottom right corner is {res}");
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// Dynamic programming
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let res = min_path_sum_dp(&grid);
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println!("The minimum path sum from the top left corner to the bottom right corner is {res}");
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// Space-optimized dynamic programming
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let res = min_path_sum_dp_comp(&grid);
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println!("The minimum path sum from the top left corner to the bottom right corner is {res}");
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}
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