Algorithms: Dynamic Programming Tutorials and Code Examples - Page 13

Levenshtein Edit Distance in JavaScript

Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed to turn one token sequence into another..

javascript

function edit_distance(a, b) {
    alg_require(a instanceof Int32Array);
    alg_require(b instanceof Int32Array);
    let n = a.length;
    let m = b.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((a.length == n));
    alg_require((b.length == m));
    if (n < m) return edit_distance(b, a);
    let dp = new Int32Array(alg_size(alg_add(m, 1)));
    let i = 0;

Nov 15, 2026 javascript

Algorithms: Dynamic Programming

Levenshtein Edit Distance in Java

Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed to turn one token sequence into another..

java

    static int edit_distance(int[] a, int[] b) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(b, "b");
        int n = a.length;
        int m = b.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((m >= 0) && (m <= 1000000)));
        alg_require((a.length == n));
        alg_require((b.length == m));
        if (n < m) return edit_distance(b, a);
        int[] dp = new int[alg_size(Math.addExact(m, 1))];
        int i = 0;

Nov 15, 2026 Java

Algorithms: Dynamic Programming

Minimum Coin Change in PHP

Minimum coin change finds the fewest coins needed to make an exact amount when each denomination can be reused.

php

function minimum_coins(array $coins, int $amount): int {
    alg_require(array_is_list($coins));
    $m = count($coins);
    alg_require((($m >= 0) && ($m <= 1000000)));
    alg_require((count($coins) == $m));
    alg_require((($amount >= 0) && ($amount <= 1000000)));
    for ($alg_i = 0; $alg_i < count($coins); $alg_i++) {
        $alg_value = $coins[$alg_i];
        alg_require(($alg_value > 0));
    }
    $dp = array_fill(0, alg_size(alg_add($amount, 1)), 0);
    $x = 1;

Nov 15, 2026 PHP

Algorithms: Dynamic Programming

Levenshtein Edit Distance in C++

Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed to turn one token sequence into another..

cpp

int edit_distance(const std::vector<int>& a, const std::vector<int>& b) {
    alg_require(a.size() <= 1000000);
    alg_require(b.size() <= 1000000);
    int n = (int)a.size();
    int m = (int)b.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((int)b.size() == m));
    if (n < m) return edit_distance(b, a);
    std::vector<int> dp(alg_size(alg_add(m, 1)), 0);
    int i = 0;

Nov 15, 2026 C++

Algorithms: Dynamic Programming

Levenshtein Edit Distance in C#

Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed to turn one token sequence into another..

csharp

    static int edit_distance(ReadOnlySpan<int> a, ReadOnlySpan<int> b) {
        checked {
            int n = a.Length;
            int m = b.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((m >= 0) && (m <= 1000000)));
            alg_require((a.Length == n));
            alg_require((b.Length == m));
            if (n < m) return edit_distance(b, a);
            int[] dp = new int[alg_size((m + 1))];
            int i = 0;
            int j = 0;

Nov 15, 2026 csharp