Algorithms: Dynamic Programming

int palindromic_subsequence(const std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    std::vector<int> dp(alg_size(alg_add(n, 1)), 0);
    int left = alg_sub(n, 1);
    int right = 0;
    int diagonal = 0;
    int old = 0;
    while ((left >= 0)) {
        dp[left] = 1;

    static int palindromic_subsequence(ReadOnlySpan<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int[] dp = new int[alg_size((n + 1))];
            int left = (n - 1);
            int right = 0;
            int diagonal = 0;
            int old = 0;
            while ((left >= 0)) {
                dp[left] = 1;

function palindromic_subsequence(array $a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $dp = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $left = alg_sub($n, 1);
    $right = 0;
    $diagonal = 0;
    $old = 0;
    while (($left >= 0)) {
        $dp[$left] = 1;

    static int matrix_chain(int[] dimensions) {
        java.util.Objects.requireNonNull(dimensions, "dimensions");
        int n = Math.subtractExact(dimensions.length, 1);
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((dimensions.length == Math.addExact(n, 1)));
        alg_require((n >= 1));
        for (int alg_i = 0; alg_i < dimensions.length; alg_i++) {
            int alg_value = dimensions[alg_i];
            alg_require(((alg_value > 0) && (alg_value <= 1000)));
        }
        int[] dp = new int[alg_size(Math.multiplyExact(n, n))];
        int length = 2;

function matrix_chain(dimensions) {
    alg_require(dimensions instanceof Int32Array);
    let n = alg_sub(dimensions.length, 1);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((dimensions.length == alg_add(n, 1)));
    alg_require((n >= 1));
    for (let alg_i = 0; alg_i < dimensions.length; alg_i++) {
        let alg_value = dimensions[alg_i];
        alg_require(((alg_value > 0) && (alg_value <= 1000)));
    }
    let dp = new Int32Array(alg_size(alg_mul(n, n)));
    let length = 2;