Play with words

Problem Statement :

Shaka and his brother have created a boring game which is played like this:

They take a word composed of lowercase English letters and try to get the maximum possible score by building exactly 2 palindromic subsequences. The score obtained is the product of the length of these 2 subsequences.

Let's say A and B are two subsequences from the initial string. If Ai & Aj are the smallest and the largest positions (from the initial word) respectively in A; and Bi & Bj are the smallest and the largest positions (from the initial word) respectively in B, then the following statements hold true:
Ai <= Aj,
Bi <= Bj, &
Aj < Bi.
i.e., the positions of the subsequences should not cross over each other.

Hence the score obtained is the product of lengths of subsequences A & B. Such subsequences can be numerous for a larger initial word, and hence it becomes harder to find out the maximum possible score. Can you help Shaka and his brother find this out?

Input Format

Input contains a word S composed of lowercase English letters in a single line.

1 < |S| <= 3000

each character will be a lower case english alphabet.

Output Format

Output the maximum score the boys can get from S.

Solution :


                            Solution in C :

In C++ :

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

char a[3333];
int n;
int f[3033][3033];

int get(int l, int r) {
    if (l > r) return 0;
    if (l == r) {
        f[l][r] = 1;
    if (f[l][r] != 0) {
        return f[l][r];
    f[l][r] = max(get(l + 1, r), get(l, r - 1));
    if (a[l] == a[r]) {
        f[l][r] = max(f[l][r], get(l + 1, r - 1) + 2);
    return f[l][r];

int main() {
    string s;
    cin >> s;
    n = s.size();
    for (int i = 0; i < n; i++) {
        a[i + 1] = s[i];
    int ans = 0;
    for (int i = 1; i < n; i++) {
        ans = max(ans, get(1, i) * get(i + 1, n));
    cout << ans << endl;
    return 0;

In Java :

 * Created by zhengf1 on 12/18/2014.
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Dec101_C {
    public static void main(String[] args){
        Scanner sc = new Scanner(;
        String str = sc.nextLine();
        int n = str.length();
        int[][] L = new int[n][n];
        for (int i = 0; i < n; i++)
            L[i][i] = 1;

        int i = 0;
        int j = 0;
        int cl = 0;
        for (cl=2; cl<=n; cl++)
            for (i=0; i<n-cl+1; i++)
                j = i+cl-1;
                if (str.charAt(i) == str.charAt(j) && cl == 2)
                    L[i][j] = 2;
                else if (str.charAt(i) == str.charAt(j))
                    L[i][j] = L[i+1][j-1] + 2;
                    L[i][j] = Math.max(L[i][j - 1], L[i + 1][j]);
        int res = 0;
        for(i = 1; i < n; i++){
            int v1 = L[0][i - 1];
            int v2 = L[i][n - 1];
            res = Math.max(res, v1 * v2);


In C :

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int L[3100][3100],cntt[30][3100];

int max(int a,int b)
        return b;
    return a;

int main() {
    char str[4000],c;
    int i,j,t,l,cl;
    for (cl=2; cl<=l; cl++)
        for (i=0; i<l-cl+1; i++)
            j = i+cl-1;
            if (str[i] == str[j] && cl == 2)
               L[i][j] = 2;
            else if (str[i] == str[j])
               L[i][j] = L[i+1][j-1] + 2;
               L[i][j] = max(L[i][j-1], L[i+1][j]);
    int mx=0;
    return 0;

In Python3 :

s = input()
p = [[0] * len(s) for _ in range(len(s))]
for i in range(len(s)): p[i][i] = 1
for k in range(2, len(s) + 1):
    for i in range(len(s) - k + 1):
        j = i + k - 1
        if s[i] == s[j]:
            p[i][j] = 2 + (0 if k == 2 else p[i + 1][j - 1])
            p[i][j] = max(p[i][j - 1], p[i + 1][j])
print(max(p[0][i] * p[i + 1][-1] for i in range(len(s) - 1)))

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