ZOJ3816-Generalized palindromic number (DFS digital search)

Generalized palindromic number Time Limit: 2 seconds memory limit: 65536 KB

A number that will be the same when it is written forwards or backwards is known as a palindromic number. For example, 1234321 is a palindromic number.

We call a numberGeneralized palindromic number, If after merging all the consecutive same digits, the resulting number is a palindromic number. for example, 122111 is a generalized palindromic number. because after merging, 122111 turns into 121 which is a palindromic number.

Now you are given a positive integerN, Please find the largest generalized palindromic number lessN.

Input

There are multiple test cases. The first line of input contains an integerT(About 5000) indicating the number of test cases. For each test case:

There is only one integerN(1 <=N<= 1018 ).

Output

For each test case, output the largest generalized palindromic number lessN.

Sample Input

41212312241122

Sample output

1112112211121

Question: 1 ~ The largest number in the N-1 (This number is compressed into a text string) idea: using the digital DP idea, enumerate each bit, both the left and right enumeration, from large to small enumeration.

#include <iostream>#include <cstdio>#include <cstring>#include <vector>#include <algorithm>using namespace std;typedef long long LL;const int maxn = 20;int lft[maxn],rgt[maxn];vector<int> digit;LL n,ans;int len;LL getS(int L,int R) {LL ret = 0;for(int i = 0; i < L; i++){ret *= 10;ret += lft[i];}for(int i = R; i >= 1; i--) {ret *= 10;ret += rgt[i];}return ret;}LL dfs(int L,int R,bool done) {    if(L+R == len) {        LL tmp = getS(L,R);        if(tmp <= n-1) return tmp;        else return 0;    }int end = done?digit[L]:9;LL ans = 0;for(int i = end; i >= 0; i--) {lft[L] = i;if(L+R!=len-1&&(L==0||(L>=1&&lft[L]!=lft[L-1]))&&(L!=0||i!=0)){            for(int k = 1; L+R+k <= len-1; k++) {                rgt[k+R] = i;                ans = max(dfs(L+1,R+k,done&&i==end),ans);            }}else{    ans = max(dfs(L+1,R,done&&i==end),ans);}if(ans != 0) return ans;}return 0;}void init() {ans = 0;digit.clear();scanf("%lld",&n);LL x = n;--x;while(x) {digit.push_back(x%10);x /= 10;}len = digit.size();reverse(digit.begin(),digit.end());}void solve() {    ans = dfs(0,0,true);    printf("%lld\n",ans);}int main() {int ncase;cin >> ncase;while(ncase--) {init();solve();}return 0;}

ZOJ3816-Generalized palindromic number (DFS digital search)