Codeforces 477D Dreamoon and Binary dp

Dreamoon and Binary

先预处理出从i 开始 和 从 j 开始的lcp， 然后直接dp

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 5000 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

char s[N];
int n;
short lcp[N][N];

int dp[N][N];
int sum[N][N];

int ansWay, ansLen = inf;
int bin[N];

int main() {
    for(int i = bin[0] = 1; i < N; i++) bin[i] = 2 * bin[i - 1] % mod;
    scanf("%s", s + 1);
    n = strlen(s + 1);
    for(int i = n; i >= 1; i--) {
        for(int j = n; j > i; j--) {
            if(s[i] == s[j]) lcp[i][j] = 1 + lcp[i + 1][j + 1];
            else lcp[i][j] = 0;
        }
    }
    for(int i = 1; i <= n; i++) {
        dp[i][1] = sum[i][1] = 1;
        for(int j = 2; j <= i; j++) {
            if(s[j] == '1') {
                int len = i - j + 1;
                if(len > 1) dp[i][j] = (dp[i][j] + sum[j - 1][j - 1] - sum[j - 1][max(j - len, 0)] + mod) % mod;
                if(j - len >= 1) {
                    int sameLen = lcp[j - len][j];
                    if(sameLen >= len || s[j + sameLen] >= s[j - len + sameLen])
                        dp[i][j] = (dp[i][j] + dp[j - 1][j - len]) % mod;
                }
            }
            sum[i][j] = (dp[i][j] + sum[i][j - 1]) % mod;
        }
    }
    ansWay = sum[n][n];
    memset(dp, 0x3f, sizeof(dp));
    memset(sum, 0x3f, sizeof(sum));
    for(int i = 1; i <= n; i++) {
        for(int j = i; j >= 2; j--) {
            if(s[j] == '1') {
                int len = i - j + 1;
                if(len > 1) chkmin(dp[i][j], sum[j - 1][min(j - 1, len - 1)] + 1);
                if(j - len >= 1) {
                    int sameLen = lcp[j - len][j];
                    if(sameLen >= len || s[j + sameLen] >= s[j - len + sameLen]) {
                        chkmin(dp[i][j], dp[j - 1][j - len] + 1);
                    }
                }
            }
            sum[i][i - j + 1] = min(sum[i][i - j], dp[i][j]);
        }
        dp[i][1] = 1;
        sum[i][i] = min(sum[i][i - 1], dp[i][1]);
    }
    int now = 0;
    for(int i = 1; i <= n; i++) {
        int p = n - i + 1;
        if(s[p] == '1') now = (now + bin[i - 1]) % mod;
        if(dp[n][p] == inf) continue;
        if(i >= 20) {
            if(ansLen == inf) ansLen = (now + dp[n][p]) % mod;
            break;
        }
        chkmin(ansLen, now + dp[n][p]);
    }
    printf("%d
%d", ansWay, ansLen);
    return 0;
}

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