HDU 3555 Bomb （数位dp）

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题意:

求1→N含有“49”子串的数字有多少个

分析:

数位dp入门题
考虑反着算
dp[i][s]:=从高到低第i位,前一位是不是4,不含有“49”的数字个数

代码:

////  Created by TaoSama on 2015-10-19//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;typedef long long LL;LL dp[25][2], digit[25];LL dfs(int i, int s, int e) {    if(i == 0) return 1;    if(!e && ~dp[i][s]) return dp[i][s];    LL ret = 0;    int to = e ? digit[i] : 9;    for(int d = 0; d <= to; ++d) {        if(s && d == 9) continue;        ret += dfs(i - 1, d == 4, e && d == to);    }    if(!e) dp[i][s] = ret;    return ret;}LL calc(LL x) {    int cnt = 0;    for(; x; x /= 10) digit[++cnt] = x % 10;    memset(dp, -1, sizeof dp);    return dfs(cnt, 0, 1);}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    int t; scanf("%d", &t);    while(t--) {        LL x; scanf("%I64d", &x);        printf("%I64d\n", x - calc(x) + 1);    }    return 0;}

分析:

考虑正着算
dp[i][s][ok]:=从高到低第i位,前一位是不是4,含不含有“49”,的数字个数

代码:

////  Created by TaoSama on 2015-10-19//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;typedef long long LL;LL dp[25][2][2], digit[25];LL dfs(int i, int s, int ok, int e) {    if(i == 0) return ok;    if(!e && ~dp[i][s][ok]) return dp[i][s][ok];    LL ret = 0;    int to = e ? digit[i] : 9;    for(int d = 0; d <= to; ++d) {        ret += dfs(i - 1, d == 4, ok || (s && d == 9), e && d == to);    }    if(!e) dp[i][s][ok] = ret;    return ret;}LL calc(LL x) {    int cnt = 0;    for(; x; x /= 10) digit[++cnt] = x % 10;    memset(dp, -1, sizeof dp);    return dfs(cnt, 0, 0, 1);}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    int t; scanf("%d", &t);    while(t--) {        LL x; scanf("%I64d", &x);        printf("%I64d\n", calc(x));    }    return 0;}

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