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HDU 3709 Balanced Number (数位DP)
题意:找出区间内平衡数的个数,所谓的平衡数,就是以这个数字的某一位为支点,另外两边的数字大小乘以力矩之和相等,即为平衡数。
析:数位DP,dp[i][[j][k]表示 前 i 位以 j 为支点,还差 k 平衡,枚举 j 就好。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000")#include <cstdio>#include <string>#include <cstdlib>#include <cmath>#include <iostream>#include <cstring>#include <set>#include <queue>#include <algorithm>#include <vector>#include <map>#include <cctype>#include <cmath>#include <stack>#define freopenr freopen("in.txt", "r", stdin)#define freopenw freopen("out.txt", "w", stdout)using namespace std;typedef long long LL;typedef pair<int, int> P;const int INF = 0x3f3f3f3f;const double inf = 0x3f3f3f3f3f3f;const double PI = acos(-1.0);const double eps = 1e-8;const int maxn = 1e5 + 5;const int mod = 1e9 + 7;const int dr[] = {-1, 0, 1, 0};const int dc[] = {0, 1, 0, -1};const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};int n, m;const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};inline int Min(int a, int b){ return a < b ? a : b; }inline int Max(int a, int b){ return a > b ? a : b; }inline LL Min(LL a, LL b){ return a < b ? a : b; }inline LL Max(LL a, LL b){ return a > b ? a : b; }inline bool is_in(int r, int c){ return r >= 0 && r < n && c >= 0 && c < m;}LL dp[20][20][1500];int a[20];LL dfs(int pos, int dot, int balance, bool ok){ if(!pos) return balance == 0; if(balance < 0) return 0; LL &ans = dp[pos][dot][balance]; if(!ok && ans >= 0) return ans; LL res = 0; int n = ok ? a[pos] : 9; for(int i = 0; i <= n; ++i){ res += dfs(pos-1, dot, balance+(pos-dot)*i, ok && i == n); } if(!ok) ans = res; return res;}LL solve(LL n){ int len = 0; while(n){ a[++len] = n % 10; n /= 10; } LL ans = 0; for(int i = 1; i <= len; ++i) ans += dfs(len, i, 0, true); return ans - len;//除去全是0的情况}int main(){ memset(dp, -1, sizeof dp); LL x, y; int T; cin >> T; while(T--){ scanf("%lld %lld", &x, &y); printf("%lld\n", solve(y)-solve(x-1)); } return 0;}
HDU 3709 Balanced Number (数位DP)
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