HDU 4588 Count The Carries（规律）

题目链接：点击打开链接

思路：数电中， 写真值表的时候， 我们是按照一定的规则写的。 按照这个规则， 我们可以知道比一个数小的数中， 每一位有多少个1。  所以， 对于每一位， 进位数就是1的个数除以2加上上一次进位的个数再除以2向下取整。

细节参见代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <stack>
#include <bitset>
#include <cstdlib>
#include <cmath>
#include <set>
#include <list>
#include <deque>
#include <map>
#include <queue>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
using namespace std;
typedef long long ll;
typedef long double ld;
const double eps = 1e-6;
const double PI = acos(-1);
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int seed = 131;
const ll INF64 = ll(1e18);
int n, k;
int a, b;
ll solve(int u, int v) {
    int cur = 2, maxv ;
    int lastjinwei = 0;
    ll ans = 0;
    for(int i = 30; i >= 0; i--) {
        if(v & (1<<i)) {
            maxv = i;
            break;
        }
    }
    for(int i = 0; i <= maxv; i++) {
        int cnt = 0;
        if((v+1)%cur == 0) {
            int dui = (v+1)/cur;
            int _num = (1<<i);
            cnt = dui * _num;
        }
        else {
            int dui = (v+1)/cur;
            int _num = (1<<i);
            cnt = dui * _num;
            int res = (v+1) - dui * cur;
            if(res <= cur/2) ;
            else {
                cnt += res - cur/2;
            }
        }
        int cnt2 = 0;
        if((u+1)%cur == 0) {
            int dui = (u+1)/cur;
            int _num = (1<<i);
            cnt2 = dui*_num;
        }
        else {
            int dui = (u+1)/cur;
            int _num = (1<<i);
            cnt2 = dui * _num;
            int res = (u+1) - dui * cur;
            if(res <= cur/2) ;
            else {
                cnt2 += res - cur/2;
            }
        }
        cnt -= cnt2;
        cnt += lastjinwei;
        ans += cnt/2;
        lastjinwei = cnt/2;
        cur *= 2;
    }
    while(true) {
        ans += lastjinwei/2;
        lastjinwei /= 2;
        if(lastjinwei <= 1) break;
    }
    return ans;
}
int main() {
//    ios::sync_with_stdio(false);
    while(~scanf("%d%d", &a, &b)) {
        printf("%I64d\n", solve(a-1, b));
    }
    return 0;
}