• uva 1478


    题目链接:uva 1478 - Delta Wave

    题目大意:对于每一个位置来说,能够向上,水平,向下。坐标不能位负。每次上下移动最多为1。 给定n问说有多少种不同的图。结果对10100取模。

    解题思路:由于最后都要落回y=0的位置,所以上升的次数和下降的次数是同样的,而且上升下降的关系满足出栈入栈的关系。即卡特兰数。


    所以每次枚举i,表示有i个上升,i个下降,用组合数学枚举出位置,然后累加求和。

    C(2in)f(i)=C(2i2n)f(i1)(n2i+1)(n2i+2)i(i+1)
    注意取模后的前导0

    #include <cstdio>
    #include <cstring>
    #include <iostream>
    
    using namespace std;
    typedef long long  type;
    const int MAXN = 10005;
    
    struct bign {
        int len, num[MAXN];
    
        bign () {
            len = 0;
            memset(num, 0, sizeof(num));
        }
        bign (int number) {*this = number;}
        bign (const char* number) {*this = number;}
    
        void DelZero ();
        void Put ();
    
        void operator = (int number);
        void operator = (char* number);
    
        bool operator <  (const bign& b) const;
        bool operator >  (const bign& b) const { return b < *this; }
        bool operator <= (const bign& b) const { return !(b < *this); }
        bool operator >= (const bign& b) const { return !(*this < b); }
        bool operator != (const bign& b) const { return b < *this || *this < b;}
        bool operator == (const bign& b) const { return !(b != *this); }
    
        void operator ++ ();
        void operator -- ();
        bign operator + (const type& b);
        bign operator + (const bign& b);
        bign operator - (const type& b);
        bign operator - (const bign& b);
        bign operator * (const type& b);
        bign operator * (const bign& b);
        bign operator / (const type& b);
        //bign operator / (const bign& b);
        int operator % (const int& b);
    };
    
    /*Code*/
    int main () {
        int n;
        while (scanf("%d", &n) == 1) {
            bign ans = 0;
            bign tmp = 1;
            ans = ans + tmp;
            for (int i = 1; i <= n/2; i++) {
                tmp = tmp * 1LL * (n - 2 * i + 2) * (n - 2 * i + 1);
                tmp = tmp / (1LL * i * (i + 1));;
                ans = ans + tmp;
                ans.len = min(ans.len, 100);
            }
            ans.Put();
            printf("
    ");
        }
    }
    
    void bign::DelZero () {
        while (len && num[len-1] == 0)
            len--;
    
        if (len == 0)
            num[len++] = 0;
    }
    
    void bign::Put () {
        bool flag = false;
        for (int i = len-1; i >= 0; i--) {
            if (num[i] || flag) {
                printf("%d", num[i]);
                flag = true;
            }
        }
    }
    
    void bign::operator = (char* number) {
        len = strlen (number);
        for (int i = 0; i < len; i++)
            num[i] = number[len-i-1] - '0';
    
        DelZero ();
    }
    
    void bign::operator = (int number) {
    
        len = 0;
        while (number) {
            num[len++] = number%10;
            number /= 10;
        }
    
        DelZero ();
    }
    
    bool bign::operator < (const bign& b) const {
        if (len != b.len)
            return len < b.len;
        for (int i = len-1; i >= 0; i--)
            if (num[i] != b.num[i])
                return num[i] < b.num[i];
        return false;
    }
    
    void bign::operator ++ () {
        int s = 1;
    
        for (int i = 0; i < len; i++) {
            s = s + num[i];
            num[i] = s % 10;
            s /= 10;
            if (!s) break;
        }
    
        while (s) {
            num[len++] = s%10;
            s /= 10;
        }
    }
    
    void bign::operator -- () {
        if (num[0] == 0 && len == 1) return;
    
        int s = -1;
        for (int i = 0; i < len; i++) {
            s = s + num[i];
            num[i] = (s + 10) % 10;
            if (s >= 0) break;
        }
        DelZero ();
    }
    
    bign bign::operator + (const type& b) {
        bign a = b;
        return *this + a;
    }
    
    bign bign::operator + (const bign& b) {
        type bignSum = 0;
        bign ans;
    
        for (int i = 0; i < len || i < b.len; i++) {
            if (i < len) bignSum += num[i];
            if (i < b.len) bignSum += b.num[i];
    
            ans.num[ans.len++] = bignSum % 10;
            bignSum /= 10;
        }
    
        while (bignSum) {
            ans.num[ans.len++] = bignSum % 10;
            bignSum /= 10;
        }
    
        return ans;
    }
    
    bign bign::operator - (const type& b) {
        bign a = b;
        return *this - a;
    }
    
    
    bign bign::operator - (const bign& b) {
        type bignSub = 0;
        bign ans;
        for (int i = 0; i < len || i < b.len; i++) {
            bignSub += num[i];
            bignSub -= b.num[i];
            ans.num[ans.len++] = (bignSub + 10) % 10;
            if (bignSub < 0) bignSub = -1;
            else bignSub = 0;
        }
        ans.DelZero ();
        return ans;
    }
    
    bign bign::operator * (const type& b) {
        type bignSum = 0;
        bign ans;
    
        ans.len = len;
        for (int i = 0; i < len; i++) {
            bignSum += num[i] * b;
            ans.num[i] = bignSum % 10;
            bignSum /= 10;
        }
    
        while (bignSum) {
            ans.num[ans.len++] = bignSum % 10;
            bignSum /= 10;
        }
        return ans;
    }
    
    bign bign::operator * (const bign& b) {
        bign ans;
        ans.len = 0; 
    
        for (int i = 0; i < len; i++){  
            int bignSum = 0;  
    
            for (int j = 0; j < b.len; j++){  
                bignSum += num[i] * b.num[j] + ans.num[i+j];  
                ans.num[i+j] = bignSum % 10;  
                bignSum /= 10;
            }  
            ans.len = i + b.len;  
    
            while (bignSum){  
                ans.num[ans.len++] = bignSum % 10;  
                bignSum /= 10;
            }  
        }  
        return ans;
    }
    
    bign bign::operator / (const type& b) {
    
        bign ans;
    
        type s = 0;
        for (int i = len-1; i >= 0; i--) {
            s = s * 10 + num[i];
            ans.num[i] = s/b;
            s %= b;
        }
    
        ans.len = len;
        ans.DelZero ();
        return ans;
    }
    
    int bign::operator % (const int& b) {
    
        bign ans;
    
        int s = 0;
        for (int i = len-1; i >= 0; i--) {
            s = s * 10 + num[i];
            ans.num[i] = s/b;
            s %= b;
        }
    
        return s;
    }
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  • 原文地址:https://www.cnblogs.com/lxjshuju/p/6800649.html
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