30 lines
783 B
C++
30 lines
783 B
C++
#include<cstdio>
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using namespace std;
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typedef long long LL;
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//求组合数公式原始方法
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//优点：从定义出发，易理解
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//缺点：过早溢出，比如 C1(17,54)得到了负数
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LL C1(int n, int m) {
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if (m < n - m) m = n - m; //此处加了一个小优化，使用了公式2
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LL ans = 1;
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for (int i = m + 1; i <= n; i++) ans *= i;
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for (int i = 1; i <= n - m; i++) ans /= i;
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return ans;
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}
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//求组合数的优化后办法
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//优点：从1开始除和乘，可以防止过早溢出和除法除不尽
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LL C2(int n, int m) {
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LL sum = 1;
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for (int i = 1; i <= m; i++)
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sum = sum * (n - m + i) / i;
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return sum;
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}
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int main() {
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printf("%lld\n", C1(54, 17));
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printf("%lld\n", C2(54, 17));
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return 0;
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} |