35 lines
1.0 KiB
C++
35 lines
1.0 KiB
C++
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#include <bits/stdc++.h>
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using namespace std;
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const int N = 2010;
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const int p = 1e9 + 7;
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int c[N][N];
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void init() {
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/*
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功能：第0列初始化为1，现实意义：C(n,0)=1
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理解：从n个元素中,每次取出0个元素,也就是每次都不取出元素,有几种取法?
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很明显只有1种取法,就是什么都不取这样一种情况。类似:C(n,0)=C(n,n)=1
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这是递归的base case,如果没有这个1打底，以后再怎么加法原理都是白费
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*/
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for (int i = 1; i < N; i++) c[i][0] = 1, c[i][i] = 1; // base case
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for (int i = 1; i < N; i++)
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for (int j = 1; j < i; j++)
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// 递归式最重要！这是根据数学公式得到的递推式
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// 从递推式由右向左看过去，需要由小到大填充i,j,并且，i>j
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c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % p;
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}
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int n;
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int main() {
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init();
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cin >> n;
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while (n--) {
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int a, b;
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cin >> a >> b;
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cout << c[a][b] << endl;
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}
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return 0;
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}
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