Project Euler：Problem 53 Combinatoric selections

There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, ⁵C₃ = 10.

In general,

ⁿC_r =

n!
r!(n−r)!

,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: ²³C₁₀ = 1144066.

How many, not necessarily distinct, values of ⁿC_r, for 1 ≤ n ≤ 100, are greater than one-million?

#include <iostream>
#include <string>
using namespace std;int c[101][101];int main()
{memset(c, 0, sizeof(c));for (int i = 1; i <= 100; i++){c[0][i] = 1;c[1][i] = i;c[i][i] = 1;c[i - 1][i] = i;}int count = 0;for (int n = 2; n <= 100; n++){for (int r = 2; r < n; r++){c[r][n] = c[r][n - 1] + c[r - 1][n - 1];if (c[r][n]>1000000){c[r][n] = 1000001;count++;}}}cout << count << endl;system("pause");return 0;
}

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