uva 1546 - Complete the sequence!(牛顿插值法)

题目连接：uva 1546 - Complete the sequence!

题目大意：给出一个序列的n项，求满足序列规律的后c项，要求尽量小。

解题思路：牛顿插值法，每次求两项之间的差，形成一个新的序列，直到序列公差为0时，回带回原来的序列即可。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 205;

int S, C, arr[maxn][maxn];

int main () {
    int cas;
    scanf("%d", &cas);
    while (cas--) {
        scanf("%d%d", &S, &C);
        for (int i = 0; i < S; i++)
            scanf("%d", &arr[0][i]);

        for (int i = 1; i < S; i++) {
            for (int j = 0; j < S - i; j++)
                arr[i][j] = arr[i-1][j+1] - arr[i-1][j];
        }

        for (int i = 1; i <= C; i++)
            arr[S-1][i] = arr[S-1][0];

        for (int i = S-2; i >= 0; i--) {
            int pos = S - i;
            for (int j = 0; j < C; j++)
                arr[i][j+pos] = arr[i+1][j+pos-1] + arr[i][j+pos-1];
        }

        printf("%d", arr[0][S]);
        for (int i = 1; i < C; i++)
            printf(" %d", arr[0][S+i]);
        printf("\n");
    }
    return 0;
}