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

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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;}

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