Farmer John has just given the cows a program to play with! The program contains two integer variables, x and y, and performs the following operations on a sequence a1,a2,…,an of positive integers:
Initially, x=1 and y=0. If, after any step, x≤0 or x>n, the program immediately terminates.The program increases both x and y by a value equal to ax simultaneously.The program now increases y by ax while decreasing x by ax.The program executes steps 2 and 3 (first step 2, then step 3) repeatedly until it terminates (it may never terminate). So, the sequence of executed steps may start with: step 2, step 3, step 2, step 3, step 2 and so on.
The cows are not very good at arithmetic though, and they want to see how the program works. Please help them!
You are given the sequence a2,a3,…,an. Suppose for each i (1≤i≤n-1) we run the program on the sequence i,a2,a3,…,an. For each such run output the final value of y if the program terminates or -1 if it does not terminate. Input
The first line contains a single integer, n (2≤n≤2·105). The next line contains n-1 space separated integers, a2,a3,…,an (1≤ai≤109). Output
Output n-1 lines. On the i-th line, print the requested value when the program is run on the sequence i,a2,a3,…an.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. Sample test(s) Input
4 2 4 1
Output
3 6 8
Input
3 1 2
Output
-1 -1
Note
In the first sample
For i=1, x becomes and y becomes 1+2=3.For i=2, x becomes and y becomes 2+4=6.For i=3, x becomes and y becomes 3+1+4=8.
注意到每次X都有2个转移方向,设dp[i][2],分别表示转移到i+a[i]和i-a[i], y的最终值,然后记忆化搜索就行,注意判环
/*************************************************************************> File Name: cf-174-d.cpp> Author: ALex> Mail: zchao1995@gmail.com> Created Time: 2015年05月02日 星期六 21时07分26秒 ************************************************************************/;const double pi = acos(-1.0);const int inf = 0x3f3f3f3f;const double eps = 1e-15;LL;typedef pair <int, int> PLL;N = 200110;LL dp[N][2];LL arr[N];int n;LL dfs(int u, int flag) {if (u <= 0 || u > n) {return 0;}if (dp[u][flag] != -inf) {return dp[u][flag];}dp[u][flag] = -1;int sgn = flag ? 1 : -1;LL ans = dfs(u + sgn * arr[u], flag ^ 1);if (ans != -1) {dp[u][flag] = ans + arr[u];}return dp[u][flag];}int main() {while (~scanf(“%d”, &n)) {for (int i = 2; i <= n; ++i) {scanf(“%I64d”, &arr[i]);}for (int i = 1; i <= n; ++i) {dp[i][0] = dp[i][1] = -inf; //init}for (int i = 1; i <= n; ++i) {for (int j = 0; j < 2; ++j) {dfs(i, j);}}for (int i = 1; i <= n – 1; ++i) {if (dp[i + 1][0] == -1) {printf(“%I64d\n”, dp[i + 1][0]);}else {printf(“%I64d\n”, dp[i + 1][0] + i);}}}return 0;}
，发光并非太阳的专利，你也可以发光
