uva 10025 The ? 1 ? 2 ? ... ? n = k problem(算式规律)
2013-07-31 10:20
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The ? 1 ? 2 ? ... ? n = k problem |
The problem
Given the following formula, one can set operators '+' or '-' instead of each '?', in order to obtain a given k? 1 ? 2 ? ... ? n = k
For example: to obtain k = 12 , the expression to be used will be:
- 1 + 2 + 3 + 4 + 5 + 6 - 7 = 12
with n = 7
The Input
The first line is the number of test cases, followed by a blank line.Each test case of the input contains integer k (0<=|k|<=1000000000).
Each test case will be separated by a single line.
The Output
For each test case, your program should print the minimal possible n (1<=n) to obtain k with the above formula.Print a blank line between the outputs for two consecutive test cases.
Sample Input
2 12 -3646397
Sample Output
7 2701
题目大意:给出一个数, 判断它需要从1~m(可用+、-)填充的算式求得。求m
解题思路:首先, 1~m的和一定要 > n(如果全+都无法表示的话, 更别说有-)其次,找到一个m,使得1~m的和>n之后,因为sum >= n, 所以要减掉一个数, 比如在数字k前面加个-号, 相当于sum - 2 * k,也就是说每次减掉只能是偶数, 那么就要求sum % 2 == n % 2.(负数同理)
#include<stdio.h> int main(){ int t, n, sum, i; scanf("%d", &t); while (t--){ scanf("%d", &n); if (n < 0) n = -n; for (sum = 0, i = 1; ; i++){ sum += i; if (sum >= n && (sum - n) % 2 == 0){ printf("%d\n", i); break; } } if (t) printf("\n"); } return 0;}
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