![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144112-698b4388a1440.png\")
<\/p>\n\u5bf9\u4e8e\u4e00\u4e2a\u5305\u542bn\u4e2a\u5143\u7d20\u7684\u96c6\u5408，\u6bcf\u4e2a\u5143\u7d20\u6709 \u201c\u9009\u201d \u548c \u201c\u4e0d\u9009\u201d \u4e24\u79cd\u72b6\u6001，\u603b\u5171\u67092^n\u79cd\u5b50\u96c6（\u5305\u62ec\u7a7a\u96c6）\u3002\u7528\u4e00\u4e2an\u4f4d\u7684\u4e8c\u8fdb\u5236\u6570\u6765\u8868\u793a\u4e00\u79cd\u9009\u53d6\u72b6\u6001：<\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e8c\u8fdb\u5236\u4f4d\u4e3a1：\u8868\u793a\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u88ab\u9009\u4e2d；<\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e8c\u8fdb\u5236\u4f4d\u4e3a0：\u8868\u793a\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u672a\u88ab\u9009\u4e2d\u3002<\/p>\n
\u5f02\u6216\u8fd0\u7b97：<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 X ^ X = 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X ^ 0 = X<\/p>\n
\u6ce8\u610f：\u6570\u7ec4a,b\u5b9a\u4e49\u6210\u5168\u5c40\u53d8\u91cf，\u8fd9\u6837\u5b58\u5728\u9759\u6001\u533a，\u4f1a\u81ea\u52a8\u521d\u59cb\u5316\u4e3a0，\u6709\u52a9\u4e8e\u6211\u4eec\u7684\u5f02\u6216\u8fd0\u7b97<\/p>\n
<\/p>\n
#include <bits\/stdc++.h>
\nusing namespace std;<\/p>\n
int n,cnt;
\nchar a[35], b[35];<\/p>\n
int main()
\n{
\n while(~scanf("%d",&n))
\n {
\n cnt++;
\n scanf("%s",a);
\n for(int i = 1; i <= 2 * n – 2; i++)
\n {
\n scanf("%s", b);
\n int len = strlen(b);
\n for(int j = 0; j < len; j++)
\n {
\n a[j] = a[j] ^ b[j];
\n }
\n }
\n printf("Scenario #%d\\\\n",cnt);
\n printf("%s\\\\n\\\\n",a);
\n }
\n return 0;
\n} <\/p>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144115-698b438b8f3f2.png\")
<\/p>\n
#include <bits\/stdc++.h>
\nusing namespace std;<\/p>\n
int n,x;
\nint main()
\n{
\n while(~scanf("%d",&n))
\n {
\n int ans = 0;
\n while(n–)
\n {
\n scanf("%d",&x);
\n ans = ans ^ x;
\n }
\n printf("%d\\\\n",ans);
\n }
\n return 0;
\n} <\/p>\n
\u4e24\u4e2a\u4e8c\u8fdb\u5236\u6570\u8fdb\u884c\u4e0e\u8fd0\u7b97，\u53ea\u6709\u5bf9\u5e94\u4f4d\u7f6e\u90fd\u662f1\u624d\u662f1，\u6709\u4e00\u4e2a\u4f4d\u7f6e\u662f0\u5c31\u662f0，\u4f8b\u5982：010&110 = 1，010&101 = 0<\/p>\n
\u679a\u4e3e\u6240\u6709\u5b50\u96c6：i < (1<<N)<\/span><\/p>\n 1<<N \u7b49\u4ef7\u4e8e 2^N，\u8868\u793a\u957f\u5ea6\u4e3a N \u7684\u6570\u7ec4\u5171\u6709 2^N \u4e2a\u5b50\u96c6（\u5305\u62ec\u7a7a\u96c6）\u3002<\/p>\n \u5224\u65ad\u662f\u5426\u9009\u4e2d\u5143\u7d20：i & (1<<j)<\/span><\/p>\n 1<<j：\u751f\u6210\u4e00\u4e2a \u201c\u53ea\u6709\u7b2c j \u4f4d\u662f 1，\u5176\u4f59\u4f4d\u90fd\u662f 0\u201d \u7684\u6570（\u6bd4\u5982 j=0\u21921=001，j=1\u21922=010，j=2\u21924=100）；<\/p>\n i & (1<<j)：\u6309\u4f4d\u4e0e\u8fd0\u7b97，\u53ea\u6709\u5f53 i \u7684\u7b2c j \u4f4d\u662f 1 \u65f6，\u7ed3\u679c\u624d \u2260 0（\u8868\u793a\u9009\u4e2d），\u5426\u5219 = 0（\u4e0d\u9009）\u3002<\/p>\n \u8fd9\u5757\u6bd4\u8f83\u96be\u7406\u89e3，\u6211\u4eec\u4ee5n=3，k=5\u4e3e\u4f8b，\u5047\u8bbe\u90a3\u4e09\u4e2a\u6570\u662f[1，2，3]，\u6211\u4eec\u770b\u4e0b\u9762\u8fd9\u5f20\u8868，\u8fd9\u65f6\u00a0 \u00a0 \u00a0i < (1<<3)\u5373 i<8, \u5171\u6709\u516b\u4e2a\u5b50\u96c6\u3002<\/p>\n #include <bits\/stdc++.h> int a[25];<\/p>\n int main() int f = 1;<\/p>\n for(int i = 0; i <(1<<N); i++)\/\/\u904d\u5386\u6bcf\u4e00\u79cd\u5b50\u96c6\u7684\u60c5\u51b5 \u8bf4\u660e：\u7b2c\u4e00\u5c42\u5faa\u73af\u5faa\u73af\u76f8\u5f53\u4e8e\u679a\u4e3e\u51fa\u6240\u6709\u7684\u60c5\u51b5，\u7b2c\u4e8c\u5c42\u5faa\u73af\u662f\u770b\u8fd9\u4e2a01\u4e32\u4e0a\u7684\u5404\u4f4d\u662f0\u8fd8\u662f1，\u5982\u679c\u662f0\u7684\u8bdd\u5c31\u5f53\u4f5c\u52a0\u6cb9\u7ad9\u8ba1\u6570，\u5982\u679c\u4e3a1\u5c31\u628a\u5f53\u4f5c\u8def\u53e3\u8ba1\u6570，\u8ba1\u6570\u7ed3\u675f\u4ee5\u540e\u6216\u8005\u6cb9\u4e0d\u591f\u4e86\u7684\u8bdd\u5c31\u9000\u51fa\u5224\u65ad，\u5982\u679c\u52a0\u6cb9\u7ad9\u6570\u91cf\u548c\u8def\u53e3\u6570\u91cf\u6ee1\u8db3\u8981\u6c42\u4e86\u800c\u4e14\u6cb9\u6070\u597d\u7528\u5b8c\u7684\u8bdd，\u8fd9\u6b64\u679a\u4e3e\u5230\u7684\u8fd9\u79cd\u60c5\u51b5\u5c31\u662f\u7b26\u5408\u8981\u6c42\u7684\u628a\u8ba1\u7b97\u8fdb\u6765\u3002<\/p>\n \u628a\u548c\u4e3ak\u90a3\u9053\u9898\u7406\u89e3\u660e\u767d\u4e4b\u540e\u5728\u505a\u8fd9\u4e2a\u5c31\u4f1a\u597d\u5f88\u591a\u54e6<\/p>\n #include <bits\/stdc++.h> int main() \u8fd9\u9053\u9898\u548c\u548c\u4e3aK–\u4e8c\u8fdb\u5236\u679a\u4e3e\u5f88\u76f8\u4f3c！<\/p>\n #include <bits\/stdc++.h> int main() \u6838\u5fc3\u903b\u8f91：\u4e8c\u8fdb\u5236\u679a\u4e3e\u6240\u6709\u5b50\u96c6 \u2192 \u7b5b\u9009\u83b7\u80dc\u8054\u76df \u2192 \u904d\u5386\u8054\u76df\u627e\u5173\u952e\u52a0\u5165\u8005 \u2192 \u7edf\u8ba1\u6743\u5229\u6307\u6570；<\/p>\n \u5173\u952e\u6280\u5de7：\u7528\u4f4d\u8fd0\u7b97\u5224\u65ad\u6210\u5458\u662f\u5426\u5728\u8054\u76df\u4e2d，\u7528 \u201c\u79fb\u9664\u540e\u7968\u6570\u548c\u201d \u5224\u65ad\u662f\u5426\u4e3a\u5173\u952e\u52a0\u5165\u8005；<\/p>\n #include <bits\/stdc++.h> int main() double half_votes = total \/ 2.0; \/\/\u7a7a\u96c6\u4e00\u5b9a\u4e0d\u662f\u83b7\u80dc\u8054\u76df \/\/\u5224\u65ad\u662f\u5426\u4e3a\u83b7\u80dc\u8054\u76df for(int j = 0; j < n; j++){ \u7ec4\u5408\u6982\u7387 = \u505a\u5bf9\u9898\u7684 AC \u6982\u7387\u4e58\u79ef \u00d7 \u505a\u9519\u9898\u7684 WA \u6982\u7387\u4e58\u79ef<\/span><\/p>\n \u4e00\u4e2a\u7ec4\u5408\u662f \u201c\u591a\u4e2a\u72ec\u7acb\u4e8b\u4ef6（\u6bcf\u9898\u7684\u5bf9 \/ \u9519）\u540c\u65f6\u53d1\u751f\u201d，\u56e0\u6b64\u6982\u7387\u662f\u5404\u4e8b\u4ef6\u6982\u7387\u7684\u4e58\u79ef\u6240\u6709 \u201c\u505a\u5bf9\u9898\u6570 = cnt=x\u201d \u7684\u7ec4\u5408\u6982\u7387\u76f8\u52a0，\u5c31\u662f\u6700\u7ec8\u7b54\u6848\u3002<\/p>\n #include <bits\/stdc++.h> int main() { for (int i = 0; i < n; i++) cin >> a[i]; for (int i = 0; i < n; i++) { double ans = 0.0; \/\/ \u521d\u59cb\u5316\u7ed3\u679c\u4e3a0（\u5173\u952e！） printf("%.4lf\\\\n", ans); \u524d\u8a00![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144118-698b438e5f90d.png\")
<\/p>\n![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144118-698b438eaa897.png\")
<\/p>\n
\nusing namespace std;<\/p>\n
\n{
\n ios::sync_with_stdio(false);
\n int N, K;
\n while(cin>>N>>K)
\n {
\n for(int i = 0; i < N; i++)
\n cin>>a[i];<\/p>\n
\n {
\n int sum = 0;
\n for(int j = 0; j < N; j++)
\n {
\n if(i & (1<<j))\/\/\u8868\u793a\u5f531\u7684\u7b2cj\u4f4d\u662f1\u65f6，\u624d\u9009\u4e2d
\n {
\n sum += a[j];
\n }
\n }
\n if(sum ==K)
\n {
\n cout<<"Yes"<<endl;
\n f = 0;
\n break;
\n }
\n }
\n if(f == 1)
\n cout<<"No"<<endl;
\n }
\n return 0;
\n}<\/p>\n\u6797\u5927OJ 1505：\u9648\u8001\u5e08\u52a0\u6cb9-\u4e8c\u8fdb\u5236\u679a\u4e3e<\/h3>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144122-698b4392bcf06.png\")
<\/p>\n
\nusing namespace std;<\/p>\n
\n{
\n ios::sync_with_stdio(false);
\n int T;
\n while(cin>>T)
\n {
\n int cnt = 0;
\n for(int i = 0; i<(1<<15); i++)\/\/\u76f8\u5f53\u4e8e\u4e00\u4e2a15\u4f4d\u768401\u4e32，\u5982\u679c\u662f0，\u8868\u793a\u9047\u5230\u52a0\u6cb9\u7ad9，\u662f1\u8868\u793a\u9047\u5230\u5341\u5b57\u8def\u53e3
\n {
\n int cross_road=0, gap_station=0, tmp = T;
\n for(int j = 0; j<15; j++)
\n {
\n if(i & (1<<j) && tmp >0)
\n {
\n tmp -=1;
\n cross_road++;
\n }
\n else if(tmp > 0)
\n {
\n tmp *= 2;
\n gap_station++;
\n }
\n }
\n if(gap_station==5 && cross_road == 10 &&tmp == 0)
\n cnt++;
\n }
\n cout<<cnt<<endl;
\n }
\n return 0;
\n} <\/p>\n\u6797\u5927OJ 1518：\u7eb8\u724c\u6e38\u620f-\u4e8c\u8fdb\u5236-\u641c\u7d22<\/h3>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144125-698b4395633f3.png\")
<\/p>\n
\nusing namespace std;<\/p>\n
\n{
\n ios::sync_with_stdio(false);
\n int n, p;
\n int a[25];
\n while(cin>>n>>p)
\n {
\n int cnt = 0;
\n for(int i = 0; i <n; i++)
\n cin>>a[i];
\n for(int i = 1; i < (1<<n); i++)\/\/\u4e0d\u9700\u8981\u7edf\u8ba1\u7a7a\u96c6
\n {
\n int ans=0;
\n for(int j = 0; j < n; j++)
\n {
\n if(i & (1<<j))
\n {
\n ans+=a[j];
\n }
\n }
\n if(ans == p)
\n cnt++;
\n }
\n cout<<cnt<<endl;
\n }
\n return 0;
\n}<\/p>\n\u6797\u5927OJ 1641：\u6743\u5229\u6307\u6570<\/h3>\n
<\/ul>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144126-698b4396d8022.png\")
<\/p>\n
\nusing namespace std;<\/p>\n
\n{
\n ios::sync_with_stdio(false);
\n int T;
\n cin>>T;
\n while(T–)
\n {
\n int n;
\n cin>>n;
\n vector<int> votes(n); \/\/\u5b58\u50a8\u6bcf\u4e2a\u5c0f\u56e2\u4f53\u7684\u7968\u6570
\n int total = 0;
\n for(int i = 0; i < n; i++)
\n {
\n cin>>votes[i];
\n total += votes[i];
\n }<\/p>\n
\n vector<int> power(n, 0);<\/p>\n
\n for(int i = 1; i < (1<<n); i++){
\n int sum = 0;
\n for(int j = 0; j < n; j++)
\n {
\n if(i & (1<<j)){sum +=votes[j];}
\n }<\/p>\n
\n if(sum <= half_votes)
\n continue;<\/p>\n
\n if(i & (1<<j))
\n {
\n int sum_without_j = sum – votes[j];
\n if(sum_without_j <= half_votes)
\n power[j]++;
\n }
\n }
\n }
\n for(int i = 0; i < n; i++){
\n cout<<power[i];
\n if(i != n-1)
\n cout<<" ";
\n }
\n cout<<endl;
\n }
\n return 0;
\n}<\/p>\n\u6797\u5927OJ 1285：\u8da3\u5473\u89e3\u9898<\/h3>\n
![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260210144131-698b439b67520.png\")
<\/p>\n
\nusing namespace std;<\/p>\n
\n ios::sync_with_stdio(false);
\n int T;
\n cin >> T;
\n while (T–) {
\n int n, x;
\n double a[15], b[15], c[15];
\n double ac[15], wa[15];
\n cin >> n;<\/p>\n
\n for (int i = 0; i < n; i++) cin >> b[i];
\n for (int i = 0; i < n; i++) cin >> c[i];
\n cin >> x;<\/p>\n
\n wa[i] = (1 – a[i]) * (1 – b[i]) * (1 – c[i]); \/\/ \u4e09\u4eba\u90fd\u505a\u9519\u7684\u6982\u7387
\n ac[i] = 1 – wa[i];
\n }<\/p>\n
\n \/\/ \u679a\u4e3e\u6240\u6709\u505a\u9898\u72b6\u6001（i\u7684\u4e8c\u8fdb\u5236\u4f4d\u8868\u793a\u6bcf\u9053\u9898\u662f\u5426AC）
\n for (int i = 0; i < (1 << n); i++) {
\n int cnt = 0;
\n double p = 1.0;
\n for (int j = 0; j < n; j++) {
\n if (i & (1 << j)) { \/\/ \u7b2cj\u9898\u505a\u5bf9
\n p *= ac[j];
\n cnt++;
\n } else { \/\/ \u7b2cj\u9898\u505a\u9519
\n p *= wa[j];
\n }
\n }
\n \/\/\u628a\u6bcf\u79cd\u7ec4\u5408\u7684\u6982\u7387\u52a0\u5728\u4e00\u8d77
\n if (cnt == x) {
\n ans += p;
\n }
\n }<\/p>\n
\n }
\n return 0;
\n} <\/p>\n","protected":false},"excerpt":{"rendered":"
\n\u5bf9\u4e8e\u4e00\u4e2a\u5305\u542bn\u4e2a\u5143\u7d20\u7684\u96c6\u5408，\u6bcf\u4e2a\u5143\u7d20\u6709 \u201c\u9009\u201d \u548c \u201c\u4e0d\u9009\u201d \u4e24\u79cd\u72b6\u6001，\u603b\u5171\u67092^n\u79cd\u5b50\u96c6（\u5305\u62ec\u7a7a\u96c6）\u3002\u7528\u4e00\u4e2an\u4f4d\u7684\u4e8c\u8fdb\u5236\u6570\u6765\u8868\u793a\u4e00\u79cd\u9009\u53d6\u72b6\u6001： \u4e8c\u8fdb\u5236\u4f4d\u4e3a1：\u8868\u793a\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u88ab\u9009\u4e2d； \u4e8c\u8fdb\u5236\u4f4d\u4e3a0：\u8868\u793a\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u672a\u88ab\u9009\u4e2d\u3002
\n\u5f02\u6216\u8fd0\u7b97： X ^ X 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X ^ 0 X
\n\u6797\u5927OJ 643：teacher <\/p>\n","protected":false},"author":2,"featured_media":74905,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[7373,7933,6985,55,174,427,729],"topic":[],"class_list":{"0":"post-74913","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-server","8":"tag-acm","9":"tag-7933","10":"tag-6985","11":"tag-c","13":"tag-427","14":"tag-729"},"yoast_head":"\n