String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".
You are given a correct string s.
You can perform two different operations on this string:
- swap any pair of adjacent characters (for example, "101"
"110"); - replace "11" with "1" (for example, "110" "10").
Let val(s) be such a number that s is its binary representation.
Correct string a is less than some other correct string b iff val(a) < val(b).
Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).
The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.
The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.
Print one string — the minimum correct string that you can obtain from the given one.
4
1001
100
1
1
1
In the first example you can obtain the answer by the following sequence of operations: "1001" "1010" "1100" "100".
In the second example you can't obtain smaller answer no matter what operations you use.
题意：对一一个数的二进制表示可以进行两个操作：交换相邻两个二进制位以及合并两个1为一个1，问通过这两个操作能得到的不含前导0的最小数字是多少。题解：特判0输出0，否则输出一个1，以及k个0，k是原01串里0的个数。
1 #include<bits/stdc++.h> 2 #define clr(x) memset(x,0,sizeof(x)) 3 #define mod 1000000007 4 #define clr_1(x) memset(x,-1,sizeof(x)) 5 #define INF 0x3f3f3f3f 6 #define LL long long 7 #define pb push_back 8 #define pbk pop_back 9 using namespace std; 10 const int N=1e5+10; 11 char s[N]; 12 int n,m,zero,one; 13 int main() 14 { 15 scanf("%d",&n); 16 scanf("%s",s); 17 for(int i=0;s[i];i++) 18 { 19 if(s[i]=='0') 20 zero++; 21 else 22 one++; 23 } 24 if(n==1 && zero==1) 25 { 26 printf("0\n"); 27 return 0; 28 } 29 else 30 { 31 printf("1"); 32 while(zero) 33 { 34 printf("0"); 35 zero--; 36 } 37 printf("\n"); 38 } 39 return 0; 40 }
You might have heard about the next game in Lara Croft series coming out this year. You also might have watched its trailer. Though you definitely missed the main idea about its plot, so let me lift the veil of secrecy.
Lara is going to explore yet another dangerous dungeon. Game designers decided to use good old 2D environment. The dungeon can be represented as a rectangle matrix of n rows and m columns. Cell (x, y) is the cell in the x-th row in the y-th column. Lara can move between the neighbouring by side cells in all four directions.
Moreover, she has even chosen the path for herself to avoid all the traps. She enters the dungeon in cell (1, 1), that is top left corner of the matrix. Then she goes down all the way to cell (n, 1) — the bottom left corner. Then she starts moving in the snake fashion — all the way to the right, one cell up, then to the left to the cell in 2-nd column, one cell up. She moves until she runs out of non-visited cells. nand m given are such that she always end up in cell (1, 2).
Lara has already moved to a neighbouring cell k times. Can you determine her current position?
The only line contains three integers n, m and k (2 ≤ n, m ≤ 109, n is always even, 0 ≤ k < n·m). Note that k doesn't fit into 32-bit integer type!
Print the cell (the row and the column where the cell is situated) where Lara ends up after she moves k times.
4 3 0
1 1
4 3 11
1 2
4 3 7
3 2
题意：有一个人在n*m的方格里走，每次只能走通往上下左右的一步。不过他有既定路线：先从（1,1）到（n,1），然后蛇形地走，每次从(k,2)走(k,m)然后到(k-1,m)接着到(k-1,2)然后到（k-2,2）这样不断循环。然后问你他走第k步的时候在哪里。
题解：先处理(1,1)到(1,n)的情况，然后通过取模整除处理余下情况。
1 #include<bits/stdc++.h> 2 #define clr(x) memset(x,0,sizeof(x)) 3 #define mod 1000000007 4 #define clr_1(x) memset(x,-1,sizeof(x)) 5 #define INF 0x3f3f3f3f 6 #define LL long long 7 #define pb push_back 8 #define pbk pop_back 9 using namespace std; 10 const int N=1e5+10; 11 LL n,m,k,s,row,col,t; 12 int main() 13 { 14 scanf("%I64d%I64d%I64d",&n,&m,&k); 15 if(k<n) 16 { 17 printf("%I64d 1\n",k+1); 18 return 0; 19 } 20 k-=n-1; 21 m--; 22 s=k%m; 23 t=k/m; 24 if(s==0) 25 { 26 row=n-t+1; 27 col=(t&1)?m+1:2; 28 } 29 else 30 { 31 row=n-t; 32 col=(t&1)?m+2-s:1+s; 33 } 34 printf("%I64d %I64d\n",row,col); 35 return 0; 36 }
You are given a sequence a1, a2, ..., an of one-dimensional segments numbered 1 through n. Your task is to find two distinct indices iand j such that segment ai lies within segment aj.
Segment [l1, r1] lies within segment [l2, r2] iff l1 ≥ l2 and r1 ≤ r2.
Print indices i and j. If there are multiple answers, print any of them. If no answer exists, print -1 -1.
The first line contains one integer n (1 ≤ n ≤ 3·105) — the number of segments.
Each of the next n lines contains two integers li and ri (1 ≤ li ≤ ri ≤ 109) — the i-th segment.
Print two distinct indices i and j such that segment ai lies within segment aj. If there are multiple answers, print any of them. If no answer exists, print -1 -1.
5
1 10
2 9
3 9
2 3
2 9
2 1
3
1 5
2 6
6 20
-1 -1
题意：给你一堆一维的线段的左右端点，让你找出一条线段完全被包含在另一条线段的情况，并输出这两条线段编号。若没有输出-1 -1。
题解：经典黑书线段覆盖题，按左端点为第一关键字从小到大，右端点为第二关键字从大到小排序就好了。
1 #include<bits/stdc++.h> 2 #define clr(x) memset(x,0,sizeof(x)) 3 #define mod 1000000007 4 #define clr_1(x) memset(x,-1,sizeof(x)) 5 #define INF 0x3f3f3f3f 6 #define LL long long 7 #define pb push_back 8 #define pbk pop_back 9 using namespace std; 10 const int N=3e5+10; 11 struct sem 12 { 13 int l,r,id; 14 }seg[N]; 15 bool cmp(sem a,sem b) 16 { 17 if(a.l==b.l) return a.r>b.r; 18 return a.l<b.l; 19 } 20 int u,v,n,maxr,id; 21 int main() 22 { 23 scanf("%d",&n); 24 for(int i=1;i<=n;i++) 25 { 26 scanf("%d%d",&seg[i].l,&seg[i].r); 27 seg[i].id=i; 28 } 29 sort(seg+1,seg+n+1,cmp); 30 for(int i=2;i<=n;i++) 31 { 32 if(seg[i].l==seg[i-1].l) 33 { 34 printf("%d %d\n",seg[i].id,seg[i-1].id); 35 return 0; 36 } 37 else if(seg[i].r<=seg[i-1].r) 38 { 39 printf("%d %d\n",seg[i].id,seg[i-1].id); 40 return 0; 41 } 42 } 43 printf("-1 -1\n"); 44 return 0; 45 }
You are given a sequence of n positive integers d1, d2, ..., dn (d1 < d2 < ... < dn). Your task is to construct an undirected graph such that:
- there are exactly dn + 1 vertices;
- there are no self-loops;
- there are no multiple edges;
- there are no more than 106 edges;
- its degree set is equal to d.
Vertices should be numbered 1 through (dn + 1).
Degree sequence is an array a with length equal to the number of vertices in a graph such that ai is the number of vertices adjacent toi-th vertex.
Degree set is a sorted in increasing order sequence of all distinct values from the degree sequence.
It is guaranteed that there exists such a graph that all the conditions hold, and it contains no more than 106 edges.
Print the resulting graph.
The first line contains one integer n (1 ≤ n ≤ 300) — the size of the degree set.
The second line contains n integers d1, d2, ..., dn (1 ≤ di ≤ 1000, d1 < d2 < ... < dn) — the degree set.
In the first line print one integer m (1 ≤ m ≤ 106) — the number of edges in the resulting graph. It is guaranteed that there exists such a graph that all the conditions hold and it contains no more than 106 edges.
Each of the next m lines should contain two integers vi and ui (1 ≤ vi, ui ≤ dn + 1) — the description of the i-th edge.
3
2 3 4
8
3 1
4 2
4 5
2 5
5 1
3 2
2 1
5 3
3
1 2 3
4
1 2
1 3
1 4
2 3