Educational Codeforces Round 90 (Rated for Div. 2)(D 思维 E 打表)
2024-05-13 01:53:22
题目链接
D. Maximum Sum on Even Positions
题意：给你n长度的数组a 要求翻转 子区间 使得 偶数上的数之和尽量最大。
做法:用偶数位置减去奇数位置的值 就相当于求子序列最大值，随便dp一下就好了，这类题 主要思路就是化简为以前遇到过的经典题。同理奇数位置减去偶数也跑一遍即可。
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 1005
#define inf 1e9
#define pb push_back
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define per(i,a,b) for(int i=a;i>=b;i--)
using namespace std;inline ll read()
{ll x=0,w=1; char c=getchar();while(c<'0'||c>'9') {if(c=='-') w=-1; c=getchar();}while(c<='9'&&c>='0') {x=(x<<1)+(x<<3)+c-'0'; c=getchar();}return w==1?x:-x;
}
const int N=1e6+10;
int n;
ll a[N],res,ans;
int main()
{int _=read();while(_--){n=read();ans=0;rep(i,1,n) {a[i]=read();if(i%2==1) ans+=a[i];}ll mx=0,res=0,sum=0;for(int i=2;i<=n;i+=2){sum=max(0ll,a[i]-a[i-1]+sum);mx=max(mx,sum);//mx=max(mx,max(a[i]-a[i-1]+mx,0ll));}sum=0;for(int i=3;i<=n;i+=2){sum=max(0ll,a[i-1]-a[i]+sum);mx=max(mx,sum);}printf("%lld\n",ans+mx);}
}
/*
4
5
1 2 3 4 55
5 4 3 2 14
10
7 8 4 5 7 6 8 9 7 3*/
E. Sum of Digits
题意：给你 n 和 k 求最小的x 使得 x 、 x+1 、x+2 的各位数上的和等于n
做法：这题提供打表的做法，这类n不是很大的情况，而且自己一时半会也想不到什么好的思路，就可以用这种方法搞一发。
1、当k>=2的时候是可以暴力跑的
2、k=0 直接构造 最低位尽量填9就可以了。
3、至于k=1 怎么弄呢？暴力跑又很大，超时。
其实很简单，当n是奇数 n/2+1 按照k=0 的构造就好了， 然后构造出的答案减1 才是最小值
当n是偶数
就是第一个数 的第一位尽量是9 第二位尽量是8 （如果够的话。）只进位一次。
那么设 x x+1 f(x) =y f(x+1)=y+1-9 n=2*y-8 计算出y 然后 第一位尽量是9 第二位尽量是8 构造就可以了。
暴力打表程序：
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 1005
#define inf 1e9
#define pb push_back
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define per(i,a,b) for(int i=a;i>=b;i--)
using namespace std;inline ll read()
{ll x=0,w=1; char c=getchar();while(c<'0'||c>'9') {if(c=='-') w=-1; c=getchar();}while(c<='9'&&c>='0') {x=(x<<1)+(x<<3)+c-'0'; c=getchar();}return w==1?x:-x;
}
int f(int x)
{int ans=0;while(x) ans+=x%10,x=x/10;return ans;
}
unordered_map <int,int>mp;
string run(int x)
{string ans="";if(x%9!=0) ans+=x%9+'0';for(int i=1;i<=x/9;++i) ans+='9';return ans;
}
string run1(int x)
{string ans="";if(x>=9) ans+='9',x-=9;if(x>=8) ans+='8',x-=8;for(int i=1;i<=x/9;++i) ans+='9';if(x%9!=0) ans+=x%9+'0';reverse(ans.begin(),ans.end());return ans;
}
int main()
{//cout<<run1(28)<<endl;freopen("output.txt", "w", stdout);for(int i=0;i<=1000000;++i) mp[i]=f(i);for(int i=0;i<=150;++i){printf("{");for(int k=0;k<=9;++k){int flag=0;if(i==0){printf("-1");continue;if(k!=9) printf(",");}if(k==0){string ans=run(i);cout<<ans;if(k!=9) printf(",");continue;}else if(k==1){string ans;if(i<10){if(i==1) printf("0");else if(i==2) printf("-1");else if(i==3) printf("1");else if(i==4) printf("-1");else if(i==5) printf("2");else if(i==6) printf("-1");else if(i==7) printf("3");else if(i==8) printf("-1");else if(i==9) printf("4");if(k!=9) printf(",");continue;}if(i%2==0){int d=(i+8)/2;ans=run1(d);}else{int d=i/2+1;ans=run(d);int flag=1;for(int i=ans.size()-1;i>=0;--i){if(ans[i]=='0'){ans[i]='9';}else{ans[i]=ans[i]-1;break;}}//这里应该是模拟减1}cout<<ans;if(k!=9) printf(",");continue;}int res=0;for(int j=0;j<=k;++j) res+=mp[j];//printf("i:%d k:%d res:%d\n",i,k,res);if(res==i){printf("%d",0);if(k!=9) printf(",");continue;}for(int j=k+1;j<=1000000&&!flag;++j){res+=mp[j]-mp[j-k-1];if(res==i){printf("%d",j-k);if(k!=9) printf(",");flag=1;break;}}if(!flag) printf("%d,",-1);}puts("},");}}
AC 代码
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll ans[151][12]={{-1-1-1-1-1-1-1-1-1-1},
{1,0,-1,-1,-1,-1,-1,-1,-1,-1,},
{2,-1,-1,-1,-1,-1,-1,-1,-1,-1,},
{3,1,0,-1,-1,-1,-1,-1,-1,-1,},
{4,-1,-1,-1,-1,-1,-1,-1,-1,-1,},
{5,2,-1,-1,-1,-1,-1,-1,-1,-1,},
{6,-1,1,0,-1,-1,-1,-1,-1,-1,},
{7,3,-1,-1,-1,-1,-1,-1,-1,-1,},
{8,-1,-1,-1,-1,-1,-1,-1,-1,-1,},
{9,4,2,-1,-1,-1,-1,-1,-1,-1,},
{19,9,-1,1,0,-1,-1,-1,-1,-1,},
{29,5,-1,-1,-1,-1,-1,-1,-1,-1,},
{39,19,3,-1,-1,-1,-1,-1,-1,-1,},
{49,6,-1,-1,-1,-1,-1,-1,-1,-1,},
{59,29,-1,2,-1,-1,-1,-1,-1,-1,},
{69,7,4,9,1,0,-1,-1,-1,-1,},
{79,39,-1,-1,-1,-1,-1,-1,-1,-1,},
{89,8,-1,-1,-1,-1,-1,-1,-1,-1,},
{99,49,5,3,-1,-1,-1,-1,-1,-1,},
{199,18,-1,19,9,-1,-1,-1,-1,-1,},
{299,59,-1,8,2,-1,-1,-1,-1,-1,},
{399,28,6,-1,-1,1,0,-1,-1,-1,},
{499,69,-1,4,-1,-1,-1,-1,-1,-1,},
{599,38,-1,29,8,-1,-1,-1,-1,-1,},
{699,79,7,18,19,9,-1,-1,-1,-1,},
{799,48,-1,7,3,-1,-1,-1,-1,-1,},
{899,89,-1,5,-1,-1,-1,-1,-1,-1,},
{999,58,17,39,7,2,-1,-1,-1,-1,},
{1999,189,-1,28,18,-1,1,0,-1,-1,},
{2999,68,-1,17,29,-1,-1,-1,-1,-1,},
{3999,289,27,6,4,7,9,-1,-1,-1,},
{4999,78,-1,49,6,-1,-1,-1,-1,-1,},
{5999,389,-1,38,17,-1,8,-1,-1,-1,},
{6999,88,37,27,28,3,-1,-1,-1,-1,},
{7999,489,-1,16,39,-1,7,-1,-1,-1,},
{8999,98,-1,59,5,-1,2,-1,-1,-1,},
{9999,589,47,48,16,5,6,1,0,-1,},
{19999,198,-1,37,27,-1,19,9,-1,-1,},
{29999,689,-1,26,38,-1,5,8,-1,-1,},
{39999,298,57,69,49,4,18,7,-1,-1,},
{49999,789,-1,58,15,-1,4,6,-1,-1,},
{59999,398,-1,47,26,-1,17,5,-1,-1,},
{69999,889,67,36,37,15,3,4,-1,-1,},
{79999,498,-1,79,48,-1,16,3,-1,-1,},
{89999,989,-1,68,59,-1,29,2,-1,-1,},
{99999,598,77,57,25,14,15,19,1,0},
{199999,1989,-1,46,36,-1,28,18,-1,1},
{299999,698,-1,89,47,-1,14,17,-1,2},
{399999,2989,87,78,58,25,27,16,-1,3},
{499999,798,-1,67,69,-1,13,15,-1,4},
{599999,3989,-1,56,35,-1,26,14,-1,5},
{699999,898,97,189,46,24,39,13,-1,6},
{799999,4989,-1,88,57,-1,25,12,-1,7},
{899999,998,-1,77,68,-1,38,29,-1,8},
{999999,5989,197,66,79,35,24,28,11,9},
{1999999,1998,-1,289,45,-1,37,27,-1,10},
{2999999,6989,-1,188,56,-1,23,26,-1,11},
{3999999,2998,297,87,67,34,36,25,-1,12},
{4999999,7989,-1,76,78,-1,49,24,-1,13},
{5999999,3998,-1,389,89,-1,35,23,-1,14},
{6999999,8989,397,288,55,45,48,22,-1,15},
{7999999,4998,-1,187,66,-1,34,39,-1,16},
{8999999,9989,-1,86,77,-1,47,38,-1,17},
{9999999,5998,497,489,88,44,33,37,21,18},
{19999999,19989,-1,388,189,-1,46,36,-1,19},
{29999999,6998,-1,287,65,-1,59,35,-1,20},
{39999999,29989,597,96,76,55,45,34,-1,21},
{49999999,7998,-1,589,87,-1,58,33,-1,22},
{59999999,39989,-1,488,188,-1,44,32,-1,23},
{69999999,8998,697,387,289,54,57,49,-1,24},
{79999999,49989,-1,196,75,-1,43,48,-1,25},
{89999999,9998,-1,689,86,-1,56,47,-1,26},
{99999999,59989,797,588,187,65,69,46,31,27},
{199999999,19998,-1,487,288,-1,55,45,-1,28},
{299999999,69989,-1,296,389,-1,68,44,-1,29},
{399999999,29998,897,789,85,64,54,43,-1,30},
{499999999,79989,-1,688,186,-1,67,42,-1,31},
{599999999,39998,-1,587,287,-1,53,59,-1,32},
{699999999,89989,997,396,388,75,66,58,-1,33},
{799999999,49998,-1,889,489,-1,79,57,-1,34},
{899999999,99989,-1,788,95,-1,65,56,-1,35},
{999999999,59998,1997,687,286,74,78,55,41,36},
{1999999999,199989,-1,496,387,-1,64,54,-1,37},
{2999999999,69998,-1,989,488,-1,77,53,-1,38},
{3999999999,299989,2997,888,589,85,63,52,-1,39},
{4999999999,79998,-1,787,195,-1,76,69,-1,40},
{5999999999,399989,-1,596,386,-1,89,68,-1,41},
{6999999999,89998,3997,1989,487,84,75,67,-1,42},
{7999999999,499989,-1,988,588,-1,88,66,-1,43},
{8999999999,99998,-1,887,689,-1,74,65,-1,44},
{9999999999,599989,4997,696,295,185,87,64,51,45},
{19999999999,199998,-1,2989,486,-1,73,63,-1,46},
{29999999999,699989,-1,1988,587,-1,86,62,-1,47},
{39999999999,299998,5997,987,688,94,189,79,-1,48},
{49999999999,799989,-1,796,789,-1,85,78,-1,49},
{59999999999,399998,-1,3989,395,-1,188,77,-1,50},
{69999999999,899989,6997,2988,586,285,84,76,-1,51},
{79999999999,499998,-1,1987,687,-1,187,75,-1,52},
{89999999999,999989,-1,896,788,-1,83,74,-1,53},
{99999999999,599998,7997,4989,889,194,186,73,61,54},
{199999999999,1999989,-1,3988,495,-1,289,72,-1,55},
{299999999999,699998,-1,2987,686,-1,185,89,-1,56},
{399999999999,2999989,8997,996,787,385,288,88,-1,57},
{499999999999,799998,-1,5989,888,-1,184,87,-1,58},
{599999999999,3999989,-1,4988,989,-1,287,86,-1,59},
{699999999999,899998,9997,3987,595,294,93,85,-1,60},
{799999999999,4999989,-1,1996,786,-1,286,84,-1,61},
{899999999999,999998,-1,6989,887,-1,389,83,-1,62},
{999999999999,5999989,19997,5988,988,485,285,82,71,63},
{1999999999999,1999998,-1,4987,1989,-1,388,189,-1,64},
{2999999999999,6999989,-1,2996,695,-1,284,188,-1,65},
{3999999999999,2999998,29997,7989,886,394,387,187,-1,66},
{4999999999999,7999989,-1,6988,987,-1,193,186,-1,67},
{5999999999999,3999998,-1,5987,1988,-1,386,185,-1,68},
{6999999999999,8999989,39997,3996,2989,585,489,184,-1,69},
{7999999999999,4999998,-1,8989,795,-1,385,183,-1,70},
{8999999999999,9999989,-1,7988,986,-1,488,92,-1,71},
{9999999999999,5999998,49997,6987,1987,494,384,289,81,72},
{19999999999999,19999989,-1,4996,2988,-1,487,288,-1,73},
{29999999999999,6999998,-1,9989,3989,-1,293,287,-1,74},
{39999999999999,29999989,59997,8988,895,685,486,286,-1,75},
{49999999999999,7999998,-1,7987,1986,-1,589,285,-1,76},
{59999999999999,39999989,-1,5996,2987,-1,485,284,-1,77},
{69999999999999,8999998,69997,19989,3988,594,588,283,-1,78},
{79999999999999,49999989,-1,9988,4989,-1,484,192,-1,79},
{89999999999999,9999998,-1,8987,995,-1,587,389,-1,80},
{99999999999999,59999989,79997,6996,2986,785,393,388,91,81},
{199999999999999,19999998,-1,29989,3987,-1,586,387,-1,82},
{299999999999999,69999989,-1,19988,4988,-1,689,386,-1,83},
{399999999999999,29999998,89997,9987,5989,694,585,385,-1,84},
{499999999999999,79999989,-1,7996,1995,-1,688,384,-1,85},
{599999999999999,39999998,-1,39989,3986,-1,584,383,-1,86},
{699999999999999,89999989,99997,29988,4987,885,687,292,-1,87},
{799999999999999,49999998,-1,19987,5988,-1,493,489,-1,88},
{899999999999999,99999989,-1,8996,6989,-1,686,488,-1,89},
{999999999999999,59999998,199997,49989,2995,794,789,487,191,90},
{1999999999999999,199999989,-1,39988,4986,-1,685,486,-1,181},
{2999999999999999,69999998,-1,29987,5987,-1,788,485,-1,182},
{3999999999999999,299999989,299997,9996,6988,985,684,484,-1,183},
{4999999999999999,79999998,-1,59989,7989,-1,787,483,-1,184},
{5999999999999999,399999989,-1,49988,3995,-1,593,392,-1,185},
{6999999999999999,89999998,399997,39987,5986,894,786,589,-1,186},
{7999999999999999,499999989,-1,19996,6987,-1,889,588,-1,187},
{8999999999999999,99999998,-1,69989,7988,-1,785,587,-1,188},
{9999999999999999,599999989,499997,59988,8989,1985,888,586,291,189},
{19999999999999999,199999998,-1,49987,4995,-1,784,585,-1,190},
{29999999999999999,699999989,-1,29996,6986,-1,887,584,-1,281},
{39999999999999999,299999998,599997,79989,7987,994,693,583,-1,282},
{49999999999999999,799999989,-1,69988,8988,-1,886,492,-1,283},
{59999999999999999,399999998,-1,59987,9989,-1,989,689,-1,284},
{69999999999999999,899999989,699997,39996,5995,2985,885,688,-1,285}};
int main()
{int _;scanf("%d",&_);while(_--){int n,k;scanf("%d%d",&n,&k);printf("%lld\n",ans[n][k]);}
}
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