Educational Codeforces Round 30 - C. Strange Game On Matrix（貪心）__CodeForces

C. Strange Game On Matrix time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

Ivan is playing a strange game.

He has a matrix a with n rows and m columns. Each element of the matrix is equal to either 0 or 1. Rows and columns are 1-indexed. Ivan can replace any number of ones in this matrix with zeroes. After that, his score in the game will be calculated as follows: Initially Ivan's score is 0;  In each column, Ivan will find the topmost 1 (that is, if the current column is j, then he will find minimum i such that ai, j = 1). If there are no 1's in the column, this column is skipped;  Ivan will look at the next min(k, n - i + 1) elements in this column (starting from the element he found) and count the number of 1's among these elements. This number will be added to his score. 

Of course, Ivan wants to maximize his score in this strange game. Also he doesn't want to change many elements, so he will replace the minimum possible number of ones with zeroes. Help him to determine the maximum possible score he can get and the minimum possible number of replacements required to achieve that score. Input

The first line contains three integer numbers n, m and k (1 ≤ k ≤ n ≤ 100, 1 ≤ m ≤ 100).

Then n lines follow, i-th of them contains m integer numbers — the elements of i-th row of matrix a. Each number is either 0 or 1. Output

Print two numbers: the maximum possible score Ivan can get and the minimum number of replacements required to get this score. Examples input

4 3 20 1 01 0 10 1 01 1 1

output

4 1

input

3 2 11 00 10 0

output

2 0

Note

In the first example Ivan will replace the element a1, 2.

題意：

給你n*m的矩陣和k，讓你在每一列的裡找i最小的1，從這個1向下出發（包含），直到長度為len=min(k,n-i+1)。其中的1的個數加到總分數中。

每一列找完之後，得到總分數。現在可以操作：把任意個1變為0。

現在想要總分數最大。求最大總分數和此時操作的最小次數。

POINT：

貪心。每一列都是一個獨立的問題。

每一列算出當前位置向下len個長度的1的個數有多少。記一個max。這個可以用o（n）的效率跑出來。

然後遍曆每一列，cnt=0。

【遇到1】，看看可以得到分數等不等於max，等於加上cnt。不等於就cnt++。

#include <stdio.h>#include <algorithm>#include <string.h>#include <iostream>#include <math.h>#include <map>using namespace std;int a[111][111];int num[111][111];int Max[111];int main(){    int n,m,k;    scanf("%d %d %d",&n,&m,&k);    for(int i=1;i<=n;i++){        for(int j=1;j<=m;j++){            scanf("%d",&a[i][j]);        }    }    int ansscore=0;    int ans=0;    for(int j=1;j<=m;j++){        int num1=0;        int len=min(k,n);        for(int i=1;i<=len;i++){            if(a[i][j]==1) num1++;        }        num[j][1]=num1;        Max[j]=max(Max[j],num[j][1]);        for(int i=2;i<=n;i++){            if(a[i-1][j]==1){                num[j][i]=num[j][i-1]-1;            }else                num[j][i]=num[j][i-1];            if(i+len-1<=n&&a[i+len-1][j]==1){                num[j][i]++;            }            Max[j]=max(Max[j],num[j][i]);        }        ansscore+=Max[j];        num1=0;        for(int i=1;i<=n;i++){            if(num[j][i]==Max[j]&&a[i][j]==1){                break;            }else if(a[i][j]==1){                num1++;            }        }        ans+=num1;    }    printf("%d %d\n",ansscore,ans);    return 0;}