Classic Problems of Classic Sorting Algorithms

1. The Dutch tricolor flag problem

　　Problem description: An array contains only three elements: 0, 1, and 2. Without counting sorting, place 0 to the left of 1 and 2 to the right of 1.

　　analyze:

　　　　　1. The idea of ​​division in quicksort can be used for reference. Divide the array into {0 area}, arr[], {2 area}

　　　　　 2. Traverse arr, when 0 is found, area 0 expands to the right, when 2 is found, area 2 expands to the left,

　　　　　3. When the current element enters zone 2, it ends.

　　

 vector<int> sortThreeColor(vector<int> A, int n) {
        // write code here
        int last0=-1;
        int first2=n;
        for(int i=0;i<n;i++){
            if(i==first2) break;
            if(A[i]==0){
                int temp=A[last0+1];
                A[last0+1]=0;
                last0 ++ ;
                A[i]=temp;
            }
            if(A[i]==2){
                int temp=A[first2-1];
                A[first2-1]=2;
                first2--;
                A[i]=temp;
                i -- ;//(Because the number exchanged in area 2 has not been judged, it needs to be judged again)
            }
        }
        return A;
    }

2. The problem of finding elements in a row-column matrix

　　Problem description: Find an element in a two-dimensional matrix with ordered rows and columns.

　　Such as matrix: 1 2 3 4 find element 6

　　　　　　2 3 3 4

　　　　　　3 4 6 7

　　Analysis: First start from the upper right corner of the matrix, if the current element e>6, go left, that is, column -1, if e<6, go down, that is, row +1, otherwise find.

　　　　 If the current element subscript is outside the bounds of the matrix, it cannot be found.