完美矩形问题

完美矩形问题的求解思路：(要达到完美矩形时，必须满足的条件)

1、所有的矩形的面积之和等于完美矩形的面积

2、完美矩形的边角四个点的个数都必须是一

3、除了边角四个点外，其他点的个数都必须为偶数

class Solution {
    public boolean isRectangleCover(int[][] rectangles) {
        int count = rectangles.length;
        int sum = 0;
        int max_x = rectangles[0][2];
        int max_y = rectangles[0][3];
        int min_y = rectangles[0][1];
        int min_x = rectangles[0][0];
        String str1 = null;
        String str2 = null;
        String str3 = null;
        String str4 = null;
        Integer t1 = null;
        Integer t2 = null;
        Integer t3 = null;
        Integer t4 = null;
        Map<String,Integer> map = new HashMap<>();
        for(int i=0;i<count;i++){
            str1 = rectangles[i][0]+"_"+rectangles[i][1];
            str2 = rectangles[i][2]+"_"+rectangles[i][3];
            str3 = rectangles[i][0]+"_"+rectangles[i][3];
            str4 = rectangles[i][2]+"_"+rectangles[i][1];
            t1 = map.get(str1);
            t2 = map.get(str2);
            t3 = map.get(str3);
            t4 = map.get(str4);
            map.put(str1, t1==null?1:++t1);
            map.put(str2, t2==null?1:++t2);
            map.put(str3, t3==null?1:++t3);
            map.put(str4, t4==null?1:++t4);
            if(rectangles[i][2]>max_x){
                max_x = rectangles[i][2];
            }
            if(rectangles[i][0]<min_x){
                min_x = rectangles[i][0];
            }
            if(rectangles[i][3]>max_y){
                max_y = rectangles[i][3];
            }
            if(rectangles[i][1]<min_y){
                min_y = rectangles[i][1];
            }
            sum += (rectangles[i][3]-rectangles[i][1])*(rectangles[i][2]-rectangles[i][0]);
        }
        str1 = max_x+"_"+max_y;
        str2 = min_x+"_"+min_y;
        str3 = max_x+"_"+min_y;
        str4 = min_x+"_"+max_y;
        t1 = map.get(str1);
        t2 = map.get(str2);
        t3 = map.get(str3);
        t4 = map.get(str4);
        if(t1!=null&&t2!=null&&t3!=null&&t4!=null&&t1==1&&t2==1&&t3==1&&t4==1&&sum==(max_x-min_x)*(max_y-min_y)) {
            map.remove(str1);
            map.remove(str2);
            map.remove(str3);
            map.remove(str4);
            for(Integer value : map.values()) {
                if((value&1)!=0) {
                    return false;
                }
            }
         }else {
             return false;
         }
         return true;
    }
}