1. Knowing 1/1/1971 is Friday(4 in array), sum up all days to today.

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    int[][] monthDay = {
        {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31},
        {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31},
    };

    public String dayOfTheWeek(int day, int month, int year) {
        // 1/1/1971 Friday 4
        int res = 4;
        for (int i = 1971; i < year; ++i) {
            int k = isLeap(i);
            for (int j = 1; j <= 12; ++j) res += monthDay[k][j];
        }    
        
        int k = isLeap(year);
        for (int i = 1; i < month; ++i) {
            res += monthDay[k][i];
        }
        
        res += day;
        res %= 7;
        
        String[] A = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};
        return A[res];
    }

    public int isLeap(int year) {
        return ((year %4 == 0 && year % 100 != 0) || year %400 == 0) ? 1 : 0;
    }

  2. 坂本友彦:

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class Solution {
public:
    string dayOfTheWeek(int d, int m, int y) {
    	// 2 = 3 + (28%7) - 1
        static int t[] = { 0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4 };

        // before February
        y -= m < 3;  

        int res = ( y + y / 4 - y / 100 +  y / 400 + t[m - 1] + d) % 7;  
        
        if (res == 0) return "Sunday";
        else if (res == 1) return "Monday";
        else if (res == 2) return "Tuesday";
        else if (res == 3) return "Wednesday";
        else if (res == 4) return "Thursday";
        else if (res == 5) return "Friday";
        return "Saturday";
    }
};